Common Core State Standards (2 assignments)

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Chapter 5

Understanding the Standards

And I’m calling on our nation’s governors and state education chiefs to develop standards and assessments that don’t simply measure whether students can fill in a bubble on a test, but whether they possess 21st century skills like problem solving and critical thinking and entrepreneurship and creativity.

—Barack Obama, March 1, 2009

Learning Outcomes

By the end of the chapter, you will be able to:

• Explain the development of the Common Core standards movement.

• Describe the basic elements of the Common Core English language arts standards.

• Discuss the basic elements of the Common Core mathematics standards.

• Recall the basic elements of the Next Generation Science Standards and the National Educational Technology Standards.

• Analyze how differentiated instruction applies to the newly emerging standards and the technology standards for students.

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Pre-Test Chapter 5

Introduction Differentiated instruction is built on a foundation of effective teaching practices. Quality cur- riculum is one of these defining principles, as what is taught serves as the basis for how it is taught. Quality curriculum has its basis in standards, or descriptions of student outcomes in content areas. The standards in the United States are undergoing major changes with the adop- tion of the Common Core State Standards and new standards in science and social studies. Initially developed by a consortium of state governors and state superintendents of instruction, they have been vetted by professional groups, state and local education representatives, and parents within each state.

These standards mark a departure from past practices, which is good news for differentiated instruction. States had previously been responsible for developing their own standards, and the creation of assessment systems based on those standards immediately followed. While this approach assured an articulation between standards and assessment, there were unintended consequences. The effect was a narrowing of the curriculum. In practice, the assessment sys- tems began to drive the curriculum and often resulted in teaching methods that were drill based, had low cognitive demand, used bubble-in-the-answer assessments, and relied on a stand-and-deliver means of presenting content. (Kendall, 2011). The new standards aim to rec- tify that approach. They describe student outcomes in terms of college and career readiness, and encourage increasingly complex cognitive tasks throughout the K-12 experience. Moreover, the manner in which they were written and adopted has encouraged districts and teachers to develop curriculum first, rather than waiting until an assessment system is in place (Kendall, 2011). Since their release, the authors of the standards have vetted a number of resources that assist teachers, parents, and community members in understanding and planning for imple- mentation (Millar, 2012).

However, some educators have concerns about these new standards, especially as they relate to accountability, or find them complicated to understand at first. This chapter unpacks the standards initiatives, examining the Common Core State Standards and the Next Generation Science Standards (social studies is still under development). Additionally, the National Educational Technology Standards for Students and their relationship to the core and content standards is presented. The relationship of these standards and teacher accountability systems concludes the chapter.

Pre-Test 1. Common Core State Standards are a result of

a. a federal government mandate to build a foundation to work collaboratively across states and districts.

b. a Department of Defense education activity. c. a state-led initiative in collaboration with teachers, school administrators, and content

experts. d. a Wall Street coalition that funded a grant to allow pooling of resources in education.

Pre-Test Chapter 5

2. A strong emphasis in the Common Core State Standards is that instruction in English lan- guage arts (ELA) a. requires significant changes in our nation’s teacher preparation programs to provide

highly qualified instructors. b. should focus on the early years and that formal reading and writing instruction should

begin much earlier that in the past. c. is a shared responsibility across all subject areas and that all teachers must teach reading

and writing. d. needs to focus on the basics of learning to read and write without the distractions of

technology. 3. The standards for mathematical practice focus on practices that

a. encourage students to set aside curiosity and persistence until they understand how mathematical processes work.

b. focus on procedure and tedium while moving toward the beauty of mathematics. c. encourage students to question how and why mathematics works the way it does. d. engage students in mathematical content in abstract ways without regard for real-life

problems. 4. Teachers can best support the learning of science and engineering concepts by

a. structured learning of factual information. b. doing the practices of science and engineering within the context of the core disciplines. c. reading and talking about the practices of science and engineering. d. studying the behaviors of scientists and engineers as they engage in inquiry and

discourse. 5. Which of the following are NOT used to measure teacher effectiveness?

a. classroom artifacts b. observation protocols c. NET-S standards d. student achievement

Answers 1. c. a state-led initiative in collaboration with teachers, school administrators, and content

experts. The correct answer can be found in Section 5.1. 2. c. is a shared responsibility across all subject areas and that all teachers must teach reading

and writing. The correct answer can be found in Section 5.2. 3. c. encourage students to question how and why mathematics works the way it does. The

correct answer can be found in Section 5.3. 4. b. doing the practices of science and engineering within the context of the core disciplines.

The correct answer can be found in Section 5.4. 5. c. NET-S standards. The correct answer can be found in Section 5.5.

The Common Core Initiative Chapter 5

5.1 The Common Core Initiative The Common Core State Standards (CCSS) are the result of a state-led initiative. Development began in 2009, when the National Governors Association and State Commissioners of Education agreed to create a set of common state standards in K-12 English language arts (ELA) and mathematics. These standards were published in 2010. The Next Generation Science Standards were released in April 2013, and committees are working on the creation of core standards in social studies. Adoption of the standards is voluntary. When states adopt the CCSS, they agree that those standards will comprise at least 85 percent of their state’s standards, while state- specific standards may comprise the remaining 15 percent. As of 2013, 45 states, the District of Columbia, four territories, and the Department of Defense Education Activity have adopted the CCSS. Their implementation is based on the timelines and the context within each state (NGA & CCSSO, 2010).

The federal government was not involved in the development of the standards but supported their implementation (IDEA Partnership, 2012). The United States Department of Education made acceptance of the CCSS as one of the criteria for awarding competitive grant funds to the states (e.g., Race to the Top). The Department of Education also funded the centers that are developing assessments aligned to the CCSS.

Why a Common Core?

The CCSS address college and career readiness skills that will prepare students to succeed in education and training after high school. They are aligned with college and work expectations and include relevant, rigorous content with the intent of applying knowledge through high- order skills. They are internationally benchmarked, or compared to similar skills in other coun- tries, so students are prepared to succeed in a global economy and society, and to ensure that they are globally competitive (NGA & CCSSO, 2010).

The CCSS evolved from earlier state standards-based movements, where disparate standards made it difficult to communicate common progress among the states. With the CCSS, expec- tations are consistent for all. Moreover, they form a foundation to work collaboratively across states and districts, allowing for a pooling of resources and expertise to create curricular tools, professional development, and common assessments. A common set of standards ensures con- sistent expectations for student learning regardless of the geographical location or socioeco- nomic status. It provides the framework to develop a quality curriculum for all students. The broad goals and principles aim to ensure that receiving a quality education is not dependent on a student’s zip code (Kendall, 2011).

The CCSS are research and evidence based, and informed by practices in top performing coun- tries to provide a clear and consistent framework. They were developed in collaboration with teachers, school administrators, and content experts, with multiple rounds of feedback from teachers, researchers, higher education professionals, and the general public, and a review by a validation committee. The standards focus on conceptual understandings and procedures starting in the early grades, and are repeated throughout the grades, providing teachers with the time needed to teach core concepts and giving students the opportunity to master them

The Common Core Initiative Chapter 5

(NGA & CCSSO, 2010). English language arts and math were the first subjects cho- sen for the CCSS because they build skill sets in other subject areas and are the most frequently assessed subjects for account- ability purposes (Kendall, 2011).

Concerns about Common Core

Some administrators, policymakers, and families have expressed apprehension about these new standards, though most concerns tend to be not about their content but about their implementation. Several political leaders mistrust the “common” part of the Common Core State Standards, believing that local control is the best way to meet the needs of learners. Some educa- tors have watched as other promising edu- cational initiatives were poorly applied, misused, or unfunded. They are reserving their enthusiasm about the new reform until they have seen it in action. Still others wonder whether the standards are developmentally appropriate, or whether enough thought has been given to how they will be met by students with special needs. Finally, teachers who for many years have worked with the previous standards may be anxious about the sheer volume of new information to learn and implement, and some fear they will not receive adequate preparation, resources, and support.

A prevalent worry involves how the standards will be used for accountability, and whether students, teachers, and schools will be fairly assessed when it comes to determining how well the standards have been met. For example, New York and Kentucky, the first states to develop their own tests aligned to the CCSS, reported a significant decrease in student scores across all content areas and for all demo- graphic groups (Hernandez & Gebeloff, 2013). These early reports about student declines are disturbing, with many critics stating that the standards are too high, others citing more time needed for teachers and students to adjust to new requirements. Most other states are implementing the standards, but are waiting until the 2014–2015 school year to apply the corresponding assessments that will be available through nationwide consortia and that promise new testing methodologies. These problems with assessment are not a fault of the standards, but they will need to be addressed if the CCSS are to be effective.

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▲ College and career readiness for all students are the goals of the new standards. Do you feel that your high school educa- tion prepared you fully for your future?

Think About It

Based on what you already know about the Common Core State Standards, do you feel optimistic about their potential to change edu- cation? Why or why not? What more do you need to learn about CCSS to have an informed opinion?

Common Core Standards in English Language Arts Chapter 5

5.2 Common Core Standards in English Language Arts The standards emphasize that instruction in English language arts (ELA) is a shared respon- sibility across all subject areas, and that all teachers must teach reading and writing (NGA & CCSSO, 2010). The standards in reading, writing, speaking and listening, and language are anchored by College and Career Readiness Anchor Standards (CCR). These anchor standards define 32 broad competencies that form the basis for literacy expectations in K-12 topics that apply across all grades. The standards apply to ELA and also, beginning at sixth grade, to lit- eracy in history, social studies, science, and technical subjects. These standards are articulated at each level, with grade-level descriptions of what students should know. For example, the CCR anchor standard 3 in writing is stated as follows:

Write narratives to develop real or imagined experiences or events using effective technique, well-chosen details and well-structured event sequences.

This standard in the writing strand for second grade is stated as:

Write narratives in which they recount a well-elaborated event or short sequence of events, include details to describe actions, thoughts, and feelings, use temporal words to signal event order, and provide a sense of closure (CCSS.ELA-Literacy.W.2.3).

The same standard for sixth grade describes more sophisticated writing techniques, details, and sequences (as noted by additions W.6.3a-e below), while keeping the coherence of the same CCR anchor standard:

(CCSS.ELA-Literacy.W.6.3): Write narratives to develop real or imagined experiences or events using effective technique, relevant descriptive details, and well-structured event sequences.

W.6.3a. Engage and orient the reader by establishing a context and introducing a narrator and/or characters; organize an event sequence that unfolds naturally and logically.

W.6.3b. Use narrative techniques, such as dialogue, pacing, and description, to develop experiences, events, and/or characters.

W.6.3c. Use a variety of transition words, phrases, and clauses to convey sequence and sig- nal shifts from one time frame or setting to another.

W.6.3d. Use precise words and phrases, relevant descriptive details, and sensory language to convey experiences and events.

W.6.3e. Provide a conclusion that follows from the narrated experiences or events.

The standards keep this organizational structure in each grade level, demonstrating that a con- cept that is learned in early grades is further developed later on.

ELA Standards for Reading

The reading standards focus on a holistic view of comprehension as an evolving skill, and empha- size developing meaning from the start of reading. As seen in Table 5.1, these standards are based around the idea of gradually increasing the complexity of text so that by the end of high school, students are ready for the demands of college-level and career-level reading. This requires

Common Core Standards in English Language Arts Chapter 5

progressive development in reading comprehension so students can gain more from what is read. The anchor standards are grouped according to concepts of key ideas, craft and structure, integrating knowledge and ideas, range of reading, and text complexity. Comprehension skills and higher levels of vocabulary are emphasized at younger ages using texts that are grounded in the content areas—science, social studies, history, and others. Throughout the grades and within the standards, reading occurs in classic and contemporary literature as well as challeng- ing informational texts in a range of subjects. While the CCSS has no reading list, Appendix A of the Common Core website (www.corestandards.org) gives annotated examples of sample texts that meet the standards for each grade level, which are intended to help teachers and dis- tricts choose appropriate curriculum.

Table 5.1 College and career readiness anchors for reading

Strand Standard

Key Ideas and Details CCSS.ELA-Literacy.CCRA.R.1 Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

CCSS.ELA-Literacy.CCRA.R. 2 Determine central ideas or themes of a text and analyze their development; summarize the key supporting details and ideas.

CCSS.ELA-Literacy.CCRA.R.3 Analyze how and why individuals, events, or ideas develop and interact over the course of a text.

Craft and Structure CCSS.ELA-Literacy.CCRA.R .4 Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.

CCSS.ELA-Literacy.CCRA.R.5 Analyze the structure of texts, including how specific sentences, paragraphs, and larger portions of the text (e.g., a section, chapter, scene, or stanza) relate to each other and the whole.

CCSS.ELA-Literacy.CCRA.R .6 Assess how point of view or purpose shapes the content and style of a text.

Integration of Knowledge and Ideas

CCSS.ELA-Literacy.CCRA.R.7 Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

CCSS.ELA-Literacy.CCRA.R.8 Delineate and evaluate the argument and specific claims in a text, including the validity of the reasoning as well as the relevance and sufficiency of the evidence.

CCSS.ELA-Literacy.CCRA.R.9 Analyze how two or more texts address similar themes or topics in order to build knowledge or to compare the approaches the authors take.

Range of Reading and Level of Text Complexity

CCSS.ELA-Literacy.CCRA.R.10 Read and comprehend complex literary and informa- tional texts independently and proficiently.

Note: To build a foundation for college and career readiness, students must read widely and deeply from among a broad range of high-quality, increasingly challenging literary and informational texts. Through extensive reading of stories, dramas, poems, and myths from diverse cultures and different time periods, students gain literary and cultural knowledge as well as familiarity with various text structures and elements. By reading texts in history/social studies, science, and other disciplines, students build a foundation of knowledge in these fields that will also give them the background to be better readers in all content areas. Students can only gain this foundation when the curriculum is intentionally and coherently structured to develop rich content knowledge within and across grades. Students also acquire the habits of reading independently and closely, which are essential to their future success.

Source: English Language Arts Standards. Accessed from http://www.corestandards.org.

Common Core Standards in English Language Arts Chapter 5

Text Complexity One of the most important concepts in the reading standards is anchor standard 10, Read and comprehend complex literary and informational texts independently and proficiently. Research has shown that complexity of text is a necessary condition for developing higher order and critical thinking skills, and that students who can read and respond in this manner are better equipped for college or career-level reading (Kendall, 2011). The CCSS describe a three-part model for evaluating complex literary and informational texts using quantitative tools, qualita- tive dimensions, and the relationship among the reader, the task, and the text. This model is displayed in Figure 5.1.

Quantitative tools are those aspects of reading typically measured using mathematical for- mulas that calculate difficulty level using word length, sentence length, and word frequency, as measured by readability formulae for grade level or Lexile scores indicating a scale of text diffi- culty. Common systems include the Flesch-Kincaid Grade Level test, which assigns a U.S. grade level to a text, and the Lexile Framework for Reading, which assigns a score to both reader and text so they can be appropriately matched. As Appendix A of the Common Core ELA standards points out, formulas that use word and sentence length to calculate difficulty are not fail proof; longer words and sentences are not always more challenging than short ones. For example, many readers who recognize “sunflower” would likely struggle with “qi.” However, such mea- sures provide a fast and generally accurate place to start.

Qualitative dimensions require human readers to make judgments about the text complexity. These judgments may include recognizing multiple meanings of text, or varying levels of pur- pose (such as persuasion, or hidden purposes, like defending an agenda that was not identified). They also include looking at text structure (including manipulations of time and sequence), language conventionality (conversational style versus figurative language or other unfamiliar styles), and the background knowledge that the text requires of a reader. CCSS Appendix A offers sample analyses of the complexity of excerpted texts.

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Reader and Task

Q ua

lit at

iv e

Q uantitative

Figure 5.1: Three factors for measuring text complexity

This is the three-part model the CCSS describes for evaluating complex literary and informational texts. It uses quantitative tools, qualitative dimensions, and the relationship among the reader, the task, and the text.

Source: English Language Arts Standards. Measuring Text Complexity: Three Factors. Accessed from http://www.corestandards.org/ELA-Literacy/standard-10-range-quality-complexity/measuring-text-complexity-three-factors.

Common Core Standards in English Language Arts Chapter 5

The third dimension is that of matching the reader to task, which considers variables inherent in the readers when determining if a text is appropriate for an individual student. These fac- tors may include motivation, interest, knowledge, experiences, and the purpose for reading the text. Using this dimension to establish text complexity requires that teachers know the subject and the student, and use professional judgment to assess which texts would be appropriate. For example, not all students are ready for the same level of difficulty. Teachers will need to guide text selection for students who read above or below their suggested grade complexity level. Fortunately, the standards recognize the importance of professional judgment and anchor the complexity standards on this principle (Kendall, 2011).

Foundational Skills The fundamental literacy skills identified by the National Reading Panel, phonemic aware- ness, phonics, fluency, vocabulary, and text comprehension, are included in the ELA stan- dards (NICHHD, 2000). They are described as foundational skills, those that foster students’ working knowledge of concepts of print, alphabetic principle, phonics and word recognition, and fluency. These foundational skills are included in the ELA standards for grades K-5, but not beyond.

The foundational skills include noteworthy recommendations to teachers. While these skills are considered to be components of a comprehensive reading program, the focus of the standards is on outcomes, not the process. For example, the introduction to the foundational skills cautions teachers that good readers will need less practice with these skills and poor readers will need more practice; teachers must discern what is appropriate for each child, and not teach what students may already know (NGA & CCSSO, 2010). In other words, the purpose of learning phonetic patterns in words is to aid in fluent recognition of the word and its potential mean- ing, thus aiding in comprehension of the sentence and passage. Students who quickly and automati- cally apply these concepts will need fewer exercises in identifying these phonetic principles; those who are struggling may need more. This guidance may be most appreciated for teachers who have been required to use scripted curriculum programs for all students, even for those who were able to move to higher level literary texts.

ELA Standards for Writing

Table 5.2 lists the anchor standards for writing. These standards are grouped according to the strands of text types and purpose, production and distribution of writing, research to build and present knowledge, and range of writing. The standards require students to write across three text types. They learn to write arguments using sound logic and reasoning based on evidence. In order to do this, they must learn to express opinions in writing from the earliest grades (Kendall, 2011). Students learn how to convey ideas clearly by writing informative texts that demonstrate their understanding of concepts they are learning. Students also learn narrative writing, clearly conveying events or experiences. They learn the concept of communicating in a manner that an audience would understand, to adapt their writing for its intended purpose, and to learn production skills of editing, revising, organizing, and disseminating their writing. These standards emphasize research skills in short, focused projects as well as longer term in- depth research. In order to accomplish these goals, students must engage in frequent, routine

Think About It

What aspects of differentiation support the general recommendations of the ELA founda- tional skills in reading?

Common Core Standards in English Language Arts Chapter 5

writing, devoting significant time and effort, and producing numerous pieces throughout the grades (Kendall, 2011). Appendix C of the Common Core website (www.corestandards.org) gives annotated examples of student writing that meet the standards for each grade level.

Table 5.2 College and career readiness anchor standards for writing

Strand Standard

Text Types and Purposes CCSS.ELA-Literacy.CCRA.W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence.

CCSS.ELA-Literacy.CCRA.W.2 Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.

CCSS.ELA-Literacy.CCRA.W.3 Write narratives to develop real or imagined experi- ences or events using effective technique, well-chosen details and well-structured event sequences.

Production and Distribution of Writing

CCSS.ELA-Literacy.CCRA.W.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

CCSS.ELA-Literacy.CCRA.W.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.

CCSS.ELA-Literacy.CCRA.W.6 Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.

Research to Build and Present Knowledge

CCSS.ELA-Literacy.CCRA.W.7 Conduct short as well as more sustained research projects based on focused questions, demonstrating understanding of the subject under investigation.

CCSS.ELA-Literacy.CCRA.W.8 Gather relevant information from multiple print and digital sources, assess the credibility and accuracy of each source, and integrate the information while avoiding plagiarism.

CCSS.ELA-Literacy.CCRA.W.9 Draw evidence from literary or informational texts to support analysis, reflection, and research.

Range of Writing CCSS.ELA-Literacy.CCRA.W.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.

Note: To build a foundation for college and career readiness, students need to learn to use writing as a way of offering and supporting opinions, demonstrating understanding of the subjects they are studying, and conveying real and imagined experiences and events. They learn to appreciate that a key purpose of writing is to communi- cate clearly to an external, sometimes unfamiliar audience, and they begin to adapt the form and content of their writing to accomplish a particular task and purpose. They develop the capacity to build knowledge on a subject through research projects and to respond analytically to literary and informational sources. To meet these goals, students must devote significant time and effort to writing, producing numerous pieces over short and extended time frames throughout the year.

Source: English Language Arts Standards. Accessed from http://www.corestandards.org.

Think About It

How might acknowledging student interests become an effective way to develop student writing across the grades? What other aspects of the differentiated instruction model could support these College and Career Readiness anchor standards for writing?

Common Core Standards in English Language Arts Chapter 5

ELA Standards for Speaking and Listening

Table 5.3 lists the anchor standards for speaking and listening. These standards are grouped in two major areas, comprehension and collaboration, and presentation of knowledge and ideas. Students develop these skills through multiple opportunities to take part in academic discus- sions and conversations in one-on-one, small-group, and whole-class settings. Comprehension and presentation skills are also developed by using increasingly complex information, ideas, and evidence, using a variety of media, including digital sources (NGA & CCSSO, 2010). Appendix A of the Common Core website describes the role of oral language in literacy development (www.corestandards.org).

Table 5.3 College and career readiness anchor standards for speaking and listening

Strand Standard

Comprehension and Collaboration

CCSS.ELA-Literacy.CCRA.SL.1 Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.

CCSS.ELA-Literacy.CCRA.SL.2 Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

CCSS.ELA-Literacy.CCRA.SL.3 Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric.

Presentation of Knowledge and Ideas

CCSS.ELA-Literacy.CCRA.SL.4 Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

CCSS.ELA-Literacy.CCRA.SL.5 Make strategic use of digital media and visual displays of data to express information and enhance understanding of presentations.

CCSS.ELA-Literacy.CCRA.SL.6 Adapt speech to a variety of contexts and commu- nicative tasks, demonstrating command of formal English when indicated or appropriate.

Note: To build a foundation for college and career readiness, students must have ample opportunities to take part in a variety of rich, structured conversations—as part of a whole class, in small groups, and with a partner. Being productive members of these conversations requires that students contribute accurate, relevant information; respond to and develop what others have said; make comparisons and contrasts; and analyze and synthesize a multitude of ideas in various domains.

New technologies have broadened and expanded the role that speaking and listening play in acquiring and sharing knowledge and have tightened their link to other forms of communication. Digital texts confront students with the potential for continually updated content and dynamically changing combinations of words, graphics, images, hyperlinks, and embedded video and audio.

Source: English Language Arts Standards. Accessed from http://www.corestandards.org.

Think About It

Flexible grouping is one of the general principles of differentiated instruction (discussed in Chapter 3). How might using this concept support the Common Core standards in speak- ing and listening? What other aspects of the differentiated instruction model also support these anchor standards?

Common Core Standards in English Language Arts Chapter 5

ELA Standards for Language

Table 5.4 lists the anchor standards for language. These standards are grouped according to conventions of standard English, knowledge of language, and vocabulary acquisition and use. Conventions and vocabulary extend across reading, writing, speaking, and listening. Knowledge of language standards emphasize the use of formal English in writing and speak- ing as well as choice in the many other ways that language is used in expression. Vocabularies develop through a mix of conversations, direct instruction, and reading (IDEA Partnership, 2012). The standards are meant to help students continuously expand their repertoire of words and phrases using general academic and domain-specific vocabulary. General academic words are those that are commonly used in academic writing but are seldom used in informal speech. For example, the term multiple opportunities is more often expressed in informal conversation as many chances. Domain-specific words, such as fractal, species, phylum, and cardiovascular are specific to a content area. Understanding domain-specific words is reinforced in the reading and writing standards, as well as literacy standards for the subject areas (Kendall, 2011).

Table 5.4 College and career readiness anchor standards for language

Strand Standard

Conventions of Standard English

CCSS.ELA-Literacy.CCRA.L.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

CCSS.ELA-Literacy.CCRA.L.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.

Knowledge of Language CCSS.ELA-Literacy.CCRA.L.3 Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.

Vocabulary Acquisition and Use

CCSS.ELA-Literacy.CCRA.L.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing mean- ingful word parts, and consulting general and specialized reference materials, as appropriate.

CCSS.ELA-Literacy.CCRA.L.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.

CCSS.ELA-Literacy.CCRA.L.6 Acquire and use accurately a range of general academic and domain-specific words and phrases sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate inde- pendence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression.

Note: (On range and content of student language use)To build a foundation for college and career readiness in language, students must gain control over many conventions of standard English grammar, usage, and mechanics as well as learn other ways to use language to convey meaning effectively. They must also be able to determine or clarify the meaning of grade-appropriate words encountered through listening, reading, and media use; come to appreciate that words have nonliteral meanings, shadings of meaning, and relationships to other words; and expand their vocabulary in the course of studying content. The inclusion of Language standards in their own strand should not be taken as an indication that skills related to conventions, effective language use, and vocabu- lary are unimportant to reading, writing, speaking, and listening; indeed, they are inseparable from such contexts.

Source: English Language Arts Standards. Accessed from http://www.corestandards.org.

Common Core Standards in English Language Arts Chapter 5

ELA Standards for History/Social Studies, Science, and Technical Subjects

The ELA standards in history/social studies, science, and technical subjects begin in sixth grade. In the elementary grades, the CCR anchor standards for reading, writing, speaking and listening, and language are applied across a variety of subject areas, building the skills needed to interact with informational texts in the content areas. In the upper grades, the CCR anchor standards in reading and writing form the basis for literacy expectations in these subject areas.

The basic premise of the ELA standards for history/social studies, science, and technical subjects is that college and workforce training programs require literacy skills based on sophisticated nonfiction. Because reading is such an important skill for building knowledge, the standards require students to learn discipline-specific reading in order to understand particular termi- nology and phrases, attend to details and concepts, and evaluate and synthesize arguments and information. This involves being able to apply literacy skills when reading primary and secondary sources in history and social studies. It also involves reading and understanding challenging scientific and technical texts that use diagrams and data to convey information and illustrate concepts. When writing in the areas of history and social studies, students are required to use narrative in analyzing individuals, places, and historical events. When writing in science and technical subject areas, students must be able to write descriptions of procedures and results in a manner that others could replicate (NGA & CCSSO, 2010).

The reading and writing standards, with descriptions of what students should know, are orga- nized by middle school grades 6-8, and high school grades 9-10 and 11-12. They have the same structure as other ELA standards; organized by strand, anchor standard, and subject specific standard. Except for the fact that these standards apply to subject-specific or discipline-specific areas, they are written in a similar language and with similar terms as their corresponding stan- dards in reading and writing. Table 5.5 offers a side-by-side comparison of two standards, one in reading (standard 3) and one in writing (standard 6) across the upper grades 6-8, 9-10, and 11-12.

In the reading example in Table 5.5, note that the CCR anchor standard forms the basis for standards in reading informational text as well as for the standards in reading for science and technical subjects. The column Reading: Informational Text shows a seventh grade example (CCSS.ELA-Literacy.RI.7.3) to correspond with the grade 6-8 example in in the column Science and Technical Subjects (CCSS.ELA-Literacy.RST.6-8.3). The logic of CCR anchor standard 3 in reading is followed within each subsequent grade level, 9-10 and 11-12.

The same table structure is used for the CCR anchor standard 6 in writing. Here, the language of the anchor standard, the grade level standards in writing, and the standards for science and technical subjects are quite similar. Each standard, as written, can be applied to writing within an ELA curriculum as well as discipline-specific curriculum.

Think About It

How do you, as a lifelong learner, come to understand the meaning of newly encoun- tered vocabulary? What strategies do you use? Where is it that you initially encounter these new terms? What influence would a quality curriculum have on the develop- ment of new vocabulary for students? How might student interest contribute to this development?

Common Core Standards in English Language Arts Chapter 5

Table 5.5 Side-by-side comparison of ELA anchor standards in reading and writing in science and technical subjects

Reading: Key Ideas and Details: Anchor Standard 3 (CCSS.ELA-Literacy.CCRA.R.3)

Analyze how and why individuals, events, or ideas develop and interact over the course of a text.

Grade Level Reading: Informational Text Science and Technical Subjects

6-8 CCSS.ELA-Literacy.RI.7.3

Analyze the interactions between individuals, events, and ideas in a text (e.g., how ideas influence individuals or events, or how indi- viduals influence ideas or events).

CCSS.ELA-Literacy.RST.6-8.3

Follow precisely a multistep procedure when carrying out experiments, taking measure- ments, or performing technical tasks.

9-10 CCSS.ELA-Literacy.RI.9-10.3

Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connec- tions that are drawn between them.

CCSS.ELA-Literacy.RST.9-10.3

Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.

11-12 CCSS.ELA-Literacy.RI.11-12.3

Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop over the course of the text.

CCSS.ELA-Literacy.RST.11-12.3

Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text.

Writing: Production and Distribution of Writing: Anchor Standard 6 (CCSS.ELA-Literacy.CCRA.W.6 )

Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.

Grade Level Writing Science and Technical Subjects

6-8 CCSS.ELA-Literacy.W.7.6

Use technology, including the Internet, to produce and publish writing and link to and cite sources as well as to interact and collabo- rate with others, including linking to and citing sources.

CCSS.ELA-Literacy.WHST.6-8.6

Use technology, including the Internet, to produce and publish writing and present the relationships between information and ideas clearly and efficiently.

9-10 CCSS.ELA-Literacy.W.9-10.6

Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other informa- tion and to display information flexibly and dynamically.

CCSS.ELA-Literacy.WHST.9-10.6

Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other informa- tion and to display information flexibly and dynamically.

11-12 CCSS.ELA-Literacy.W.11-12.6

Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information.

CCSS.ELA-Literacy.WHST.11-12.6

Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information.

(continued)

Common Core Standards in English Language Arts Chapter 5

Note: (Writing in History/Social Studies, Science and Technical Subjects)

Students’ narrative skills continue to grow in these grades. The standards require that students be able to incor- porate narrative elements effectively into arguments and informative/explanatory texts. In history/social studies, students must be able to incorporate narrative accounts into their analyses of individuals or events of historical import. In science and technical subjects, students must be able to write precise enough descriptions of the step- by-step procedures they use in their investigations or technical work that others can replicate them and (possibly) reach the same results.

Source: NGA & CCSSO, 2010.

ELA Standards and Differentiated Instruction

The anchor standards for ELA do not specify any particular teaching method. Indeed, method- ology was purposefully absent from the standards and their descriptions to allow for the profes- sional judgment of teachers in determining how to teach them. The standards also recognize the variability in abilities, needs, learning rates, and achievement levels of students in most classrooms. This language and the recommendations for reading, writing, speaking and listen- ing, and language found within the standards documents support the concepts of differentiated instruction. Refer to Figure 1.1 in Chapter 1, where the concepts of differentiated instruction were first introduced. Consider how the ELA standards are compatible with the general prin- ciples of differentiation (respectful tasks, flexible grouping, quality curriculum, teaching up, building community). Additionally, Appendix B of the Common Core website (NGA & CCSSO, 2010) suggests texts for each grade level, demonstrating the progression of text complexity throughout the grades. Consider how these suggestions are compatible with differentiating content in response to student characteristics (readiness, interests, and learning profile).

Think About It

What is the value in having the same anchor standards reinforced grade after grade? What drawbacks might there be to incorporating the same standards throughout the grades?

V O I C E S F R O M T H E C L A S S R O O M

Reading World History: A Core Approach

As a ninth grade world history teacher, I initially thought that the Common Core standards in ELA would have little to do with me. After all, in my own profession, the broad questions of what to teach in the social studies had its own local debates that kept my focus on analyzing the political climate, not the Common Core standards. Our district finally adopted a comprehensive set of world history standards and curriculum patterned after recommendations from the National Center for History in the Schools (NCHS), the National Council for the Social Studies (NCSS), and the hard-won standards for history adopted by our state department of education. I worked on some of those committees, and I am proud of the curriculum we have and know it well. Adding the CCSS for read-

(continued)

Common Core Standards in English Language Arts Chapter 5

ing and writing in social studies is new for me, but I like the integration. I still have the same world history content standards, and I use the Common Core literacy standards as a guide to develop other skills, such as citing evidence from the text and being able to write about what they read. One thing to understand about the Common Core standards is that they are new to the students as well as to the teachers. Students are learning to expect work on core literacy skills within the sub- ject area in addition to concentrating on the content.

For example, we were studying the apartheid system in South Africa and the role of Nelson Mandela in helping the Black majority win their political rights. While we used the textbook as one content source, we also used excerpts from The Long Walk to Freedom: The Autobiography of Nelson Mandela. We began with Part One: A Country Childhood, Chapter 4; Mandela’s account of the ceremonies marking his coming of age (at 16) and the speech by a tribal chieftain that planted the seeds of understanding of the role of apartheid in South African society. Although written in a simple prose, I knew that many of the students would not identify with the cultural conditions in this account or understand some of the vocabulary terms.

Before adding the Common Core literacy standards to the curriculum, I would have planned the lesson to ensure that students who were struggling could understand the content and context through discussion, or a video, or news clips, or simplified written accounts of Mandela’s life. But the new standards require that students also read from primary sources and that they learn the meaning of words and phrases as they are used in the text. The standards advise that all students should have access to complex text regardless of their reading ability. I could not merely give this autobiography to the advanced readers and provide a simpler text for the rest. Instead of asking students to read things that I thought they could handle, I wanted all to be exposed to the tougher but more interesting material, even knowing that some would struggle, at least initially.

At first, some students didn’t understand the chapter, but I put them in discussion groups, and said that we were going to look at the first paragraph, and break it apart, and take it step by step. Instead of preteaching vocabulary, I let them identify terms that were unfamiliar to them, and gave them the opportunity to use their research skills to find the meaning. Some of the cultural practices in this passage were also strange, so students who were interested either read ahead or did some further research to find out more about rites of passage for males as well as for females. I was able to show them that with a few supports, they were able to understand something that they did not comprehend on the first read.

I enjoy using what I know about the content and applying it toward skills that help students read, write, and speak about world history. I feel that my content knowledge brings richness to the stu- dents’ literacy development in a manner that would not be possible if I were a reading specialist or only a history specialist.

—Frances B., world history teacher

Critical Thinking Questions

1. How does this scenario support the notion that instruction in literacy skills is a shared responsibil- ity within the school and within all content areas?

2. Which of the general principles of differentiation are evident in this scenario?

Source material: Mandela, N. (1994). The Long Walk to Freedom: The Autobiography of Nelson Mandela. Boston: Little, Brown and Company. Retrieved from http://www.mandeladay.com/images/uploads/the-autobiography-of-nelson-mandela.pdf.

Common Core Standards in Mathematics Chapter 5

5.3 Common Core Standards in Mathematics The Common Core standards in mathematics represent a shift in instructional emphasis toward higher levels of cognitive demand. The standards are divided into two sets, mathematical prac- tice and mathematical content. The mathematical practice standards describe ways that stu- dents should engage with mathematics content as they grow in maturity from kindergarten through high school. The mathematical content standards stress a balance between procedural skill and conceptual understanding (IDEA Partnership, 2010). They are intended to build a foundation of procedural skill and fluency as well as conceptual understanding from the earli- est grades. Taken together, the CCSS mathematical standards aim to develop procedural fluency and conceptual understanding of mathematical content through engagement and methods that focus on the process of learning.

Implementation of these standards requires a paradigm shift for many teachers, and challenges them to develop instructional strategies that promote active engagement through discourse and involvement with real-world applications. While knowing mathematical procedures are impor- tant, the standards emphasize that deep conceptual understanding is equally important. Lack of understanding causes students to rely too heavily on procedures, and prevents them from engaging in useful mathematical practices, such as applying math to practical situations, using technology mindfully, or explaining mathematics accurately (Zimba, 2011).

The purpose of the following discussion is to present an overview of the mathematical stan- dards in view of their potential intersection with concepts of differentiated instruction. As you read through these descriptions, make note of potential applications to elements of DI, such as the general teaching principles, the instructional elements of content, process, and product, and learner characteristics. This overview is not intended to thoroughly explain the mathematical standards. For a closer reading and understanding of the mathematical practice and content standards, refer to the Additional Resources section of this chapter.

Mathematical Practice

The standards for mathematical practice shown in the feature, CCSS Standards for Mathematical Practice, focus on the processes that students should use to learn and engage with mathemati- cal content in meaningful ways. These standards focus on practices that encourage students to question how and why mathematics works the way it does, to look for solutions to real-life problems using mathematical principles, to develop a mindset of curiosity and persistence, and to ultimately move beyond procedure and tedium to experience the elegance, beauty, and truth of mathematics. These are laudable goals that will most likely involve a change of mindset for teachers and students alike.

Practice Standard 1: Make Sense of Problems and Persevere in Solving Them This standard (making sense of problems and perseverance) addresses problem solving from two perspectives: drawing on one’s knowledge and understanding of concepts and proce- dures to develop an appropriate response, and having the mindset to persist to a successful outcome (Larson, Fennell, Adams, Dixon, Kobett, & Wray, 2012). Practice standard 1 reflects several assumptions toward learning mathematics. First, problem solving is not about learn- ing procedures, rather it is about learning concepts and procedures to solve new problems. Second, it assumes that this problem-solving capacity is a different experience for every student. Effective problem solving depends not only on the variables in the task, but also the student’s

Common Core Standards in Mathematics Chapter 5

interpretation of the problem. Third, because this problem-solving interpretation is a differ- ent experience for each student, it is often a source of frustration. Teachers have to walk a fine line in setting up a situation that is possible to solve without protecting students from mental struggle. Students must have the opportunity to work through their frustration without aban- doning the task or feeling overwhelmed. Protecting students from mental struggle denies them the opportunity to develop skills of perseverance (Larson et al., 2012).

Teacher actions that facilitate practice standard 1 are to provide good problems (see suggestions in the feature, Creating Good Problems) and to guide students in the problem-solving process by providing opportunities for discussion with others. Building successful prob- lem solvers involves a realization that powerful learn- ing occurs even when the answer evades the student. Success is not simply measured by the right answer, but also by the effort and perseverance involved in the problem-solving process (Larson et al. 2012).

Practice Standard 2: Reason Abstractly and Quantitatively The goal of practice standard 2 is for students to reason with and about mathematics. In other words, students learn to take a specific situation and generalize it, or make it abstract, so its mathematical principles could be applied in other situations. They learn to reason about the ideas and mathematical properties of a situation without the details (Zimmerman, Carter, Kanold, & Toncheff, 2012). Reasoning is the means through which the students make sense of mathematics so that it becomes useful.

Teachers promote mathematical reasoning through discourse, which involves teacher-to- student communication that probes student thinking beyond a suggested answer. Discourse also involves discussion among students, peer-to-peer exchanges that support or challenge stu- dent explanations and provide justification for their thinking. When students engage in this practice, they share and adjust their thinking based on math information gathered through

CCSS Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quantitatively

3. Construct viable arguments and critique the reasoning of others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of structure

8. Look for and express regularity in repeated reasoning

Source: NGA & CCSO, 2010.

Think About It

Apply the learning theories from Chapter 2 to math practice standard 1. Which theories seem to support this practice standard, and in what ways? Which theories might not com- pletely support this standard and why?

Common Core Standards in Mathematics Chapter 5

discussions and in response to questions. Reasoning is a continuous expectation for practice, beginning in the early grades and extending into high school (Zimmerman et al., 2012).

Students can analyze and justify reasoning even in very early grades. For example, in learning addition, Sarah might provide the correct answer to the question “What is 2 plus 3?” Instead of stopping there and moving on to the next sum, the teacher might ask Sarah how she came to that conclusion. Perhaps Sarah has simply memorized the problem and answer. This is one valid approach to a simple addition exercise, but the teacher can extend the discourse by asking whether anyone else got the same answer but used a different method. By hearing from students who combined a pair of manipulatives with three manipulatives and then counted the total, or from students who made tally marks on paper and then counted them, the class learns about different ways of thinking and about explaining their thinking. If Sarah had said that 2 plus 3 was 6, it would still be helpful for students to evaluate her thought process. Was her reasoning not quite solid? Or did she make a simple calculation error?

Practice Standard 3: Construct Viable Arguments and Critique the Reasoning of Others The goal of this standard is for students to construct viable arguments by making and testing their own conjectures as well as those of others in a supportive mathematical environment. Successful implementation of standard 3 is dependent on the social environment, which must have social and behavioral norms that convey respect for others, a willingness to hear all stu- dent voices, the proper use of mathematical vocabulary, and an awareness of the importance of demonstrating the mathematical processes being used.

Creating Good Problems

These six questions can help teachers design problem-solving activities.

1. Is the question interesting? Create or select problems that use information about students’ lives or interests to engage them and to foster a personal investment.

2. Does the problem involve meaningful mathematics? Do not distort the understanding of the mathematical principle by providing numbers that are overly complex, or that distract from the main objective of the lesson.

3. Does the problem provide students with an opportunity to apply and extend mathematics? Problems that come from a base of what students have already learned help them understand the purpose of the problem and are a good starting point for extending learning.

4. Is the problem challenging? The objective is not to frustrate students, but to pose a problem that develops the attitudes and perseverance necessary to be successful problem solvers.

5. Does the problem support the use of multiple strategies? Given the same set of variables, no two students will approach the problem in exactly the same way. How each student sees the problem is unique. Choose or create problems that lend themselves to discovery and discussion of the different ways they could be attacked.

6. Will students’ interactions with the problem reveal information about their mathematical under- standing? Students’ work and discourse should reveal how they are thinking, the background knowledge they bring to the task, and any assumptions they are using to solve the problem.

Source: Adapted from Larson et al., 2012, pp. 28–29.

Common Core Standards in Mathematics Chapter 5

Teachers promote this standard by establishing supportive social norms where it feels safe to communicate one’s own mathematical ideas and question the thinking of others (Larson et al., 2012). Teachers must also provide a rich array of problems that would stimulate student con- jectures and arguments, help to identify misconceptions, and guide discussion around impor- tant mathematical ideas (Larson et al., 2012). When students are engaged in this standard, they explain and justify their thinking to classmates, who listen to the explanation and judge the reasonableness of the claim based on its clarity and precision. When disagreements occur, students are able to present their claims and counterclaims with appropriate mathematical justifications.

Practice Standard 4: Model with Mathematics The goal of practice standard 4 is for students to use their knowledge of mathematics to model real-world situations, thus developing the ability to solve problems of everyday life (Larson et al., 2012). Modeling means taking a problem, thinking of a description, and coming to a mathematical solution. It applies to real-world problems from business and the community. It is the heart of what students will do when using mathematics as educated adults (McCallum & Zimba, 2011).

The word model in this standard is often misinterpreted to mean using manipulatives to rep- resent mathematical concepts. Manipulatives, either tangible, such as base-ten blocks, or pic- torial, such as drawings, are certainly elements of modeling, but there are others to consider. Students may use other instructional tools, such as diagrams, tables, charts, symbols, and for- mulas to convey a mathematical idea. The use of these models increases in sophistication as students progress through the grades. For example, a student may model the number of action figures among three friends as 5+5+5 in the first grade, and as 5 × 3 by the third grade. By high school, students may be able to take several years’ data from Internet sources (such as the per- centage of adults who smoke cigarettes, the percentage of teens who drink caffeinated soda, or ridership in public transportation) and develop a model to predict future trends (Larson et al., 2012; Zimmerman et al., 2012).

Teachers promote this practice standard by providing opportunities to solve problems that arise from daily life. Learning to model mathematically is developed by exploring and sharing solu-

tions to naturally arising situations as they present themselves, with examples that are familiar, interest- ing, or part of the students’ culture. As with practice standard 3, successful implementation of this standard is dependent on a learning environment conducive to respectful discussion and discourse about mathemat- ics (Larson et al., 2012; Zimmerman et al., 2012).

Practice Standard 5: Use Appropriate Tools Strategically The intent of practice standard 5 is for students to use a variety of tools in an active, hands-on manner. Mathematically proficient students are familiar with the strategic use of tools appro- priate for their grade or course, can use them appropriately, and are able to make decisions about when each tool is helpful (NGA & CCSSO, 2010). These tools may range from simple paper and pencil to concrete models, rulers, protractors, calculators, spreadsheets, computer algebra systems, or dynamic geometry software.

Think About It

How would you use principles of DI to develop examples that are familiar, interesting, or part of the students’ environment?

Common Core Standards in Mathematics Chapter 5

The important thing to consider about this standard is that it is not about the teacher demonstrating various tools. Students must develop understanding by applying and using mathematical tools, and by being actively engaged partici- pants in this process. In order to accomplish this, classrooms need to be equipped with adequate resources for students to use as they explore problems and their solutions (Larson et al., 2012). Teachers facilitate this practice standard by devel- oping systems for using tools and by allowing students to choose what they would consider appropriate for the problem at hand (Zimmerman et al., 2012). For example, a student solving for the angle of a triangle may choose to measure it using a protractor, or she may be able to use paper and pencil or a calculator to calculate the angle mathematically. At a higher level, a student solving for sine might choose to use a unit circle or a scientific calculator to determine the value.

Practice Standard 6: Attend to Precision The goal of practice standard 6 is for students to commu- nicate with precision, using clear definitions in discussions with teachers and peers (NGA & CCSSO, 2010). This stan- dard also addresses accuracy, such as the accurate use of vocabulary and labels to support reasoning and being accu- rate with procedures and calculations (Zimmerman et al., 2012). The intent is for students (and teachers) to commu- nicate precisely and correctly. Using correct mathematical terminology supports the development of fine distinctions, or nuances, of mathematical ideas and prepares students for future concepts. For example, when a second grade student explains that he cannot subtract a big number from a smaller number, he may not realize that he can do this with the use of posi- tive and negative integers. Similarly, describing a rectangle as having two long sides and two short sides overgeneralizes the concept of a rectangle and excludes the square from that defini- tion; describing a fraction as part of a whole could confound later realizations that fractions can also describe parts of a set (Larson et al., 2012).

In order to support the development of this standard, teachers should model appropriate use of mathematics vocabulary, symbols, and explanations (recall the comment from a sixth grade student in Voices from the Classroom, Chapter 2, that the use of top and bottom number in referring to fractions was “so fifth grade!”). Teachers supporting this standard also provide opportunities for students to share their thinking and to explain and justify their mathemati- cal ideas.

Practice Standard 7: Look For and Make Use of Structure The goal of practice standard 7 is for students to recognize and use structure to understand and learn mathematics (Larson et al., 2012). Mathematically proficient students use patterns as a tool for learning—making comparisons, looking for similarities and differences that exist across topics. In this manner, they are recognizing mathematical structure (Zimmerman et

iStockphoto/Thinkstock

▲ Teaching students to use appropri- ate tools strategically means allowing them to choose tools, such as a calcula- tor, protractor, or compass, to solve math problems. How could this apply to another content area?

Common Core Standards in Mathematics Chapter 5

al., 2012). Structure is found across the curriculum, in geometry, basic operations, place value, numerical patterns—the list goes on. For example, second graders learn the structure of dou- bles when they see the problems 7 + 8 as a doubles plus 1 fact (7 + 7 = 14 plus 1 to equal 15). Third graders may learn that names assigned to polygons are related to the number of sides (pentagon, heptagon, octagon, etc.).

Students may not always recognize structure, and should be encouraged to look for it. Helping students recognize familiar structures in problems helps them to determine what to expect, and they begin to learn how and why mathematics works the way it does. The ultimate aim of this standard is to introduce students to the aesthetic of rational thought and logical reasoning. Structure reveals the power of mathematics—that no matter the context, problems of a certain structure are worked similarly. Rather than a system of tedious formulas used with mundane tasks, mathematics is about asking questions and finding simple solutions to problems. Through attention to structure, students may come to see the clarity of mathematics and realize that it follows simple, regular rules that can explain great complexity (Xander, 2010). When support- ing the development of practice standard 7, teachers provide opportunities for students to create examples of structure on their own to share and discuss (Zimmerman et al., 2012).

Practice Standard 8: Look For and Express Regularity in Repeated Reasoning The aim of this standard is for students to look for patterns as a way to reason about and make sense of mathematics (Zimmerman et al., 2012). This involves encouraging students to move beyond solving problems to find ways to generalize and determine efficient methods for those procedures (NGA & CCSSO, 2010). If students are encouraged to pinpoint patterns between calculations, they are more likely to look for and make sense of generalizations. This is referred to as regularity in repeated reasoning. Consider this example. First grade students are asked to show the different number pairs that could be used to make 10. They may show that 9 + 1 = 10, and also that 1 + 9 = 10. As they experiment with other number pairs, 8 + 2 = 10, 7 + 3 = 10, 6 + 4 = 10, they begin to see that as the first addend decreases by one, the second addend increases by one and the sum is still 10. In other words, noticing that repeated calcula- tions of the addends for 10 produces a pattern, which is what is meant by seeking regularity. With this regularity, students begin to discover their own repeated reasoning—thinking, for example that if 5 + 5 = 10, then I know the answer to 6 + 4 without counting because 6 is one more than 5, and 4 is one less than 5. Making sense of patterns and noticing repeated reason- ing leads to their own discovery of general methods and shortcuts for computing, which is the intent of this standard.

The classroom atmosphere sets the stage for students to engage in this practice. The role of the teacher is to create and maintain the type of discovery-oriented supportive environment for this to take place. This involves providing multiple examples as well as a progression of examples to allow students to make sense of repeated reasoning and to move from a single example to building a general method. With this practice standard, teachers are cautioned to avoid teaching shortcuts too early, before the students’ understanding of the regularity of pat- terns is developed (Zimmerman et al., 2012). For example, students may write their number pairs in a table, discuss the generalizations that they notice from the table, and then test their generalizations on other number pairs, ultimately discovering their own shortcuts.

Mathematical Content Standards

The standards for mathematical content are organized by grade in K-8 and by conceptual catego- ries in high school (e.g., number and quantity, algebra, functions, etc.). The standards are further

Common Core Standards in Mathematics Chapter 5

organized according to domains and clusters. Domains are one or two words that describe the big ideas that connect standards across grade levels. For example, number and operations in base ten (NBT) is a domain in grades K-5. A cluster is a group of related standards that describe related aspects of a domain. For example, in the domain of number and operations in base ten, two standards are clustered under the concept understand place value. Each grade begins with a brief overview of its domains and clusters and an introduction that identifies and describes areas for instructional focus. Figure 5.2 is a graphic depiction of how to read the grade level standards.

Design of the Content Standards The major design of the content standards is on focus and coherence. Focus means greater mas- tery of fewer things, and spending more time on the mastery of important concepts so students can apply them to a wide range of problems. Far from drills and practice worksheets or the use of rote procedures, the way the content standards are written redefines the concept of focus. Focus demands a vibrant, activity-based classroom with ample time for discussion and reason- ing (Zimba, 2011).

The focus in the early grades is on arithmetic. This enables students to become fluent in compu- tation, in the four basic operations, and in the basic mathematical properties and their uses. It positions students with a firm foundation and the skill set to generalize to algebra, which begins in the middle grades, and then on to the use of mathematics in high school, in preparation for the mathematics that is used in careers (Zimba, 2011).

Coherence in the standards refers to how mathematical ideas fit together, or how they logi- cally flow. Throughout the standards, mathematics keeps coming together to become one uni- fied idea. The concept is that mathematic ideas may become more complex, but they are not more complicated. The same basic ideas learned earlier hold in new applications; the addition and subtraction learned in lower grades is the same process when used with fractions and in algebraic equations. A careful reading of the standards shows this progress, that underlying

f05.02_EDU673.ai

Number and Operations in Base Ten

Standard Cluster

Domain

3.NBT

Use place value understanding and properties of operations to perform multi-digit arithmetic.

1. Use place value understanding to round whole numbers to the nearest 10 or 100. 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Figure 5.2: How to read the grade level standards

Standards outline what students should know. Standards that are closely related to one another are grouped together and summarized in clusters. Domains are comprised of large groups of related standards.

Source: © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

Common Core Standards in Mathematics Chapter 5

principles guide the understanding of how and why math works, topics flow from one idea to another, and ultimately make sense. An example of coherence is the flow of ideas toward algebra in the number and operations domains from elementary to high school. In elementary school, three domains deal with numbers—operations and algebraic thinking (OA), number and operations in base ten (NBT), and number and operations in fractions (NF). These ideas come together in middle school into two domains. OA concepts lead to understanding in the domain of expressions and equations (EE), and NBT and NF lead to a single unifying idea of the number system (NSS). The concepts in these two domains, learning to deal with symbolic expression in the EE domain and a facility with the rational number system in the NSS domain, flow into the algebra domain in high school (for a graphic explanation of these concepts, refer to McCallum, 2011).

Standards The standards begin with kindergarteners’ work on the number core—learning how numbers correspond to quantities, and how to put numbers together and take them apart. For example, students will be asked how many ways can the number 6 be shown. With this form of num- ber sense, addition and subtraction is the logical next step. What follows in the standards is a continuous progression from grade to grade, stressing procedural skill and conceptual under- standing. The K-5 content standards provide a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions, and decimals, which builds the basis for suc- cessful application of more demanding concepts and procedures. This skill set prepares stu- dents in middle school to represent numbers symbolically. Middle school becomes an area of growth because of the foundational work in the elementary grades (McCallum & Zimba, 2011). Students do hands-on learning in geometry, and probability and statistics. The middle school standards prepare students for algebra, which begins in eighth grade. High school students become real users of mathematics. They learn not just how to do mathematics, but why; that math has a purpose, and has structure and coherence. One purpose of the high school stan- dards is the connection with other disciplines—science, engineering, and technology, so there is also an emphasis on modeling, making a situation into a mathematical problem (McCallum, 2011). Table 5.6 displays the progression of mathematical domains across grade levels.

Table 5.6 CCSS mathematical content standards: domains by grade level

Grades K-5 Domains

Grades 6-8 (Middle School) Domains

High School Domains (crossing a number of traditional course boundaries)

Counting and cardinality Number and quantity

Operations and algebraic thinking

Expressions and equations Algebra

Number and operations in base ten

The number system Modeling

Number and operations— fractions

Ratios and proportional relationships

Functions Functions

Geometry Geometry Geometry

Measurement and data Statistics and probability Statistics and probability

Source: NGA & CCSO, 2010; McCallum, 2011.

Science and Technology Standards Chapter 5

Mathematical Standards and Differentiated Instruction

These standards paint an encouraging picture of expectations for mathematical learning and practice. The standards also relate, in the tone of their wording as well as in their structure, to several of the concepts presented in differentiated instruction, and in the theories and strategies used to support those concepts. As with ELA, the math standards set outcomes for each grade level but do not define methods or materials necessary to support students who are well below or well above grade-level expectations, or the supports needed for English language learners and for students with special needs (NGO & CCSSO, 2010). Nevertheless, the standards state that all stu- dents must have the opportunity to learn and meet the same standards, and that they should be interpreted to allow for the widest range of students to participate, with accommodations as needed (McLaughlin, 2012). They acknowledge that grade-specific standards do not account for the variety in abilities, needs, learn- ing rates, and achievement levels of students in any given classroom, but act as signposts for the goal of college and career readiness (NGO & CCSSO, 2010). These statements validate the claim that DI is neces- sary for effective, quality instruction.

5.4 Science and Technology Standards The CCSS have a powerful support system—the science and technology standards. CCSS provide the essential literacy and math skills to enable a deep understanding of science concepts and add relevance to the technology standards. Conversely, the science and technology standards pro- vide application, convenience, depth, and meaning to the CCSS. The Next Generation Science Standards were developed in conjunction with CCSS and are purposefully aligned. The National Educational Technology Standards for Students (NETS·S) provide the guidance for developing skills needed within the context of the CCSS and NGSS.

Next Generation Science Standards

The Next Generation Science Standards (NGSS) (www.nextgenscience.org) are a joint effort of the National Research Council, the National Science Teachers Association, the American Association for the Advancement of Science, and Achieve, a nonprofit organization. The stan- dards are based on the Framework for K-12 Science Education developed by the National Research Council. These standards are based on three interrelated dimensions, science and engineering practices, crosscutting concepts, and disciplinary core ideas.

Science and engineering practices describe the behaviors of scientists and engineers as they engage in inquiry and discourse when developing and refining ideas. The standards make it clear that science and engineering concepts are learned by doing the practices of science and engineering within the context of the disciplinary core ideas, not by learning factual infor- mation in isolation. Students should engage in each of these practices over each grade band (K-2, 3-5, 6-8, and 9-12). The standards identify eight practices that grow in complexity across the grades:

Think About It

React to the statement that all students must have the opportunity to learn and meet the same math standards, with the widest range of students participating with accommoda- tions as needed. Does this statement have the potential to change mathematical teaching practices for the grade levels that you are most familiar with? Give an example that supports your answer.

Science and Technology Standards Chapter 5

a. asking questions (for science) and defining problems (for engineering) b. developing and using models c. planning and carrying out investigations d. analyzing and interpreting data e. using mathematics and computational thinking f. constructing explanations (for science) and designing solutions (for engineering) g. engaging in argument from evidence h. obtaining, evaluating, and communicating information

Crosscutting concepts, listed below, unify the study of science and engineering through their common application across all science content areas, thus bridging the domains of science and providing a way of organizing knowledge. These concepts provide the mental tools for under- standing concepts using a scientific point of view. For example, when approaching the concept of flooding, an approach that makes sense would be to make observations of the patterns of typical and atypical rainfall, look at the scale or amount of water, the systems available for drainage in the terrain, and the energy behind the movement of water, which could lead to sug- gestions for explanations and predictions, matching those predictions with actual occurrences. Repetition of these concepts as tools for investigation in one setting reinforces their familiarity in other settings, thus helping students to better understand science and engineering practices and core ideas. Explanatory material accompanying the standards (e.g., Appendix G of the NGSS) indicate that these concepts are intended for all students, even for those who in the past may have been assigned to basic science classes that emphasized factual information and lower order thinking skills. Furthermore, they are not intended to be assessed as concepts separate from practices or core ideas; such as identifying a definition of “pattern” or “system.” Since the standards preceded the development of evaluation instruments, it is wise for professionals to be aware of this sensibility and work to hold assessment creators accountable to these expectations. Crosscutting concepts include:

a. Patterns are observations that prompt questions about relationships or ways to organize and classify.

b. Cause and effect helps students to understand the causes behind events and to predict and explain events in new contexts.

c. Scale, proportion, and quantity are concepts that help students to recognize how changes in size, time, and energy affect a system’s structure or performance.

d. Systems and systems models are concepts that help students to explicitly define the param- eters or features of a system and then to develop its model in order to understand and test ideas.

e. Energy and matter are concepts that help students understand the flow of energy and matter throughout systems in order to understand possibilities and limitations.

f. Structure and function is a concept that helps students to understand that the way an object is shaped is related to its purpose.

g. Stability and change is a concept that describes the relative rate of change in a system, which can occur quickly or slowly.

Science and Technology Standards Chapter 5

Disciplinary core ideas prepare students with sufficient core knowledge so that they can acquire additional information on their own in four content areas. This selection was intentional. The limited number of core ideas is meant to avoid shallow coverage of a large number of topics and to clarify what is most important to study, thus avoiding the learning of factual information with- out accompanying conceptual grounding. Appendix E of the NGSS further explains the progression of 44 core ideas, with expectations for increasing sophistication of thinking, across each of the grade bands classified into the following areas:

a. Physical science b. Life science c. Earth and space science d. Engineering, technology, and applications of science

Conceptual Shifts in Science Standards With the goal of college and career readiness, the NGSS emphasize critical thinking, investiga- tion, and real-world application. These standards are intended to support students in “thinking like” scientists and engineers from an early age. Even primary students are taught to identify questions to investigate and use the scientific method to design their own experiments, rather than merely following instructions and making observations about results. So, instead of sim- ply making “oobleck” together out of cornstarch and water and then noting how this substance has some properties of liquids and some of solids, students might be challenged to develop and test a hypothesis about whether any substance can combine more than one state of matter. Or they might make oobleck and then use their observations of it, along with additional research, to design their own oobleck-like non-Newtonian fluid.

Like the CCSS for math, the NGSS present a smaller set of core ideas in a more integrated, coherent fashion. The focus on disciplinary core ideas in just four areas (physical science, life science, earth and space science, and engineering, technology, and applications of science) form the basis for a progression of knowledge across the grades, beginning in kindergarten. The stan- dards focus on critical thinking and primary investigation, reflecting real-world interconnec- tions—acquiring and applying science concepts to the world around us. Rather than teaching science as a set of disjointed and isolated facts, these standards focus on descriptions of what students should know and be able to do at the end of the grade level.

The NGSS paint an encouraging picture of expectations for scientific learning in the United States. The standards were developed using current research in cognitive science on how people learn, (e.g., the work of Bransford, Brown, & Cocking, 2000) which was based on the theories and strategies that support the concepts of differentiated instruction (NGSS, 2013). As with the ELA and math standards, the science standards set outcomes for each grade level but do not define methods or materials. Nevertheless, all students must have the opportunity to learn and meet

Juice Images/SuperStock

▲ The Next Generation Science Standards are based on scien- tific and critical thinking, and emphasize supporting students in investigating their own questions. Does this seem different than science classes when you were in school? Explain.

Science and Technology Standards Chapter 5

the same standards, and the widest range of students should be allowed to participate in learning the core ideas and practices of science. The title of Appendix D, All Standards, All Students, on the NGSS website, cites evidence and makes arguments for the instructional shifts that teach- ers must make for all students to be college and career ready. Differentiated instruction and Universal Design for Learning are cited as appropriate frameworks for making this a reality. This appendix is supplemented with case studies that provide examples of strategies teachers can use to ensure accessibility in seven areas: (1) economically disadvantaged, (2) race and ethnicity, (3) students with disabilities, (4) English Language Learners, (5) girls, (6) alternative education, and (7) gifted and talented students (http://www.nextgenscience.org/appendix-d-case-studies).

The feature, Example of a Next Generation Science Standard for Grade 2, shows a sample stan- dard for second grade. This example illustrates the student performance expectations (make observations and construct evidence), a core idea (some earth events happen quickly, others more slowly) using the medium of a primary investigation (observing a natural phenomenon). Since the standards do not define the method or materials, it is up to the teacher to find the real-world connections. Detailed instructions on how to read the standards (the disciplin- ary core idea codes, connections to other grade levels and to ELA and math) are accessed at http://www.nextgenscience.org/how-to-read-the-standards. Next Generation Science Standards were launched in 2013, so there are relatively few examples of classroom practice demonstrat- ing these standards. One excellent resource has been developed by Paul Anderson, a science teacher, who takes each of the practices, crosscutting concepts and disciplinary core ideas and illustrates them with a series of short videos. The link is listed here and at the end of this chapter. http://www.youtube.com/playlist?list=PLllVwaZQkS2rtZG_L7ho89oFsaYL3kUWq

Example of a Next Generation Science Standard for Grade 2

2-ESS1 Earth’s Place in the Universe

Students who demonstrate understanding can:

Make observations from media to construct an evidence-based account that Earth events can occur quickly or slowly. [Clarification Statement: Examples of events and timescales could include volcanic explosions and earthquakes, which happen quickly and erosion of rocks, which occurs slowly.]

Science and Engineering Practices:

Constructing Explanations and Designing Solutions

Make observations (firsthand or from media) to construct an evidence-based account for natural phenomena.

Disciplinary Core Ideas ESS1.C: The History of Planet Earth

Some events happen very quickly; others occur very slowly, over a time period much longer than one can observe. (2-ESS1-1)

Crosscutting Concepts: Stability and Change

Things may change slowly or rapidly. (2-ESS1-1)

Source: Next Generation Science Standards. Accessed from http://www.nextgenscience.org/next-generation-science-standards.

Science and Technology Standards Chapter 5

Connections to ELA and Math The NGSS were developed concurrently with the CCSS, and feature connections with ELA and mathematics to advance learning in these content areas from a science perspective. (See, for example, Appendix L for connections to CCSS in mathematics at http://www.nextgen- science.org/sites/ngss/files/Appendix-L_CCSS%20Math%20Connections%2006_03_13.pdf and Appendix M for connections to CCSS in ELA at http://www.nextgenscience.org/sites/ngss/files/ Appendix%20M%20Connections%20to%20the%20CCSS%20for%20Literacy_061213.pdf).

These connections are illustrated in Figure 5.3. Note the convergence of the NGSS with math and ELA standards depicted in the white area of the diagram. The overlapping math and science standards are depicted in the purple area of the diagram, English and science standards in the green area, and the math and English standards in the orange area.

f05.03_EDU673.ai

S2. Develop and use models

M4. Model with mathematics

S5. Use mathematics and computational thinking

E2. Build strong base of knowledge through content rich texts

E5. Read, write, and speak grounded in evidence

M3 and E4. Construct viable arguments and critique

reasoning of others

S7. Engage in argument from

evidence

E1. Demonstrate independence in reading complex texts, and writing and speaking about them

E7. Come to understand other perspectives and cultures through reading, listening,

and collaborations

M1. Make sense of problems and persevere

in solving them

M2. Reason abstractly and quantitatively

M6. Attend to precision

M7. Look for and make use of structure

M8. Look for and express regularity in repeated reasoning

S1. Ask questions and define problems

S3. Plan and carry out investigations

S4. Analyze and interpret data

S6. Contruct explanations and design solutions

E6. Use technology

and digital media

strategically and capably M5. use appropriate tools strategically

S8. Obtain,

evaluate and

communicate information

E3. Obtain, synthesize, and

report findings clearly and effectively in

response to task and purpose

Math

ELA

Science

Figure 5.3: Relationships and convergences found in the CCSS and the NGSS

The labels that precede each practice/portrait indicate the discipline and number associated with the content standards in ELA/literacy, mathematics, and science.

Source: Cheuk, T. (2013). Relationships and Convergences found in the CCSS and the NGSS, Understanding Language: Science. Reprinted with permission.

Science and Technology Standards Chapter 5

Think About It

Given the newness of the Next Generation Science Standards, most states and districts have not yet developed the corresponding cur- riculum. What advice would you give curriculum developers to ensure that all students have the opportunity to learn and interact with these standards?

National Education Technology Standards for Students

The National Education Technology Standards for Students (NETS•S) were developed by the International Society for Technology in Education (ISTE) for evaluating the skills and knowl- edge students need to learn effectively and live productively in an increasingly global and digi- tal world. Although the NETS•S predate the CCSS, they are particularly relevant because media and technology are integrated throughout the CCSS and NGSS, both in critical analysis and production of media. Of course, implementing the NETS•S does not happen on its own. ISTE identified several essential conditions that promote technology integration in schools (ISTE, 2007). In order to be successful, the school-based community must be supportive. Teachers need school policies that reflect a vision supportive of technology use, reliable and equitable access to equipment and connectivity, ongoing professional learning, and consistent and reli- able technology support. Implementing the NETS•S in the curriculum is also relevant to con- cepts of differentiated instruction. DI concepts are closely related to essential conditions of a curriculum framework that integrates content standards with technology resources, engaging student-centered learning approaches, and continuous assessment and evaluation of learning. With this in mind, technology integration is not considered an add-on set of standards that teachers must balance with other demands. It actually can become a viable means for effective implementation of CCSS, NGSS, and DI concepts—allowing for flexibility in student group- ings, access to diversity of content, and assessment support that would be difficult to implement in its absence.

The NETS•S standards are used by teachers as guidelines to structure technology use and instruction at each grade level in six broad areas—creativity and innovation; communication and collaboration; research and information fluency; critical thinking, problem solving, and decision making; digital citizenship; and technology operations and concepts.

As is evident by the titles of these standards, simply being able to use technology (as covered in the standard technology operations and concepts) is no longer enough. The standards are meant to guide students as they use technology to analyze, learn, and explore. The outcomes they pro- duce also correlate with the CCSS. For example, in the mathematical standards, technology is used as a tool to support mathematics. Technology does not do the math; the students do the math. They must use technology appropriately, be strategic in its use, and know how to interpret the results (McCallum & Zimba, 2011). Similarly, in the ELA standards, students use technol- ogy to gather information and to produce products, but they must be able to interpret what they find, use the information appropriately, express themselves with clarity, and use technology strategically in production of their work.

Science and Technology Standards Chapter 5

Four performance indicators explain the intent of each standard. For example, the performance indicators for standard 1, creativity and innovation, are:

Students demonstrate creative thinking, construct knowledge, and develop innovative prod- ucts and processes using technology. Students:

a. apply existing knowledge to generate new ideas, products, or processes; b. create original works as a means of personal or group expression; c. use models and simulations to explore complex systems and issues; d. identify trends and forecast possibilities. (ISTE, 2007)

The six standards and their performance indicators are quite broad and can be difficult for teachers and students to understand. In the interest of building the knowledge base of a learn- ing community, ISTE developed an implementation wiki where teachers can share ideas, hopes, frustrations, and ask for help, accessed at http://nets-implementation.iste.wikispaces.net/. Teachers who post to this wiki agree to license their work through the share-alike creative com- mons attribution, meaning that the work can be shared for any non-commercial use as long as the author is acknowledged.

For example, primary teachers were concerned that their students may not grasp the concepts behind the standards as they were written, so they modified the language to make it more student friendly. For each NETS•S standard, they developed a student-friendly title and an explanation, and shared it on the wiki. Table 5.7 lists the results of their efforts along with the NETS•S standards. To explore this concept further, visit http://nets-implementation.iste. wikispaces.net/Student+Friendly+Standard+Names. The graphics show potential technology applications for each standard that are suitable for K-2 students. The web page, accessed on the wiki, provides links to these free or low cost web-based programs. While many of the programs listed are most suitable for K-2 students, others, such as Glogster and Wordle are suitable for students of any age.

Table 5.7 NETS•S, student-friendly standard names, and student-friendly explanations

NETS•S Standard

Student-Friendly Standard Name

Student-Friendly Explanations

1. Creativity and Innovation

Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.

Make it! Use your technology to show your creativity

2. Communication and Collaboration

Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.

Say it!

Share it!

Use technology to communicate

Use technology to collaborate

3. Research and Information Fluency

Students apply digital tools to gather, evaluate, and use information.

Find it! Use technology to show our information literacy

(continued)

Science and Technology Standards Chapter 5

4. Critical Thinking, Problem Solving, and Decision Making

Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.

Solve it! Use technology to think criti- cally, solve problems, and be decision makers.

5. Digital Citizenship

Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.

Protect it! When you use technology, remember to follow the rules of digital citizenship.

6. Technology Operations and Concepts

Students demonstrate a sound understanding of technology concepts, systems, and operations.

Use it! Using technology devices and programs will improve your learning.

Source: Adapted from NETS•T © 2007 International Society for Technology in Education. ISTE® is a registered trademark of the International Society for Technology in Education.

Think About It

What student-friendly titles for the NETS•S standards can you come up with for other grade levels? Also, try creating some student-friendly titles for the CCSS ELA and math- ematics standards.

Profiles for Technology-Literate K–12 Students

Another element of the NETS•S Project is the specification of technology profiles. Developed for specific grade ranges (K–2, 3–5, 6–8, and 9–12), the profiles identify 10 performance indi- cators that a student should master before the completion of the top grade in the range to be considered technology literate. To accomplish this feat, school faculties must systematically work together to ensure that the performance indicators are mastered. The profiles for each grade range are presented in the feature, Technology Profiles by Student Grade Band and Age. The numbers that appear in parentheses refer to the NETS•S 2007 standard(s) to which the per- formance indicator corresponds.

Despite efforts during the last decade, technology integration is still a hit-or-miss proposi- tion in many schools. Exemplary school districts integrate well on many levels, with adequate classroom equipment, 1:1 initiatives, use of personal or bring-your-own device programs, smart boards, and appropriate connectivity that makes technology integration within the cur- riculum possible. Other districts struggle with connectivity standards and security policies that are overly restrictive, lack of equipment, or lack of professional development in the use of technology and media (for example, a storage room with unused interactive whiteboards, because faculty members lack knowledge in how to use them). New assessment programs will eventually bring about the need for greater technology use, but these new guidelines will not be fully implemented until 2015 and beyond. University preparation programs have geared up by incorporating NETS•T (technology standards for teachers) into teacher preparation pro- grams. Unless school districts have the willingness to integrate, technology use for instruction is still scattered, with students applying most of their technology skills to personal use outside of school.

Science and Technology Standards Chapter 5

Technology Profiles by Student Grade Band and Age

Grades PreK–2 (Ages 4–8)

The following experiences with technology and digital resources are examples of learning activities in which students might engage during PreK–grade 2 (ages 4–8):

• Illustrate and communicate original ideas and stories using digital tools and media-rich resources. (1, 2)

• Identify, research, and collect data on an environmental issue using digital resources and propose a developmentally appropriate solution. (1, 3, 4)

• Engage in learning activities with learners from multiple cultures through email and other elec- tronic means. (2, 6)

• In a collaborative work group, use a variety of technologies to produce a digital presentation or product in a curriculum area. (1, 2, 6)

• Find and evaluate information related to a current or historical person or event using digital resources. (3)

• Use simulations and graphical organizers to explore and depict patterns of growth, such as the life cycles of plants and animals. (1, 3, 4)

• Demonstrate safe and cooperative use of technology. (5)

• Independently apply digital tools and resources to address a variety of tasks and problems. (4, 6)

• Communicate about technology using developmentally appropriate and accurate terminology. (6)

• Demonstrate the ability to navigate in virtual environments such as electronic books, simulation software, and websites. (6)

Grades 3–5 (Ages 8–11)

The following experiences with technology and digital resources are examples of learning activities in which students might engage during grades 3–5 (ages 8–11):

• Produce a media-rich digital story about a significant local event based on first-person inter- views. (1, 2, 3, 4)

• Use digital-imaging technology to modify or create works of art for use in a digital presentation. (1, 2, 6)

• Recognize bias in digital resources while researching an environmental issue with guidance from the teacher. (3, 4)

• Select and apply digital tools to collect, organize, and analyze data to evaluate theories or test hypotheses. (3, 4, 6)

• Identify and investigate a global issue and generate possible solutions using digital tools and resources (3, 4)

• Conduct science experiments using digital instruments and measurement devices. (4, 6)

• Conceptualize, guide, and manage individual or group learning projects using digital planning tools with teacher support. (4, 6)

• Practice injury prevention by applying a variety of ergonomic strategies when using technology. (5)

(continued)

Science and Technology Standards Chapter 5

• Debate the effect of existing and emerging technologies on individuals, society, and the global community. (5, 6)

• Apply previous knowledge of digital technology operations to analyze and solve current hardware and software problems. (4, 6)

Grades 6–8 (Ages 11–14)

The following experiences with technology and digital resources are examples of learning activities in which students might engage during grades 6–8 (ages 11–14):

Describe and illustrate a content-related concept or process using a model, simulation, or concept- mapping software. (1, 2)

Create original animations or videos documenting school, community, or local events. (1, 2, 6)

Gather data, examine patterns, and apply information for decision making using digital tools and resources. (1, 4)

Participate in a cooperative learning project in an online learning community. (2)

Evaluate digital resources to determine the credibility of the author and publisher and the timeliness and accuracy of the content. (3)

Employ data-collection technology such as probes, handheld devices, and geographic mapping sys- tems to gather, view, analyze, and report results for content-related problems. (3, 4, 6)

Select and use the appropriate tools and digital resources to accomplish a variety of tasks and to solve problems. (3, 4, 6)

Use collaborative electronic authoring tools to explore common curriculum content from multicul- tural perspectives with other learners. (2, 3, 4, 5)

Integrate a variety of file types to create and illustrate a document or presentation. (1, 6)

Independently develop and apply strategies for identifying and solving routine hardware and soft- ware problems. (4, 6)

Grades 9–12 (Ages 14–18)

The following experiences with technology and digital resources are examples of learning activities in which students might engage during grades 9–12 (ages 14–18):

• Design, develop, and test a digital learning game to demonstrate knowledge and skills related to curriculum content. (1, 4)

• Create and publish an online art gallery with examples and commentary that demonstrate an understanding of different historical periods, cultures, and countries. (1, 2)

• Select digital tools or resources to use for a real-world task and justify the selection based on their efficiency and effectiveness. (3, 6)

• Employ curriculum-specific simulations to practice critical thinking processes. (1, 4)

• Identify a complex global issue, develop a systematic plan of investigation, and present innova- tive sustainable solutions. (1, 2, 3, 4)

• Analyze the capabilities and limitations of current and emerging technology resources and assess their potential to address personal, social, lifelong learning, and career needs. (4, 5, 6)

• Design a website that meets accessibility requirements. (1, 5)

(continued)

Differentiation and Its Relationship to Accountability Measures Chapter 5

Technology is a friend of differentiated instruction. Many of the suggestions offered in the gen- eral framework of differentiation are too labor intensive to carry out without it. The NETS•S standards, and the learning profiles suggested by those standards, can be an effective frame- work for accomplishing the important student-centered work that differentiation entails.

5.5 Differentiation and Its Relationship to Accountability Measures

Although the standards movement has been an active part of teaching for over a decade, recent developments have attempted to link state standards and assessment to teacher evaluations and indicators of performance. Federal initiatives (e.g., Race to the Top) and state legislation are beginning to demand evaluation systems that differentiate teacher effectiveness based on stu- dent achievement (usually described by student performance models) and evaluation systems that measure teacher effectiveness using observation protocols, classroom artifacts, portfolios, student work, and professional growth plans. Several teacher evaluation models, such as the Marzano Teacher Evaluation Model (Marzano, 2012) and the Teacher Advancement Program (TAP, Milken, 2000) are used in many states and are providing preliminary data as to the effectiveness of these systems (Daley & Kim, 2011; Jerald & Van Hook, 2011; Pieczura, 2012; Sawchuk, 2012). Older state standards were used to develop these models, but as the CCSS, NGSS, and social studies standards become integrated into curriculum frame- works, they will also become part of teacher evaluation models. These models have cer- tain commonalities, most notably clear artic- ulation of standards and lesson objectives, unit and lesson plans, indications of student progress toward those objectives, and plans for differentiation in order to meet diverse student abilities, interests, and needs. The concept of differentiated instruction is rec- ognized as a viable means of providing equi- table access to opportunities to learn and is becoming codified into teacher evaluation systems as a way to address diversity among student populations.

Model legal and ethical behaviors when using information and technology by properly selecting, acquiring, and citing resources. (3, 5)

Create media-rich presentations for other students on the appropriate and ethical use of digital tools and resources. (1, 5)

Configure and troubleshoot hardware, software, and network systems to optimize their use for learning and productivity. (4, 6)

Source: NETS•T © 2007 International Society for Technology in Education. ISTE® is a registered trademark of the International Society for Technology in Education.

iStockphoto/Thinkstock

▲ Evaluations of teacher effectiveness have become linked to state standards and assessment in recent years, and will likely be linked to the new standards as well. What is your opinion of this practice?

Differentiation and Its Relationship to Accountability Measures Chapter 5

As with any change in educational practice, changes in textbooks, assignments, curriculum, and instructional plans ultimately follow. Some of these changes are faithful to the new reforms; others appear to apply in name only. The nonprofit educational policy organization, Achieve, Inc., has developed a technical assistance rubric for states and districts to use when evaluat- ing materials developed from the CCSS in ELA and mathematics (since the science standards were recently released, a science rubric is not yet available). Referred to as EQuIP (Educators Evaluating Quality Instructional Products), these rubrics assist teachers and districts in iden- tifying and evaluating the quality of the tasks, units, and lessons developed in response to the new standards (Achieve, 2013). Prominent within the instructional supports section of this rubric are elements of the DI model. An entire section is devoted to making the unit responsive to varied student learning needs, using language such as cultivating student interest, engage- ment and productive struggle, supports for students working below grade level, extensions for students working above grade or with high interest, and use of technology. Conceptually, the elements of differentiation are recognized and codified as quality indicators of appropriate instructional supports when implementing these standards.

C A S E S T U DY

Implementing the Common Core State Standards

Marie is a teacher in a state that is implementing the Common Core State Standards. Last year, after the state department of education released their standards based on the Common Core, the district aligned its curriculum. Now, teachers in her district are meeting in small groups to trans- late the curriculum into units and lesson plans. Their goal is to help the planning process become more efficient and less labor intensive, but to also leave room for the particular circumstances of each class. While they outlined a calendar of units, lessons, and tasks based on the standards, they also wanted to ensure that teachers could pace the curriculum according to the needs of their class instead of adhering to a strict coverage schedule, and could make provisions for flexibility in response to student interest and readiness. They decided to use a professional learning community model (PLC) by grade level and subject area within the district to guide their meetings. They also chose to use the EQuIP rubric as a tool to evaluate the units and lessons used for each grade level.

Marie is chairing the sixth grade ELA team. Since differentiation is an element of the EQuIP rubric, her team has decided to use the DI model as an overall philosophy to guide this project. For each unit, they used the backward design method, identifying and developing essential questions to guide the unit and lesson development. They have also selected elements of UDL and problem- based learning as general strategies. The team met regularly over the summer to develop a basic curricular outline for the school year. Now that the school year has started, they are meeting weekly to reflect on what worked and what did not during the previous week, to tweak the units and les- sons according to the learners in their classrooms, and to generally support each other in develop- ing strategies.

Critical Thinking Questions

1. As Marie’s sixth grade team continues to develop these plans and evolve their support systems, which DI concepts would lend themselves to team planning of tasks, units, and lessons?

2. Which DI concepts would guide individual classroom lesson implementation?

3. What other advice or suggestions would you give to Marie and her team in moving the sixth grade ELA team forward?

Post-Test Chapter 5

Summary Is it possible for teachers to differentiate, given the pressures of the standards, assessments, and evaluation systems? Policies developed in response to the No Child Left Behind Act of 2001 have had strong consequences for students and teachers. Teachers often felt pressured to aban- don differentiation efforts and teach to standards that were tested, leading many educational leaders to express skepticism that differentiation was even possible (Cuban, 2012).

While many teachers have worried that there is a conflict between standards and customiza- tion, the newly released CCSS and NGSS almost demand differentiation of method in order to achieve intended student outcomes. The NETS•S can be thought of as enabling standards; when applied within the CCSS and NGSS, they provide the contemporary tools that enable more efficient student outcomes.

Nevertheless, the standards are merely the starting point—essential, but not sufficient for a quality curriculum and improved student outcomes. Educators will need instructional mate- rials that align to the standards, resources, tools, and time to adjust classroom practice. New assessments must be developed to measure student progress. Federal, state, and district policies will need to be reexamined to ensure they support alignment of the CCSS and the NGSS with student achievement. We are truly living in interesting times.

Post-Test 1. Common Core State Standards are a result of

a. a federal government mandate to build a foundation to work collaboratively across states and districts.

b. a Department of Defense education activity. c. a state-led initiative in collaboration with teachers, school administrators, and content

experts. d. a Wall Street coalition that funded a grant to allow pooling of resources in education.

2. A strong emphasis in the Common Core State Standards is that instruction in English lan- guage arts (ELA) a. requires significant changes in our nation’s teacher preparation programs to provide

highly qualified instructors. b. should focus on the early years and that formal reading and writing instruction should

begin much earlier that in the past. c. is a shared responsibility across all subject areas and that all teachers must teach read-

ing and writing. d. needs to focus on the basics of learning to read and write without the distractions of

technology.

Post-Test Chapter 5

3. The standards for mathematical practice focus on practices that a. encourage students to set aside curiosity and persistence until they understand how

mathematical processes work. b. focus on procedure and tedium while moving toward the beauty of mathematics. c. encourage students to question how and why mathematics works the way it does. d. engage students in mathematical content in abstract ways without regard for real-life

problems. 4. Teachers can best support the learning of science and engineering concepts by

a. structured learning of factual information. b. doing the practices of science and engineering within the context of the core

disciplines. c. reading and talking about the practices of science and engineering. d. studying the behaviors of scientists and engineers as they engage in inquiry and

discourse. 5. Which of the following are NOT used to measure teacher effectiveness?

a. classroom artifacts b. observation protocols c. NET-S Standards d. student achievement

6. The Common Core State Standards focus upon a. constant comparative statistics that are grade-level appropriate. b. conceptual understanding and procedures to be introduced and mastered before stu-

dents move on. c. a series of norm-referenced scope and sequence charts that students in all countries

have mastered. d. conceptual understandings and procedures that are repeated throughout the grades.

7. The National Reading Panel identified five foundational literacy skills: phonemic aware- ness, phonics, fluency, vocabulary, and text comprehension. Adoption of Common Core State Standards implies that a. these conceptual understandings and procedures are essential and should be repeated

throughout the grades. b. these are components of a comprehensive reading program, but the focus should be

outcomes, not processes. c. use of scripted curriculum programs will now build on these five essential components. d. these components are research dated and no longer foster students’ working knowledge

of concepts of print, alphabetic principle, phonics and word recognition.

Post-Test Chapter 5

8. Providing students opportunities to reason abstractly and quantitatively is a Common Core State Standard in mathematics that is a. a means through which students think about a situation once they have all the details. b. a continuous expectation for practice, beginning in the early grades and extending into

high school. c. introduced in the sixth grade and reviewed each grade thereafter. d. distinctly different than the ELA standard of reading, writing, speaking and listening.

9. Students collaborate and learn from each other how to test the water quality of the pond behind their school. They remember features of a system they used when setting up the fish tank in their classroom, and others have tested the pH balance of their swimming pools at home. This repetition of concepts as tools for investigation is an example of a. the concepts of stability and change. b. crosscutting concepts. c. possibilities and limitations. d. performance indicators.

10. Which of the following was an unexpected outcome of the standards movement in education? a. Teacher performance is based upon teacher involvement in politics. b. Teacher performance is based upon student achievement. c. Teacher performance is based upon the use of technology. d. Teacher performance is based upon student and parent comments.

Answers 1. c. a state-led initiative in collaboration with teachers, school administrators, and content

experts. The correct answer can be found in Section 5.1. 2. c. is a shared responsibility across all subject areas and that all teachers must teach read-

ing and writing. The correct answer can be found in Section 5.2. 3. c. encourage students to question how and why mathematics works the way it does. The

correct answer can be found in Section 5.3. 4. b. doing the practices of science and engineering within the context of the core disci-

plines. The correct answer can be found in Section 5.4. 5. c. NET-S Standards. The correct answer can be found in Section 5.5. 6. d. conceptual understandings and procedures that are repeated throughout the grades.

The correct answer can be found in Section 5.1. 7. b. these are components of a comprehensive reading program, but the focus should be

outcomes, not processes. The correct answer can be found in Section 5.2. 8. b. a continuous expectation for practice, beginning in the early grades and extending into

high school. The correct answer can be found in Section 5.3. 9. b. crosscutting concepts. The correct answer can be found in Section 5.4.

10. b. Teacher performance is based upon student achievement. The correct answer can be found in Section 5.5.

Learning Activities Chapter 5

Key Ideas • The Common Core State Standards (CCSS) is an initiative started by the National

Governors Association and the State Commissioners of Education. The CCSS are writ- ten in two areas: English language arts (ELA) and mathematics. They address college and career readiness skills that will help prepare students to succeed in education and train- ing after high school.

• College and Career Readiness Anchor Standards (CCR) anchor grade level ELA stan- dards in reading, writing, speaking and listening, and language. The standards apply to English language arts in grades K-12 and to literacy in history, social studies, science, and technical subjects in grades 6-12.

• The reading standards include increasingly complex and challenging texts. Quantitative tools, qualitative dimensions, and matching the reader to the task are factors that mea- sure text complexity.

• The writing standards require students to write across three text types: arguments, infor- mative texts, and narrative writing.

• The speaking and listening standards require students to comprehend, collaborate, and present knowledge and ideas.

• The language standards require the use of standard English, knowledge of formal English and informal language choices, and academic and domain-specific vocabulary acquisi- tion and use.

• The CCSS in mathematics are divided into two sets, mathematical practice and math- ematical content. The eight practice standards describe activities of engagement with mathematics throughout the grades. The content standards describe outcomes that are balanced between procedural skill and conceptual understanding.

• The Next Generation Science Standards (NGSS) are based on three dimensions: science and engineering practices; seven crosscutting concepts that have applications across all science content areas; and disciplinary core ideas in four areas (physical science; life sci- ence; earth and space science; and engineering, technology, and scientific applications).

• The National Education Technology Standards for Students (NETS•S) are guidelines to structure technology use and instruction in six broad areas—creativity and innovation; communication and collaboration; research and information fluency; critical thinking, problem solving, and decision making; digital citizenship; and technology operations and concepts. Since media and technology skills are integrated throughout the CCSS and NGSS, the NETS•S are valuable tools for implementation.

• The standards form the basis of a quality curriculum and describe student outcomes that are active, collaborative, respectful, and rigorous, which are concepts endorsed by dif- ferentiated instruction recommendations. Moreover, teacher evaluation systems and sys- tems for evaluating materials used to implement CCSS have differentiated instructional practices as part of their structures.

Learning Activities 1. The Learning Design Collaborative offers modules to help support core content teachers

in grades 6-12 to implement Common Core ELA standards. The modules help teachers to

Learning Activities Chapter 5

identify the tasks, skills, instruction, and results needed to apply the CCSS to content areas of science, social studies, and other areas. Go to http://www.literacydesigncollaborative.org/

Begin with the video section as an introduction to the modules and the design templates. Within the video section, view Literacy Matters and one other video on changing teacher practices. Download one module of your choice: English Language Arts, Science and Technical Subjects, History/Social Studies. Answer the following questions: a. After studying the module, identify four areas that support a differentiated instructional

concept in basic principles, differentiation by learner characteristic, differentiation by teaching element, content, process, or product.

b. Identify at least two Universal Design for Learning elements in the module. c. Add one further suggestion for differentiating instruction.

2. Mathematics Assessment Project http://map.mathshell.org/materials/index.php offers les- sons and assessment resources linked to the CCSS in mathematics. From the home page, orient yourself to the site by clicking on Instructions. Then click on Lessons, and review one lesson at any grade level. a. Identify at least four elements of differentiated instruction that are present in this lesson. b. Identify which, if any, NETS•S standards are present in the lesson. If none are available,

what could be added? c. Add one further suggestion for differentiating instruction.

3. Read the essay Mathematics and Beauty posted by Xander, and write a reflection on your own realization of the elegance of mathematics. http://yozh.org/2010/09/28/ mathematics_and_beauty/

4. Quantitative measures of text complexity (readability and Lexile score) require calculation, and are usually performed using computer programs. While the Lexile formula is propri- etary, readability formulas have been available to the public for decades. Did you know that you can measure readability using a word processor? In MS Word 2007, click File on the menu bar, and then click Options. In Options, select Proofing. Under the section head When correcting spelling and grammar in Word, select: Check grammar with spelling and Show read- ability statistics. After you enable this feature, open a file that has at least 100 words, and select Review on the menu bar. Click Spelling and Grammar. When Word finishes checking the spelling and grammar, it will display information about the reading level of the docu- ment. The readability score uses the Flesch-Kincaid formula, and is loosely correlated to grade level; for example, the score 8.0 would designate an approximate eighth-grade read- ability level.

Find a passage of at least 100 words (more is better) obtained from the Internet or retyped from a textbook. Run the readability statistics on the passage. Be sure to report the location and source of the passage.

5. Review two video segments on the CCSS from the Hunt Institute found at this link: http:// www.youtube.com/user/TheHuntInstitute#g/u. Identify at least two principles of DI that fit with the concepts of these standards and explain the potential relationship.

6. Read the Core! Choose one grade level in the ELA, math, or science standards and select a domain. Examine the same domain in the grades below and above. Describe the progression of skills, the coherence of ideas, and the increasing complexity of ideas. How does the con- cept of differentiation apply to this domain?

Key Terms Chapter 5

Critical Thinking Questions 1. What evidence supports the claim that the CCSS and NGSS demonstrate elements of instruc-

tional theories that are compatible with differentiated instruction? 2. Give an example of how a task listed in the NETS•S technology profile supports the imple-

mentation of one or more differentiated instruction concepts. 3. Write a response in favor of CCSS and NGSS to critics who claim that the standards represent

a federal takeover of educational policy and practices. 4. How can the ability to implement differentiated instruction assist teachers in documenting

their effectiveness during the teacher evaluation process?

Key Terms Arguments refer to writing that supports a claim using reasoning and evidence.

Cluster is a group of related mathematical content standards that describe related aspects of a domain.

Coherence refers to how ideas fit together and logically flow. The mathematics and science standards have concepts that come together over time in one unified idea.

College and Career Readiness Anchor Standards (CCR) are anchor standards defining 32 broad competencies that form the basis for ELA literacy expectations across kindergarten through 12th grade.

Common Core State Standards (CCSS) are a core of state K-12 English language arts (ELA) and mathematics standards that are aligned with college and work expectations.

Complexity of text refers to the idea of gradually increasing complexity of reading material so that by the end of high school, students are ready for the demands of college and career- level reading. Complexity of text is evaluated by quantitative, qualitative, and reader variable measures.

Constructing viable arguments refers to the ability of students to make and test suppositions and assumptions in solving a problem and to communicate these effectively to others.

Crosscutting concepts are organizing schemas in the NGSS that have common application across all science content areas.

Disciplinary core ideas describe increasingly sophisticated content in the NGSS that is intended to prepare students with sufficient knowledge in physical science, life science, earth science, and engineering, technology and scientific applications in order to acquire additional information on their own.

Domain-specific vocabulary refers to words that are specific to content areas.

Domains describe the big ideas in mathematics that connect standards across grade levels.

Key Terms Chapter 5

EQuIP Rubrics (Educators Evaluating Quality Instructional Products) are used to evalu- ate materials developed from the Common Core standards in English language arts and mathematics.

Focus refers to a greater mastery of fewer things, spending more time on the mastery of important concepts in a logical structure with multiple connections.

Foundational skills are elements of the ELA standards in K-5 that foster students’ work- ing knowledge of concepts of print, alphabetic principle, phonics and word recognition, and fluency.

General academic vocabulary refers to words that are used in academic writing but seldom used in informal speech.

Informative texts are forms of writing that clearly convey ideas.

Making sense of problems involves using learned concepts and procedures as well as perse- verance, and is a valuable exercise even when the correct answer is not always evident.

Matching the reader to task is a variable used to measure complexity of text by considering motivation, interest, knowledge, experiences, and the purpose for reading the text. This mea- sure requires getting to know both the subject and the student, and using professional judg- ment to assess which texts would be appropriate.

Mathematical content standards describe procedural skills and conceptual understandings that students are expected to know and do as a result of K-12 mathematical study.

Mathematical practice standards describe ways that students engage with the content of mathematics from kindergarten through high school years.

Modeling is the ability of students to model real-world situations. Models include manipula- tives (base-ten blocks, pictures, drawings) diagrams, tables, charts, symbols and formulas that convey a mathematical idea.

Narrative texts are forms of writing that convey experiences or events.

National Education Technology Standards for Students (NETS•S) serve as guidelines for technology integration in grades K-12.

Next Generation Science Standards (NGSS) describe disciplinary core ideas in physical science, life science, earth and space science, and engineering, technology, and scientific applications.

Precision refers to the ability of students to communicate precisely and accurately, and to attend to accuracy when using procedures and calculations.

Qualitative dimensions are variables used to measure complexity of text using elements such as recognizing multiple meanings of text, varying levels of purpose, text structure, language conventionality, figurative language, and the background knowledge that the text requires of a reader. Qualitative dimensions require judgment of a human reader, that is, they are not cal- culated by a formula or a machine.

Additional Resources Chapter 5

Quantitative tools are variables used to measure complexity of text using mathematical for- mulae that calculate difficulty levels using word length, sentence length, and word frequency, such as readability scores or Lexile scores.

Reasoning abstractly and quantitatively refers to the ability to take a specific situation and to generalize it, or to make it abstract, so that its mathematical principles could be applied in other situations.

Regularity in repeated reasoning refers to the ability to discover patterns and to generalize from these patterns in order to determine more efficient methods for procedures.

Science and engineering practices describe the behaviors of scientists and engineers as they engage in inquiry and discourse when developing and refining ideas.

Standards are descriptions of student outcomes in content areas.

Strategic use of tools refers to students’ ability to choose and use a variety of mathematical tools (rulers, protractors, calculators, etc.) appropriate for their grade or course in an active hands-on manner.

Structure describes the similarities, differences, and patterns evident in mathematics. Knowing structure develops rational thought and logical reasoning and is related to the aes- thetics of mathematics, finding simple and elegant solutions that can explain great complexity.

Additional Resources Why We Need Common Core: “I choose C.” This is a humorous look at why we need Common

Core standards. http://www.youtube.com/watch?v=dY2mRM4i6tY

Resources for Understanding the Common Core State Standards. This comprehensive website is a guide to other websites, articles, and lesson vignettes. http://www.edutopia.org/common-core-state-standards-resources

Common Core State Standards and Assessments Collection: Tools. This website from the IDEA partnerships lists a number of presentation tools and discussion formats for teachers to learn more about using Common Core standards. http://www.ideapartnership.org/component/content/article.html?id=1522:ccss-and-a- collection-tools&catid=327:-common-core-state-standards-ccss-collection

Common core standards and differentiated instruction. Katie McKnight introduces differenti- ated instruction within the context of Common Core standards. http://www.youtube.com/watch?v=Ys-OWfOpHoM

Tips for differentiating instruction with common core standards. Katie McKnight describes tips for differentiation, such as taking an inventory of what teachers are already doing. http://www.youtube.com/watch?v=RN3i0Ws06vA

Next Generation Science Standards. The standards for science were released April, 2013. http://www.nextgenscience.org

Additional Resources Chapter 5

Common Core State Standards. The official standards are found at this website. http://www.corestandards.org

Common Core Standards: There’s An App For That. Vicki Windman’s blog from Tech & Learning, 33(6), 38–42, lists dozens of apps for mobile devices. Accessed from http://www.techlearning.com/features/0039/theres-an-app-for-that/53332

Silicon Valley mathematic initiative. This site has resources for implementing CCSS in mathematics. http://www.svmimac.org/

International Society for Technology in Education. The National Educational Technology Standards for Teachers, Students, and Administrators are found at this site. https://www.iste.org/

EQuIP Rubrics. The rubrics for evaluating material developed in response to the CCSS (and that include language promoting differentiated instruction) can be found at http://www.achieve.org/EQuIP.

Literacy in Physics: Reading a Primary Source. In this video, a high school physics teacher shows students how to read and analyze a research article about bridges. She discusses the overlap of the ELA standards into science. https://www.teachingchannel.org/videos/problem-solving-with-technology?fd=1

Reading Like a Historian: Sourcing. In this video, a high school history teacher leads students through primary source document. https://www.teachingchannel.org/videos/reading-like-a-historian-sourcing

Opportunities and Challenges in Next Generation Standards. This short paper, authored by Stage, Asturias, Cheuk, Daro, & Hampton from the April 2013 issue of Science describes how the NGSS build on the CCSS in ELA and Math. http://ell.stanford.edu/sites/default/files/Science-2013-Stage-276-7.pdf

NGSS Practices Video Series. Paul Anderson offers an overview of the NGSS at the follow- ing link. http://teachscience4all.wordpress.com/2013/01/21/ngss-practices-video-series/

Next Generation Science Standards. Paul Anderson takes each of the practices, crosscutting concepts, and disciplinary core ideas and illustrates them with a series of short videos. http://www.youtube.com/playlist?list=PLllVwaZQkS2rtZG_L7ho89oFsaYL3kUWq

A Teacher’s Guide to Fixing No Child Left Behind. This video discusses problems created by No Child Left Behind (test obsession, narrow curricula, blaming teachers) and the Obama administration’s proposals for addressing them. Sponsored by the U.S. Department of Education. http://www.youtube.com/watch?v=LV7od-RU1Jw