WEEK 4 SELF ASSESSMENT
nmonfort
self_assessment_week_4.docxThe purpose of this assignment is to self-assess your learning during the first four weeks of the course.
Evidence of your learning may include new writing as well as paraphrasing entries ( do not cut and paste from the discussion board) from your math journal or your posts (in the Learner's Support Forum, weekly posts, and responses to posts).
1. Growth in your mathematical thinking
2. New perspectives you have on teaching and learning mathematics
3. Ways in which you have supported your colleagues in their learning and have deepened on-line conversations
4. Describe how you will incorporate ideas you have learned in this course from the past four weeks into your classroom. Be sure to address the following topics: Multicultural Classrooms, Discrimination and bias, and Learning Environments.
· Create a concise self-assessment document using word processing software (e.g. Microsoft Word). Your document should be a minimum of 3 pages long (including examples) no more than 4. III. GRADING RUBRIC
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Assignment Requirement |
Points Possible |
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Include at least two strong pieces of evidence for all three criteria of self-assessment |
9 |
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Include a detailed explanation describing how each piece of evidence demonstrates the criteria |
9 |
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Description of how concepts from # 4 ( above) will be incorporated into your teaching |
10 |
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Paper is well-written and organized |
2 |
TOTAL POINTS POSSIBLE: 30
All the posts to use for the assignments
In reading through the selected articles, I found that both Mathematics: Strategies for Teaching Limited English Proficient Students and Equity for Language Learners provided a comprehensive summary of considerations, accommodations, and strategies that teachers can utilize when teaching English language learners in their classrooms.
Two important points that I took away from the article Equity for Language Learners focused on identifying language goals and structuring language activities within the mathematics classroom. Both of these points were focused on in great detail in my SEI Endorsement course. As teachers, we need to understand the great deal of language that is associated with mathematics in order to structure appropriate learning experiences for our ELL students. The article discussed identifying language goals in addition to content goals. Having practiced this through my last course, I have found that this strategy really helps me to clearly identify how I want my students to express their understanding of content knowledge. As the article discussed, pairing content and language objectives helps teachers to identify the language structures that students need to display their understanding. When writing language and content objectives for my lessons, I try to make the languages objective mirror that content objective as closely as possible. The main difference between the two objectives is that the content objective focuses on what students will learn and that language objective focuses on how they will display their knowledge. For instance, here are content objectives and differentiated language objectives from a recent lesson that I completed with my 4th graders in the past:
Content Objective: Students will identify the place and value of a digit through the hundred thousand place value.
Language Objectives:
1. Students will state the place and value of a digit through the hundred thousand place value.
2. Students will write the value of a digit through the hundred thousand place value in standard form.
3. Students will write the name of the place of a digit through the hundred thousand place value.
Differentiated Language Objectives:
4. Using a provided sentence frame, students will state the place and value of a digit through the hundred thousand place value.
5. Provided a reference chart, students will write the value of a digit through the hundred thousand place value in standard form.
6. Using a provided sentence frame, students will write the name of the place of a digit through the hundred thousand place value. (i.e. In 5,467, the digit 4 is in the hundreds place).
This article also discussed the tremendous impact sentence frames can have on developing content and language knowledge for ELL students. In my classroom, I have begun to use sentence frames across both ELA and mathematics lessons. In doing so, I have found that the use of a sentence frame provides students with a predictable structure that they can use to express content specific ideas. Students can focus more upon content when they are not overwhelmed by language structure. Sentence frames encourage the appropriate use of content area vocabulary. My ELL student is able to access and express lesson material to a much greater degree when the language tasks are appropriately scaffold.
I think that the article Mathematics: Strategies for Teaching Limited English Proficient Students provided a solid overview of the stages of language acquisition and the types of language proficiency to consider when working with limited English proficient students in our classrooms. The article’s discussion of BICS vs. CALP (Basic Interpersonal Communication Skills and Cognitive Academic Language Proficiency) identified the variety of language and cultural challenges ELL students can face when entering US schools for the first time. One important piece of information that I took away from this article was that ELL students are not just learning a new language, they are learning a new culture and that culture is intertwined in the way academic material is presented in school.
I also think that the article’s discussion of misconceptions about language learners provided valuable insight as to the challenges that LEP students can be facing even when they appear to be English proficient. This portion of the article made me think of the variety of proficiency levels that ELL students can have in reading, writing, listening, and speaking. For instance, my ELL student is fluent in spoken English, but his reading and writing is extremely limited. This website: http://www.wida.us/standards/CAN_DOs/ provides descriptions of what students can do at each of these proficiency levels as well as ideas for differentiating instruction (proficiency levels are based on an annual ACCESS assessment). Even if your student hasn’t taken the ACCESS test, I think that the descriptors can be helpful in identifying what ELL students in your classroom may be able to do and what language constructs that may be working towards.
This website also has a wealth of information on teaching ELL students and how to appropriately structure language experiences in the classroom. This link: http://www.wida.us/resources/ will bring you to a series of bulletins while this link http://www.wida.us/ will bring you to the WIDA home page. (Just in case anyone wants additional information!)
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If you examine the template used, how many different profiles might you see in a typical classroom?
Examining the template, I think that there could potentially be 16 different profiles of students within a typical classroom. However, based upon my knowledge of language development, I think that some of the profiles would be more likely to occur than others.
In considering different profiles that could be represented by the template…
Are there categories of proficiencies that might benefit from the same type of intervention, and if so, what are they?
Or, does every profile need an individual, proscribed intervention? Explain your thinking.
I think that a balance between common and specialized interventions is the most appropriate way to create lesson accessibility within a classroom. All students can benefit from accommodations/interventions such as explicit strategy instruction (i.e. how to solve multi-step word problems), pre-teaching key vocabulary/concepts, and direct skill instruction (i.e. how to solve multi-digit multiplication problems using the standard algorithm). Presenting information in multiple ways and providing students with multiple approaches for problem solving is beneficial to all students. I also think that students with different category profiles can benefit from similar types of interventions that may not be necessary for all general education students. For instance, a student who has difficulty recording written calculations as a result of fundamental language differences between his/her native language and English (i.e. different writing direction, or different organization of writing on a page) may benefit from the use of graph paper, or number sentence frames when completing written calculations. This type of accommodation would also benefit a Special Education student with visual-spatial difficulties. We could also consider an ELL student who benefits from the use of a word/concept bank because of his/her limited proficiency with academic language. This student would benefit from a word bank in incorporating academic terms into his/her written and oral explanations. This accommodation would also benefit a student who has short-term memory deficits or language retrieval difficulties as a result of a communication disability. At the same time, some accommodations may only be appropriate for specific students. For instance, an ELL student from Russia with limited English proficiency may benefit from the use of an English-Russian dictionary, or a chart comparing numbers written in English and in Russian. Unlike the other accommodations described above, other students in the classroom would not benefit from this accommodation (because they do not necessarily speak Russian). In summation, some interventions and instructional techniques will be beneficial for all students, while other interventions should be more student specific. The key with incorporating interventions and accommodations into our lessons appropriately is knowing and understanding the needs of the students we have in front of us.
In considering the presented problem about Juan and his brownies…
1. For what grade level do you suppose this task is appropriate?
I think that students could begin to work towards solving this problem in fourth grade. Parts (a) and (b) would be appropriate for 4th grade students to solve. Fourth grade students learn concepts of factorization and division that could be beneficial in solving this problem. (i.e. they learn how to list all factors of a number and they continue to develop the concepts of division that they were exposed to in third grade). The reasoning required in this problem would also be appropriate for fourth graders beginning to develop their problem solving abilities for multi-step word problems. While this problem may be challenging for some students in fourth grade, I think that it would be a beneficial problem to work through with students as a class.
Part (c) would be more challenging for fourth grade students due to calculations with monetary values and division. I think that part (c) would be more appropriate for students in middle school grades. I could also see students working more independently to solve this problem in 5th (possibly), 6th, or 7th grade.
2. In which category (ies) of the template would you expect students to display difficulty?
Depending upon the students in a particular classroom, I would expect that students could potentially experience difficulty with this task in any of the areas on the template.
Spoken/Oral Language: Students with limited spoken/oral language skills may have difficulty with the wording of the problem, or with specific mathematical terms. Potentially challenging words could include: dozen, package, spent, ingredients, determine, charge, and profit. While the word dozen is a mathematical term that students may be unfamiliar with, the words ingredients and determine may be difficult for students to understand, or decode while reading the problem. Other words such as spent, package, charge, and profit could be difficult for students because of their potential for multiple meanings (i.e. package can be an action, or it can be something you receive in the mail). Additionally, students with spoken or oral language difficulties may have a difficult time comprehending the written or spoken problem. Background knowledge of some ELL students may be limited and some students may not have a complete understanding the concept of a bake sale. Students with limited spoken/oral language skills in their native language may not have a repertoire of background knowledge to connect to the new terms being presented through the problem. Students with spoken/oral language deficits in English may have difficulty comprehending the problem, or may not be able to clearly/accurately express their ideas using English language.
Written/Symbolic: Students with limited skills in written/symbolic language may have difficulty recoding calculations and reasoning to assist them in working through the problem. These students may have difficulty reading and comprehending the presented word problem as a result of relative specific weaknesses in their knowledge of written language. Students with limited written/symbolic language may not be able to record the specific mathematical calculations (i.e. number sentences, symbols (x, =, /, $), or numerals) in order to appropriately solve the problem. These students will have difficulty answering the presented questions on paper through recording their solutions and thinking for others to read. These students may also experience difficulty with recording and calculating monetary values (i.e. $5.40, or $5.40/36).
3. If a student had difficulty in the written mathematical category, what intervention might you identify to move the student to proficiency?
Specific interventions and accommodations could assist a student with limited written/symbolic language skills in completing this task. Interventions/accommodations include:
- Use of a vocabulary word wall with visual representations of key terms
- Place value chart for writing monetary values
- Number strip/reference sheet for writing numerals appropriately (show direction, numeral formation)
- Sentence frames and equation frames to assist with written calculations and expressions (i.e. ____ x ____ = ______, or, “Juan should put _______ brownies in each bag because __________”).
- Use of a table to organize written information
Number of Bags Number of Cookies in Each Bag Total Number of Cookies
- Direct instruction on writing and performing mathematical calculations (i.e. multiplication, division, monetary calculations)
- Visual models and manipulatives
- Explicitly connect written and spoken language
- Allow students to express thoughts orally before recording in writing
- Use of a reference sheet with key terms and models of recorded calculation procedures
- Use of a word bank for written explanations
- Recorded list of pre-taught vocabulary
- Graph paper for written calculations
- Checklists for completing multistep calculations
- Problem solving checklist
4. How might you proceed in making this task accessible to each and every student including ELL students, SPED students, and regular education students?
In order to make this task accessible to every student in my mathematics classroom (ELL students, Special Education students, and general education students) I would first pre-teach important vocabulary and terms. I would ensure my students had a knowledge of a strategic problem solving process, and that they understood the necessary mathematical concepts needed to solve this problem (i.e. can the students complete calculations with money, multiply, and divide). Then, I would review the problem with the students. I would most likely provide the students paper copies of the prompt, as well as project a larger version of the question onto the white board. I would read the prompt aloud with students and pause to discuss the language and phrasing of the prompt. This will provide multiple means by which the students can access the information within the presented problem. Together, we would set up the problem as though we were going to work through a four-step problem solving process (Understand, Plan, Solve, Look Back). As a group, we would identify important information within the problem (underline it), circle the questions we need to ask, and identify the number of parts we need to answer (number them). I would then, most likely, allow some students to work on the problem independently, while others worked in small groups (based on the level of support needed). All students would also be provided with supports such as those described in question three above as they were needed. Following the solution process, I would put students in groups, or pairs to share and discuss their solution methods. Groups could then debrief by sharing their ideas with the class.
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July 23, 2014 6:56 PM
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1. How might you describe this student's strengths and weaknesses?
Since there are no marks or notes in any of the four quadrants for Student 1’s diagram, I am led to believe that this student has not yet developed oral or written proficiency in their ability to explain mathematical concepts in either their primary language, or in English.
2. What interventions might you consider to move this student to proficiency in all four areas?
In order to assist this student in moving towards proficiency in all four areas, I would first focus on developing the student’s ability to orally identify and explain mathematical concepts. I would most likely focus on providing structured vocabulary instruction paired with repeated opportunities for listening and speaking. Visuals, explicit examples, and word reference charts would assist this ELL student in developing familiarity with the language of mathematics. Direct content instruction paired with well scaffolded language opportunities would assist this student in developing his or her oral proficiency. Many hands on experiences would assist this student in developing mathematical content knowledge and the language associated with it. After this student developed oral proficiency in identifying and explaining mathematical concepts, I would provide the student with additional opportunities that paired listening and speaking with reading and writing. Sentence frames, number charts, and written examples of mathematical symbols and number sentences would assist this student in developing written proficiency in mathematics.
3. How might the interventions you described above change if a different student's profile was represented in the grid below?
If this student’s grid displayed oral and/or written proficiency in his/her primary language, my instruction would be more tailored towards accessing that prior knowledge. A student who understands and is able to explain mathematical concepts in his/her native language will most likely be able to develop oral and written proficiency in English at a faster rate than a student who does not possess such background knowledge. Interventions for this student would focus upon connecting concepts from the student’s native language (i.e. words, symbols, numerals) to concepts in English. I would use visuals, conversion charts, and word lists to help make these connections.
If this student showed oral proficiency in English, but did not show any proficiency in his/her primary language, I would focus my instruction upon developing the students writing abilities in English. Direct instruction and accommodations such as sentence frames, word banks, direct vocabulary instruction, and written examples of calculations would assist this student in developing written proficiency in English with respect to mathematical concepts.
Student 2
1. How might you describe this student's strengths and weaknesses?
The single check in the upper right-hand quadrant of the diagram indicates that this student is proficient in his/her ability to orally express mathematical concepts and ideas in English. The fact that no boxes on the left side of the diagram are checked indicates to me that this student is not proficient at orally or symbolically expressing mathematical content knowledge in his/her primary language. The fact that the lower right-hand quadrant is not checked indicates to me that this student is continuing to develop his/her ability to express his/her understanding of mathematical concepts in writing. This student is not yet proficient at expressing mathematical concepts symbolically in English.
2. What interventions might you consider to move this student to proficiency in all four areas?
I would focus on developing this student’s abilities to express mathematical concepts symbolically in English. I would incorporate interventions that drew upon the student’s strengths in oral expression. I would provide for opportunities that paired listening and speaking with reading and writing mathematical content. Pairing oral and written activities would help this student to internalize the symbolism associated with the content he/she is able to express verbally. I would also provide direct instruction and accommodations such as sentence frames, word banks, direct vocabulary instruction, and written examples of calculations to assist this student in developing written proficiency in English with respect to mathematical concepts. Hands-on activities that paired calculations/problem solving with written expression would assist this student.
3. How might the interventions you described above change if a different student's profile was represented in the grid?
If this student showed oral proficiency in both his/her primary language and in English, I would design instruction to draw upon this student’s strengths. Word banks, example problems, and instruction explicitly connecting oral and written language would assist this student in developing proficiency in written expression. I would also be careful to connect the student’s knowledge from his/her native language to his/her developing skills in English.
If this student had proficient written expression skills in his/her native language, I would provide the student with visuals, charts, and number strips to connect written symbols in English to symbols and numbers in the student’s native language.
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July 20, 2014 11:27 PM
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Hi,
I also liked the strategy of using a dry erase boards for student responses. I do this a lot in my classroom and find that it keeps even the quietest students involved. Other strategies I have incorporated are encouraging self advocacy strategies (i.e. a student can ask, "Can you repeat that?", or "Can you come back to me?" if they are unsure of an answer or response), giving students a heads up before calling on them (i.e. "Kate, your turn will be next"), or including some "easy" questions in discussions that I know all students can answer.
nerlande
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July 20, 2014 11:25 PM
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Carie,
I like how you do not feel offended when a student is looking down. Some students just need some redirection and some students have a lot going on and calling them out is not the way to get their attention," I couldn't agree with you more. Two students that I currently have in my classroom will often look as though they are not paying attention, but in reality they often need to look a something less stimulating in order to process complex auditory information. Other students may become anxious when they are called on and may become more fixated on being called out than upon the lesson at hand. Knowing the students we have in our classrooms and all of their background and history is so important. Very often, our response to student behavior is specific to the child we have in front of us. Nerlande
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July 20, 2014 11:17 PM
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I have found that engagement can be a powerful instructional tool. Within my class, I currently have one particular ELL student who can become easily frustrated and discouraged when the language of a task is beyond his comprehension level. I have found, however, that if the nature of the task is one that engages him, he will often persevere through the challenges because his interest in the activity outweighs his frustrations. Have you found similar tendencies among your student population?
Nerlande
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July 20, 2014 11:16 PM
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Hi,
When reading your post, much of what you wrote made me think of how we engage our students in the presented material. I think that how we engage our students in learning activities is a very important instructional strategy. Engaging all students through cooperative learning, multi-sensory activities, and multiple modes of expression and representation will help our ELL students access the material they are presented with in class.
Nerlande
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July 20, 2014 11:12 PM
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Hi guys,
I selected Pieta's method as that which would provide the best transitions to operating with algebraic symbols. In looking at Pieta's partial products method, I immediately thought of using a grid to multiply the partial products. This process works the same in base ten as it does in multiplying polynomials.
You also discussed Julio's lattice method of multiplication. Aside from the lattices to organize like terms, do you view the Pieta and Julio's methods as the same? I hadn't thought this way initially until reading your post, but now I am thinking they are pretty much the same. I tend to find the lattice method of multiplication a little more visually challenging than other methods because of the diagonals, but after reading your post I saw that it is essentially the way I apply the partial product method in my classroom. Interesting how hearing something explained a little differently makes you view it in a whole new light! Nerlande
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July 20, 2014 11:09 PM
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Hi,
I thought that Pieta's method was the method that best lends itself to algebraic arithmetic. In my classroom, we connect the partial products method to the area model of multiplication in order to assist students in multiplying each part of the first factor by each part of the second factor. This could also be done using polynomials. The image below shows two ways you could use this same method with polynomials. I tend to like using the grid method with my students because it helps to keep them organized and ensures (mostly) that tey don't forget to multiply one of the pieces. photo2.JPG
Nerlande
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RE: Group 3: Equity- Stacy Ribolini
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July 20, 2014 11:04 PM
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Hi Stacy,
I always believe higher expectations throughout a school or system will have great impact. The idea of equitable not always being equal is important for providing all of our students with access to a high quality curriculum. Without appropriate accommodations, some students will not be able to access the same material as others. The key with accommodations, however, is that we remember we are making material accessible, not easier.
Nerlande
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July 20, 2014 11:02 PM
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Hi Elizabeth,
The statement from the reading about equitable not always being identical really stuck with me. I find that this is a tough concept for many children, as well as adults, to grasp. This is true especially in an educational world of standardized assessments where every child and teacher is being measured by the same bar. I think that the degree of standardization among assessments can make it difficult for teachers to remember that not all students should be instructed in the same way.
Great job,
Nerlande
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July 15, 2014 4:58 PM
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The NCTM standards for equity stressed the importance of high expectations and support for all students. The predominant message from this section that stuck with me after reading was that equitable is not identical. This portion of the standards discussed how all students deserve a challenging mathematics curriculum with well-supported teachers and ample resources. The NCTM also discussed, however, that equitable mathematics instruction will not look “identical” for all students. Some students require “reasonable and appropriate accommodations” for access and attainment of high mathematics standards. I particularly liked this portion of the reading because it reminded me of conversations I frequently have with my students regarding what is “fair.” I often tell my students that fair is not everyone getting the same thing. It is a challenging message to convey to elementary school children, but I try to help them see that “fair” is everyone getting what they need to be successful. The NCTM really touched upon this point within this portion of the standards.
The section on equity also addressed teacher actions. Teachers can communicate equity through notes, assignments, comments, and student groupings. The opposite can also be true. This portion of the standards reminded me that preconceived notions about student abilities can lead teachers to unintentionally limit students by keeping them from tasks it is believed that “they can’t do.” I found that this portion of the standards related heavily to last week’s discussions pertaining to structural factors that can limit our students.
Learning
The NCTM standard for learning mathematics placed a heavy emphasis on learning with understanding. This portion of the standards focused heavily on connecting new and existing information to promote student learning. The NCTM discussed how conceptual understanding makes knowledge useable in a variety of situations and circumstances while rote learning often cannot be transferred from one situation to the next. The NCTM also discussed the importance that learning tasks further develop and deepen content knowledge in a meaningful way. Furthermore, when learning tasks connect to prior knowledge and foster inquisitive thinking, they are more engaging to students and result in the deeper development of content knowledge. In my mind, I connected this back to this week’s discussion of engaging ELLs in the mathematics classroom. When we help out students connect mathematics content to their own knowledge, we increase the likelihood that they will retain and be able to generalize the new information.
Assessment
The NCTM section on assessment discussed the importance of assessment aligning with instructional goals. This portion of the standards stressed that assessments be used as a tool for instruction as opposed to an end measure of student knowledge. The section discussed the importance of using a variety of assessment types (formative, summative, informal observations, student work samples). I strongly agreed with the NCTM statement that educators should base decisions on a “convergence of evidence based on multiple sources.” The standard stated that in order to get an accurate picture of student performance, teachers need to look at both formative and summative assessments as well as classroom observations and other performance tasks (i.e. portfolios, journals). I find that in my classroom this is the case with all of my students. When looking at the abilities of my students, I take their performance on topic assessments as one piece of a larger picture of their mathematical abilities; particularly because so many of my students have difficulty with traditional assessment tasks (i.e. paper and pencil tests/quizzes).
Mathematics Instruction and Academic English
The article concerning Mathematics Instruction and Academic English discussed the importance of reducing the language demands of mathematics tasks for English Language Learners. Reducing language demands on academic tasks helps ELLs focus on the implications of mathematics content without being limited by their present level of English proficiency. Suggestions for reducing language demands included pre-teaching/discussing important vocabulary, including cognate instruction in mathematics lessons, using flow charts and graphic organizers, and avoiding the introduction of new concepts and new vocabulary at the same time. From classroom experience, I have found that the language of mathematics can be extremely overwhelming for ELL student if lessons are not properly introduced, or scaffolded. In order to set my students up for success on a daily basis and provide them access to challenging mathematics content, I must carefully consider the language demands of the daily lessons as well as the demands pertaining to mathematical concepts. When I provide them with appropriate scaffolding (i.e sentence frames, pre-taught tiered vocabulary, and visuals), I have found that they are more engaged in daily lessons and more proactive about their understanding of mathematics content.
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1. Reading Direction: Directly instruct students on the direction in which words are read in English. Discuss how different languages sometimes read writing in other directions. Place an arrow on the top of worksheets, or put a sticky note with an arrow on the top of text pages to remind students to read from left to right.
2. Writing Direction: Directly instruct students on letter and numeral formation. Include letter and number strips on classroom walls and student desks to assist with memory as to the way numbers and letters are written in English. Provide students with paired representations of English letters/numerals and letters/numerals in their native language to assist with representation and recall.
3. Periods vs Commas: Directly instruct students as to how commas and periods are used when writing numbers in English. Provide a two column chart to students comparing the same numbers written in English and in their native language. Discuss the differences between numbers such as 23.456 and 23,456 in English. Compare these numbers to numbers in the student's native language. Reinforce the student's understanding of mixed numbers vs. large numbers that are not mixed numbers.
4. Metric System vs. Customary System: Provide classroom investigations surrounding both the metric system and the customary system. Examine different rulers and measuring devices. Directly instruct students on the practices of converting between the two systems. Provide students with visual examples of items that represent units of measure in each system (i.e. compare something that is one inch long with something that is one centimeter long). Provide students with a conversion chart to assist them with calculations in either system.
5. Monetary Differences: Provide students with an opportunity to examine money from different parts of the world. Discuss the visual similarities and differences of the coins and bills. Provide students with price tag examples and visuals of how much particular items would cost in different monetary systems (i.e. a bag of chips would cost x dollars, y rubies, or z euros). Also directly instruct students on qualities of the customary system (i.e. how to read and write monetary values, the names and types of bills/coins, how to convert from one type of coin/bill to another (i.e. one dime is ten pennies)). Explicitly contrast the student's native monetary system with the h us system. Provide practice using and manipulating us money.
6. Differences in Computation: Identify explicit similarities and differences between different computation methods. Highlight underlying mathematical concepts that apply to both solution methods. Have the student orally explain the different solution methods aloud. Use visuals to display the conceptual understanding associated with the algorithms.
Organizational Skills
Pertaining specifically to mathematics, ELL students could benefit from:
- Instruction and strategies for reading and writing numbers (left to right, with and without decimal points and commas) (i.e. the use of place value charts)
- The use of graph paper for completing multi-digit arithmetic and for completing algorithms that are solved differently in a student's native language.
- The use of reference sheets for vocabulary and algorithm procedures
- Checklists outlining a process for solving problems (i.e. underline important information, circle the question, make a plan, solve and label, check your work).
General organizational skills ELL students could benefit from include:
- Direct instruction and strategies for organizing materials (notebooks, folders, class notes)
- Use of an assignment book, or agenda
- Color coding information by concept
- Highlighting directions
- Visual/written schedules for day or class activities
- Checklists for assignments or class activities
- Breaking projects into smaller, more manageable parts
- Break down multi-step directions into smaller steps
- Strategies for identifying key words in directions and questions
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Group 3: Monfort, Myers, Norder-Pagan, Prasad, Ribolini
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RE: Group 3: Monfort, Myers, Norder-Pagan, Prasad, Ribolini
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July 14, 2014 4:46 PM
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In looking at all of the presented methods, I think that Pieta's method (the partial products method) lends itself the most to algebraic arithmetic. When I teach my students the partial products method, I usually have them write each factor in expanded form. In this method, each portion of the first factor is multiplied by each part of the second factor. One factor (in expanded form) is written across the top of a square divided into four quadrants. The second factor (in expanded form) is written down the left side of the square. Students then find the partial products by using the square as a sort of grid system where the value of each square quadrant is equal to the product of its sides. This method is similar to the area model of multiplication only the sides of the square do not need to be drawn to scale.
This method lends itself particularly well to algebraic arithmetic because the same process can be applied to polynomials. The image below shows the process for solving the problem 45 x 35 using the partial products method. The image also shows the same method being used to find the product of (3x + 1) and (4x + 3). Just as each part of the first product is multiplied by each part of the second product when using the partial products method in multiplying base ten numbers, the same is true for multiplying polynomials. In the example, each part of 3x +1 is multiplied by each part of 4x + 3. After finding the partial products of (3x + 1) and (4x + 3), students can combine like terms to find their resulting polynomial. This process helps students become prepared to apply the distributive property of multiplication through the use of the FOIL method without using the visual of the grid.
photo.JPG
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Group 3: Monfort, Myers, Norder-Pagan, Prasad, Ribolini
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RE: Group 3: Monfort, Myers, Norder-Pagan, Prasad, Ribolini
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July 14, 2014 4:27 PM
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As you are discussing a serious issue with a student and during the discussion the student moves in closer and closer until you feel uncomfortable?
My response to this situation would probably depend upon the issue being discussed and the nature by which the student moved closer. I have found that children all have different senses of personal space and that their comfort level with personal space can often change given a particular situation. Some students may move closer during serious discussions to hear the discussion better, or to eliminate that possibility of other individuals nearby overhearing the discussion. Other children may move away if they fear that they are getting in trouble. Usually, if I feel a student entering my personal space in a threatening, or non-threatening way, I adjust my own position by turning, shifting, or moving from a seated to standing position. Having something between you and the student (i.e. a table, a chair, or even a worksheet to gesture to) can often be helpful in maintaining personal space. Occasionally, I will discuss maintaining personal space with students when it is appropriate. With my middle school students we talk about high-fives vs. hugs, or we think about “personal space hula-hoops.” Although these ideas are not necessarily appropriate for high school, my point is that sometimes addressing personal space with students is appropriate, particularly for students who have difficulty with social situations/interactions.
You have lunch duty and notice a couple of middle school girls holding hands...other students are making fun of the hand holders?
My response here would probably depend upon how I came upon the other students making fun of the girls. If I happened to overhear the other students making comments, I would probably quickly and briefly redirect the commenting and remind the students that in school we always want to be speaking kindly of others. In correcting this behavior, however, I would want to make sure that I didn’t ultimately make the situation worse for the two girls. Sometimes, direct teacher interference is not always the best response. If the girls were not bothered by the situation and the “making-fun” was only a passing comment, I may not interfere at all. If the situation did not appear to be something that would continue, I may just monitor the situation from afar as to not draw additional attention to the girls. If the girls came to me upset, however, I would mediate the situation differently. I would probably have a conversation with the girls, hear their perspectives, and then have a conversation with the other students as well.
Did you know that ELL students often come from cultures that have different norms about interacting with other people?
Through experience and through course study I have learned that student from different cultures often interact with peers and adults differently. I learned that individuals from different cultures can have different tendencies with respect to eye contact, personal space, hygiene, speaking volume, etc. While some cultures maintain eye contact out of respect, other cultures look down or away to convey the same. Knowing our students and their cultural backgrounds has a great impact on how we view our students’ behaviors and in how we respond to them.
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Hi everyone
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July 13, 2014 11:31 PM
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I habe two certifications, one in math and one in French. I was placed in french last year.
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Terminology
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July 13, 2014 11:28 PM
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. I defined discrimination as "treating another individual unfairly, or having negative thoughts towards another individual because of the way they choose to live their life, or because of who they are." Your definition summarizes mine.
Nerlande
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July 13, 2014 11:25 PM
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I am in agreement with you; this activity was much more challenging than I had initially thought. The process of articulating all of the meanings and connotations associated with these words was very challenging. I thought of it purely in the sense of the other words that preceded it. The words stereotype, bigotry, and prejudice definitely framed my response for discrimination.
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Structural Factors
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July 13, 2014 11:20 PM
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I think that curriculum can pose a challenge to student learning when it is so structured that it cannot be modified to meet student needs. Often times, it is the teachers that know their students best. We know how they think, the concepts they understand, and the challenges that they face. Following a structured set of lesson templates will not always be the best way to meet these needs. I think that curriculum needs to be a balance of common standards and student driven decisions. In my opinion, the teachers need to be the mediators between where student needs meet curriculum standards. This however, places a great deal of trust and confidence in the teachers themselves.
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Structural Factors
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July 13, 2014 11:17 PM
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At times, curriculum can be an extremely frustrating point of conversation for me because I feel that so much of it out of teacher control. The lessons and material that we need to cover in our classrooms on a daily basis are frequently determined by administration, and to a much greater degree, state and national initiatives. I think that common curriculum and standards among states are important because they ensure that all students are taught and exposed to the same material; however, I also think that to some degree teachers need to be allowed some autonomy in the process of deciding what, when, and how curriculum is covered. In my eyes, the key is a balancing act.
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Boot Straps
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July 13, 2014 11:13 PM
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Hi Lisa,
I felt the same way as I was doing the activity such as how the answer makes a big difference in the step back and forward. I work in a high income are but about 95 percent of our students are bused to the school, they are not from the area, i have seen quite a lot going on with students. As educators we have a duty to know and understand our students in orede to fully reach out to them.
Nerlande
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July 13, 2014 11:06 PM
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Hi Kristen,
I so agree with you, as humans being, sometimes we look at our lives and think that we do have anything. If we take the time to look at our neighbor, we will be surprised to see how much we have in life.
Nerlande
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Early Memories
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July 13, 2014 11:00 PM
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Hi Carrie, I read a lot of early memories and we all have something in common. The classes were quiet. i am wondered back in the days, we did not have all these on different levels like we have nowdays, I am not talking about inclusion . I believe we al could agree on your table specially the NEED ORDER section.
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Early Memories
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July 13, 2014 10:50 PM
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Hi Meghan,
That open space where you played sports was similar to my school and I believe that was more effective than today's playground. I remember when I was growing up, we used to plan different sports every day. I also believed it was more structured than free play as we have today.
nerlande
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MultiCultural website
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July 13, 2014 3:33 PM
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According to Nieto and Bode (2008), multicultural education “accepts and affirms pluralism” while simultaneously rejecting “racism and other forms of discrimination” (p. 44). Therefore, a multicultural website is one that encourages and promotes the understanding of diversity while concurrently providing knowledge and strategies for combatting racism, segregation, prejudice, and other forms of oppression. When searching the Internet for multicultural resources, I was presented with an array of websites that provided information and services pertaining to deepening the understanding of diversity. While some websites were cluttered with information and advertisements, I found that others omitted particular subgroups, or focused only on particular aspects of diversity such as race and culture. I selected the website Teaching Tolerance (http://www.tolerance.org) for this particular assignment because of its ability to address all aspects of diversity in an organized and efficient manner. Furthermore, Teaching Tolerance provides teachers and other community members with differentiated resources that combat discrimination and promote pluralism for all subgroups.
As described in the “About Us” section of the Teaching Tolerance website, the project is, “dedicated to reducing prejudice, improving intergroup relations and supporting equitable school experiences for our nation's children” (Southern Poverty Law Center, n.d.). The website focuses upon encouraging tolerance, counteracting prejudice, and increasing diversity awareness within our nation’s schools for all individuals.
The Teaching Tolerance website stands out among other multicultural websites in that it provides an organized, well-structured, searchable database of information that addresses diversity in relation to race, gender, culture, class, economic status, language, sexual orientation, age, religion, and disability. A visitor to the website can enter a specific term in the search bar (i.e. sexual orientation) and be presented with a collection of articles, resources, and activities that address promoting understanding and equity with respect to the identified subgroup. While some provided articles represent recent studies and research findings, other resource materials include cross-curriculum lesson plans and toolkits for teachers. Handouts for parents are included among the provided resources. Furthermore, search results can be filtered with respect to additional criteria such as article type, grade level, anti-bias domain, and subject. Lesson plans and classroom resources are identified as aligning to specific grades and content areas (i.e. Grades 6-8, English and Language Arts). The searchable feature of this site makes it widely accessible to a variety of audiences and simplifies the process of finding information that is relevant to a specific audience or purpose. Many other multicultural websites focused upon providing direct services to schools such as workshops and seminars, or provided additional links to external websites with information pertaining to multiculturalism. Few websites offered the presentation of a diverse assortment of information on their own site that was presented in an organized, searchable manner. Additionally, the toolkits, lessons, and other resources from Teaching Tolerance have not cost to professionals in the educational community. Unlike some of the other websites that I found, the focus here is moved away from making a profit and towards promoting equity and multiculturalism within schools.
Under the portion of the site entitled “Magazine,” site visitors can access archived articles from past issues of the project’s bi-annually published periodical. Articles provide an array of information, activities and strategies that cover race, gender, culture, class, economic status, language, sexual orientation, age, religion, and disability. Within the Spring 2014 issue alone, articles address strategies for teaching students to value religious diversity, ways staff can understand the implications of social-emotional learning, and how teachers can discuss topics such as slavery and prejudice with students. Other articles from past issues discuss a multitude of topics: best practices for creating a LGBT school climate, the implications for highlighting gender when we speak to our students, and challenging language prejudices that can exist within the classroom. Some archived issues include feature stories pertaining to individuals with disabilities—a subgroup that was frequently omitted from other multicultural websites.
A relative specific weakness in the content of this website was its ability to address the understanding of diversity on a global scale. The concepts of race, gender, culture, class, economic status, language, sexual orientation, age, religion, and disability were all addressed within the content of the website, but the context under which they were examined pertained almost exclusively to circumstances and people within the United States. While some lessons and articles within the website addressed historical events and cultural movements across the globe; the predominate focus of this website was domestic diversity, as opposed to that which can be found worldwide. Nonetheless, since the focus of the website was upon promoting the understanding of diversity within our nation’s schools, I was not surprised to identify this as a relative specific weakness within the content of the website. Overall, I found that this website inclusively addressed the many aspects of diversity (i.e. race, culture, gender, disability, etc.) in an organized and accessible manner.
References
Nieto, S. & Bode, P. (2008). Affirming Diversity: The sociopolitical context of multicultural education (5th ed.). Boston, MA: Pearson Education, Inc.
Southern Poverty Law Center. (n.d.). Teaching tolerance, a project of the southern poverty law center. Retrieved from http://www.tolerance.org
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Structural Factors
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July 9, 2014 7:17 AM
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I felt an immediate connection to two of the structural factors discussed in this section.
Curriculum: At times, curriculum can be an extremely frustrating point of conversation for me because I feel that so much of it out of teacher control. The lessons and material that we need to cover in our classrooms on a daily basis are frequently determined by administration, and to a much greater degree, state and national initiatives. I think that common curriculum and standards among states are important because they ensure that all students are taught and exposed to the same material; however, I also think that to some degree teachers need to be allowed some autonomy in the process of deciding what, when, and how curriculum is covered. In my eyes, the key is a balancing act.
Perhaps I am in a unique situation because of my student population, but I frequently become frustrated with the curriculum that I “have to teach” because it is “on the test.” Many of my students are far below grade level in mathematics and several of them are still working on developing skills in addition, subtraction, and place value. The expectation for my classroom is that we cover the grade level curriculum while working on remedial skills. I must say that this is much easier said than done; particularly when many of my students need to focus on one skill at a time. Because our district uses a very structured and sequential mathematics program, much of the instruction in my classroom on a daily basis is based upon a curriculum over which I have very little control. Do I think that my students should never learn some of the topics that are challenging for them? Absolutely not. I do, however, think that changing the order in which some topics are taught would be extremely beneficial.
I think that curriculum can pose a challenge to student learning when it is so structured that it cannot be modified to meet student needs. Often times, it is the teachers that know their students best. We know how they think, the concepts they understand, and the challenges that they face. Following a structured set of lesson templates will not always be the best way to meet these needs. I think that curriculum needs to be a balance of common standards and student driven decisions. In my opinion, the teachers need to be the mediators between where student needs meet curriculum standards. This however, places a great deal of trust and confidence in the teachers themselves.
Pedagogy: When I think of pedagogy, I think of not only the methods a teacher uses in the classroom, but of the way he/she speaks and how he/she interacts with students. To me, pedagogy is the action of the classroom: the lessons, the activities, the discussions, and the instruction. The pedagogy of a classroom can have a profound impact on what and how students learn. In our classrooms, we are faced with a diverse group of learners with a multitude of experiences, strengths, and weaknesses. Everything we do in our classrooms as teachers needs to be informed by student learning. If students cannot access our lessons, they will have a more challenging time learning the presented content. In my classroom, I do my best to make the content accessible to all of the students I have before me. While most of the daily instruction takes place in structured small groups, I do my best to incorporate a variety of independent, partner, and whole class activities. Hands-on lessons are paired with structured investigations and sequential reviews. Although I personally am not a fan of worksheets, a few of my students respond well to them and thrive upon the predictability (one student even asks, “Are we going to do a worksheet today?” almost every day). The key here, as with curriculum, is knowing your students and knowing them well.
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Terminology
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July 9, 2014 7:08 AM
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When considering the presented terms, I think of the following:
- Prejudice: To me, prejudice is a thought, or belief that is not based on fact. Prejudice may be based on past experiences, or personal beliefs. Prejudice thoughts may be generalizations, or they may be completely false.
- Stereotype: A stereotype is a belief about a particular group of people that is untrue. While prejudice does not necessarily have to do with a particular group of people. Stereotypes typically pertain to groups of people with common characteristics (i.e. individuals from the same race, religion, or the same gender). A stereotype typically takes one common factor among a group of people and generalizes certain characteristics (positive or negative) as being true for all people within that group.
- Bigotry: Bigotry is the thought that one's own beliefs, or that characteristics of one's own life are superior to those of others.
- Discrimination: Discrimination is treating another individual unfairly, or having negative thoughts towards another individual because of they way they choose to live their life, or because of who they are.
-"ism": When I think of an "ism," I generally think of a philosophy, or a way of thinking. For some reason, the first thing that came to my mind was feudalism, which was the way land was organized and handled in Medieval Europe. In this case, feudalism was the beliefs of how land should have been handled. I also thought of the word racism, which is a way of thinking about people based on their race.
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July 9, 2014 7:01 AM
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In completing this activity, some of the questions surprised me. I was also surprised to see that some of my answers yielded “steps back” that I didn’t expect. After thinking about my responses more completely, I was able to understand how some of my responses may have been slight disadvantages (i.e. parents not having gone to college, or parents not being able to attend school events). However, I didn’t initially, and do not necessarily now, view those aspects of my life as being negative; these factors are part of who I am and who I always have been. I also found that some of the questions had to do with perception and that I could easily have answered some of the questions both ways.
What did you notice about how you felt about identifying or not identifying with a statement?
I felt guilty for identifying with some of the statements (those that resulted in a positive movement) because it made me think of individuals who may not be as lucky as me with respect to certain life situations. I also felt uneasy responding to some of the statements because I felt as though the response could easily have been impacted by perception (i.e. I could see other individuals from the same background as myself answering either way).
What does this/or might this activity teach us about real life?
I think that this activity teaches us that privilege is not black and white. There are many factors that can impact an individual’s life situation. Different circumstances impact how individuals are viewed by others and how individuals view themselves. Education and perception play a large role in perceiving privilege. I also think that this activity shows us that in our classrooms, we need to consider the backgrounds of our students, how our students may view themselves, how our students may view us, and how our students may be viewed by others.
What did you learn about your own life?
Overall, I came out a few steps ahead on the bar model. If asked both before and after this activity, I would say that I am an extremely fortunate individual. I did not necessarily view my “steps backwards” as challenges that I faced. Most of them were just part of my life that I didn’t think twice about.
What are the cumulative impacts of power and privilege? What are the cumulative impacts of oppression and exclusion?
I think that power and privilege as well as oppression and exclusion can mutually be impacted by uncontrollable circumstances (where you are born, and into what type of life situation) and perception (how you view yourself and others around you).
How can we use what we've learned from this activity in our teaching?
When teaching in our classrooms, we need to consider the diverse group of students we have before us. It is important to identify areas of bias within our classrooms and curriculum. We need to be aware of the challenges students face socially, economically, and academically.
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Early Memories
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July 9, 2014 6:30 AM
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Thinking back to my elementary years, I can vividly remember the school building and schoolyard. Specific memories are more piecemeal, but do provide an overarching theme of memorable events combined with important lessons learned. The pre-k through four school I attended was a relatively small elementary school in a suburban town. Each grade level had about four or five classrooms. The building was probably built in the 1950s, or 60s, but had been renovated and was clean and well kept. Student artwork or projects were in every hallway and student profiles of the “Stars of the Week” from each classroom hung on the glass windows that incased the main office. In general, all of the classrooms were well lit and sunny during at least one part of the day. The entire building had three floors. Pre-kindergarten through first grade were on the bottom floor, all offices and specialist classrooms were on the ground level floor along with the cafeteria and gymnasium, and grades two through four were on the top floor. The playground was a large wooden structure made of pressure-treated wood (something which scarcely exists now), tall metal slides, and strings of money bars. We typically had two recess periods—a morning recess during snack time, and a longer after lunch recess—during which I remember playing games on the structures, participating in rounds of Red Rover, and sitting inside oversized tires on cold winter days. All of the classrooms were cozy and well decorated with colorful bulletin boards and student work samples. All in all, I was very lucky to grow up in a school that was clean, well supported, and filled with caring school staff.
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SIX
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July 6, 2014 11:55 PM
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Hi Monique,
I think that the process of creating a multicultural classroom is continuous and fluid. The way we teach and what we teach needs to also be fluid. We need to consider the students we have in front of us at any given moment and consider what content and social education will be suit their needs. Within a multicultural classroom, I think that we need to address the whole child as opposed to only the curriculum standards. Considering your bullets pertaining to multicultural education for all students and multicultural education as a process, I think that we could summarize the pedagogy associated with teaching in a multicultural classroom as one associated with observation, reflection and action to ensure that all students have access to curriculum content and receive enriching educational experiences.
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July 6, 2014 11:54 PM
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Lisa,
I think that your bullets hit upon many of the key points contained within our text. Reading through your clarifying bullets, I think that a predominant focus in a multicultural mathematics classroom would be emphasis on who our students are and the backgrounds from which they come. In order to provide all of our students a balanced, unbiased education, we need to understand their view points and perspectives. We must also teach our students to learn and accept the perspectives of others. We need to expose them to cultures and views beyond those that they have already experienced. Since our students will be continuously changing and since one can never truly know all there is to know about other.
Nerlande
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July 6, 2014 11:44 PM
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Hi Alyssa,
I also believe that the strengths of this classroom would be vested in its senses of mutual respect and responsibility. Teachers and students would understand and respect that all members of the classroom community have strengths and weaknesses and that all members have valuable perspectives to offer in classroom discussions and investigations. The classroom would provide a safe learning environment for students and teachers to learn from and about one another. Students would be engaged in lessons that were both valuable for future learning and interesting through connections to their everyday lives. Combinations of group work, individual assignments, investigations, and direct instruction would help to support all types of learners. Information would be presented through multiple means of representation, and students would be able to display understanding through multiple means of expression.
Nerlande
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VENN
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July 6, 2014 11:39 PM
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Hi Lisa,
I agree with you on that idea of considering an effective math class. I believe these students need us as educators to help them achieve to the best of their knowledge. Also,teachers should instruct students on a variety of viewpoints as well as teach skills in confronting racism and discrimination.
Nerlande
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NAMES!
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July 6, 2014 10:36 PM
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Hi Stacy,
Your names have a deep root. I like how your parents used tehir imagination to the fullest. It is surprising to know tha you have haitian Creole in your area. I always thought they were in the most common states. To have quite a lot like that is surprising.
Nerlande
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NAMES!
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July 6, 2014 10:29 PM
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Hi Dacey,
Your story was fascinated. I actually named my daughter a meaningful name which is means Victory since most people did not think I was going to be able to have kids. Looking at your post, your school is very small. I love the diversity of your school with thirty languages.
Multicultural education is antiracist education
- Education must be consciously antiracist and all individuals must be mindful of favoritism in all contexts.
- Teachers should instruct students on a variety of viewpoints as well as teach skills in confronting racism and discrimination.
- Working for social justice is everyone’s responsibility and should not fall solely on individuals impacted by discriminating perspectives.
This section discussed the importance of explicitly identifying favoritism and discrimination, discussing such issues with students, and instilling a sense of social responsibility in our students. After reading this section, I felt a strong connection to past articles I have read on character education.
Multicultural education is basic education
- Multicultural education must be considered part of an “excellent education” and cannot be external to the core curriculum.
- Teaching commonalities in history and culture, as well as multiple viewpoints, promotes multicultural literacy.
- Questions pertaining to the equity and access of a high-quality education promote multicultural literacy. This will, in turn, encourage understanding and empathy among students.
This section discussed a change in mindset that must occur with respect to multiculturalism. The author discussed how multicultural education must be viewed as a vital part of the daily curriculum and must not be viewed as an "add-on" or occasional addition to lessons, or units.
Multicultural education is important for all students
- All students are miseducated when the education they are presented with is biased, or partial.
- Cultural blindness becomes validated by partial, or biased education.
- Multicultural education is about all people and is created for all people.
This section discussed why and how multicultural education is important for all individuals. Particularly, the author argued that students from less diverse communities may actually benefit more from multicultural education so that they can identify their mainstream culture as a culture of its own as opposed to "the norm."
Multicultural education is education for social justice
- Multicultural education must connect theoretical ideas with reflection and practice.
- Students must be prepared to serve as active members of a community. They must be taught to address problems of inequality and injustice.
- Students and teachers benefit from explicit conversations concerning power and inequality. Discussions should connect to real world examples.
Teaching students not only to identify injustice, but how to act in response to inequality is a vital component to multicultural education. Providing students with specific real world examples that directly connect to their lives will be most effective.
Multicultural education is a process
- Knowledge of other cultures and perspectives is never complete.
- Multicultural education involves relationships between people.
- One can never stop being a multicultural person.
This section discussed that multicultural education is never complete. The process of learning is continuous and we must teach our students to understand that there are always new perspectives to learn and new viewpoints to be considered.
Multicultural education is critical pedagogy
- Changes in the views and ideologies of the decision maker will change what and how content/lessons are taught.
- Multicultural education should encourage students to take risks, be curious, and question.
- Multicultural education should acknowledge and not suppress diversity.
This section discussed teaching practices and actions to instill within our students. As teachers, we must think critically, ask questions, and reflect on our actions in order to instill these qualities in our students.
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VENN
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July 2, 2014 10:54 PM
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Multicultural Reflective Professional Practice
In the Venn diagram, the component that each area has is:
a) The context which represents a learning environment/situation/place such as classroom.
b) The subject indicated the learning area such as Mathematics of Physics.
c) The teacher indicates the source of instructions and guidelines.
d) Finally, the student indicates the receiver of instructions.
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Context |
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Teacher |
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Student |
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Subject |
The intersection between the subject circle and student circle is the relationship that exists between students and subjects. It is how students view particular subjects and how well they “get along” with them. Some students usually perform better in certain subjects than others.
Subject
Responsiveness
A culturally responsive teaching involves the cultural knowledge of students. This is to facilitate the teaching process and effectively help students. In Mathematics, ethno mathematics forms this culturally responsive teaching. It entails studying mathematics while considering and integrating cultures where mathematics arise (Gay 48). Teachers have to know and approach mathematics teaching from a framework that is culturally responsive. The teachers should be able to demonstrate both education and developmental concepts to their mathematics students. They should also engage as well as model the concepts for teaching mathematics.
The components to include are a designed and culturally responsive curriculum, good learning environment and ready teachers and students (Gay 67). For example, teachers should be open to the divergent approaches adopted by students while thinking or solving problems. They should also be open to activism, advocacy and critical consciousness.
The strength with this teaching is that it is an interactive kind of training, unlike the conventional ones. Teachers and students learn from each other.
