ECE 354 Assessment & Intervention During Early Childhood / week 5 discussion 1 and 2, Final projects

What is Special Education? 1

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Pre-Test

1. 1. You can use the terms disability and handicap interchangeably. T/F 2. 2. The history of special education began in Europe. T/F 3. 3. The first American legislation that protected students with disabilities was passed in the 1950s.

T/F 4. 4. All students with disabilities should be educated in special education classrooms. T/F 5. 5. Special education law is constantly reinterpreted. T/F

6. Answers can be found at the end of the chapter.

11 Schooling and Cognition

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Learning Objectives By the end of this chapter, you should be able to:

• Relate how the experience of schooling impacts cognitive development.

• Evaluate strategies for facilitating emergent literacy skills and teaching children how to read.

• Describe the causes of learning disabilities associated with reading, such as dyslexia.

• Summarize how children learn math.

• Relate the process of memory to mathematical learning disability.

• Examine the effects of intervention programs such as Head Start on academic outcomes for at-risk children.

• Describe the challenges dual language learners face and different methods for teaching them.

Pretest Questions

Pretest Questions

1. Two children are only a few weeks apart in age, but one is old enough to make the cutoff for school, whereas the slightly younger child misses the cutoff and starts school a year later. Because the children are almost identical in age and maturation, their cognitive development in areas like memory will be about the same at the end of the school year. T/F

2. The process of learning to read begins before children enter kindergarten or first grade. T/F

3. Reading is similar to language development in that children acquire both easily and naturally. T/F

4. Dyslexia is primarily a problem of reversing letters during reading. T/F 5. Children who are behind in math achievement when they start school tend to stay

behind in math achievement. T/F 6. Children who participate in Head Start preschools show beneficial cognitive effects that

last throughout school. T/F

Early in the school year, a new student, Vanessa, arrives in the United States from Colombia and is placed in Ms. Henderson’s kindergarten classroom. Vanessa is quite bright and speaks only a little English. Henderson is concerned about her ability to teach Vanessa the skills and concepts needed to prepare her for first grade due to Vanessa’s limited English. The district in which Henderson teaches has only a few students who are English language learners or dual language learners. The district’s policy for educating bilingual children is to place them in an immersion program, where they are completely taught in English. However, Vanessa struggles with many of the academic concepts she is taught because of her limited English.

The teacher talks to Vanessa’s family and discovers she has an older cousin who speaks both English and Spanish. Henderson knows that having a tutor and teaching children in both lan- guages is another educational approach for dual language learners. These are referred to as dual language programs and are designed to ease the transition to English. The cousin agrees to work with Vanessa at home on English and some of the literacy concepts. She also agrees to work as a volunteer one day a week in Vanessa’s classroom.

There are several noteworthy aspects of Henderson’s strategy. First, she involved the family in Vanessa’s education. Although this is important for all children, it is particularly critical for dual language learners in order to obtain a better understanding of their environment and prior educational and language experience. Second, Henderson recognized that there are multiple ways to educate dual language learners. Although she could not change district policy, she was flexible in her approach to helping Vanessa.

Questions to Think About

1. What are the advantages and disadvantages of Henderson’s approach? 2. If you were in Henderson’s shoes, what else would you do to help Vanessa? Explain

your answer. 3. Using your knowledge from the language development chapter, what does our

understanding of children’s language skills suggest about bilingual education?

Introduction

Introduction Formal schooling dates to ancient times. More than 4,000 years ago, boys in ancient Mesopo- tamia received lessons in literacy and numeracy. Then, as today, the classroom was aligned so that rows of desks faced the teacher, who guided the children in their lessons (Cole, 2005). Perceptions of the purpose of school are also similar. As it is today, schooling in ancient Meso- potamia was viewed as leading to a social and occupational status otherwise unavailable to a person (Cole, 2005).

The focus on reading and math even in ancient times suggests the key role these subjects play in education. Today new insights into the cognitive processes that underlie reading and math knowledge have the potential to inform best practices for educating children. The aim of research is to better understand how children process information like sounds, letters, and magnitudes, and then translate this knowledge into instruction.

The very experience of school can impact cognitive development, as we see in the case study at the outset of this chapter. Unfortunately, sometimes children are not fully ready for school, and we will read about intervention efforts such as Head Start.

Our goal in this chapter is to depict cognitive development and learning in the context of schooling. In various parts of the chapter, social-constructivist theory draws our attention to the roles guidance and teaching play in development and learning. Information-processing theory plays a notable role in current cognitive development research about education. Con- sequently, the theory will be discussed throughout the chapter, particularly as we investigate the processes involved in developing reading and math skills.

Core Themes, Schooling, and Cognition Nature and nurture. Our consideration of schooling in this chapter naturally emphasizes the effects of the environment on children’s cognitive development and learning. The impact of the environment extends from schools to homes as we consider how factors prior to school- ing—such as those associated with poverty—impact school readiness. Nature, of course, interacts with the environment. For example, this is evident in our discussion of neurological correlates of reading difficulties.

Continuity and discontinuity. A predominant question in research on schooling and cognition asks what factors prepare a child for success in school. For instance, we will see how individ- ual differences in early phonological skills are linked to later reading ability. This focus on fac- tors that predict later school success emphasizes continuity in development. We will also see continuity as we examine how early school achievement relates to later school performance. To illustrate, we note in the section on math and schooling how mastery of fractions predicts later school achievement for adolescents.

Performance and competence. The nature of this chapter also means that the performance– competence theme comes into play a bit differently than in many of our previous chapters. Throughout the text, we have addressed the theoretical challenge of precisely defining a competence (for example, the question of what counts as object permanence mastery that was posed in Chapter 2) and then developing a measurement that minimizes performance demands.

Section 11.1Schooling’s Impact on Cognitive Development

In this chapter the relationship between performance and competence is much closer than we typically encounter, sometimes to the point that performance and competence are diffi- cult to distinguish. Competency in math or reading is very often defined by performance on a standardized task. Competency and performance are, in this sense, the same. Consequently, the performance–competence theme is not one that features very prominently in this chapter.

Domain general and domain specific. Finally, we will see evidence in this chapter of domain- general processes impacting school performance. As we have seen elsewhere, the EFs are an example of a domain-general process that impacts learning in school. We will also encounter domain-specific processes in this chapter; for instance, we will see how two domain-specific skills bear different relationships to children’s reading ability.

11.1 Schooling’s Impact on Cognitive Development Evidence from the past 70 years indicates that schooling impacts cognitive processes like working memory, planning, decision making, and the organization and categorization of information (Baker, Salinas, & Eslinger, 2012). Thus, in addition to impacting the acquisition of specific content (such as factual information found on IQ tests, as discussed in Chapter 10), schooling also impacts domain-general cognitive processes. Processes like planning and deci- sion making are, of course, called on throughout our lives; consequently, effective schooling not only transmits information but also influences the way one processes information.

For instance, in a categorization task like those discussed in Chapter 5, adults in Mexico were given three items and asked to classify which two were the “same in their meaning” (Sharp, Cole, & Lave, 1979, p. 29). One group of adults had attended high school, whereas another group had received only minimal education. When given items such as horse, eggs, and chicken, the educated adults used the abstract category animal to classify horse and chicken as the same. In contrast, the group with minimal education clas- sified the same items functionally by bringing together chicken and eggs because chickens lay eggs.

Both groups knew the meanings of the words in the problem. Their dif-

ferent categories, therefore, did not reflect differences in their content knowledge. Instead, schooling impacted the way the educated adults thought about and solved the problem. They capably detected and used abstract categories to organize the concepts. Such findings do not mean that unschooled adults cannot think abstractly. Rather, schooling familiarizes individu- als with certain cognitive approaches to problems. These approaches, like using abstraction

Monkeybusinessimages/iStock/Thinkstock The experience of schooling positively impacts children’s cognitive development in broad areas like planning, decision making, and memory.

Section 11.1Schooling’s Impact on Cognitive Development

to classify objects, are readily manifested when educated individuals encounter school-like tasks such as the categorization task just discussed (Cole, 2005).

Attending school also fosters the development of cognitive skills and strategies. For instance, consider what happens when two groups of children are nearly identical in age, but one group just makes the cutoff for school entry and the other group waits a year for entry. The children who had experienced first-grade schooling were more skilled at memory than kindergarten- ers who were on average just a month younger (Morrison, Smith, & Dow-Ehrensberger, 1995). The educational experiences of first grade improved memory performance even though, chronologically, the two groups of children were nearly identical.

Follow-up research using the age cutoff to measure the effect of preschool and kindergarten similarly finds that schooling improves young children’s executive functioning (Burrage et al., 2008). With respect to our nature–nurture theme, we see the influence of nurture (schooling experience) on producing differences in cognitive development even when maturational dif- ferences were presumably minimal because of the closeness in age between the groups.

One way the experience of schooling promotes memory development is found in the approach teachers use when they instruct children. Teachers prompt children to remember informa- tion (such as, “Who knows the names of the cities we talked about yesterday?”) and to use strategies (“If you are having trouble remembering, go back and look at the picture”) dur- ing the course of the day (Grammer, Coffman, & Ornstein, 2013). The frequency of teachers’ memory prompts and discussion of memory strategies has been linked to better memory per- formance and strategy use among first graders (Coffman, Ornstein, McCall, & Curran, 2008).

Effective Classrooms Overall, experiences in classrooms vary in their impact on academic achievement. The list that follows describes four general features of classroom environments that are positively associated with student achievement for children and adolescents:

1. The environment is inclusive, with every child valued. Teacher interactions with each child demonstrate respect. The teacher encourages respectful interactions among all peers and proactively handles disrespectful interactions.

2. The environment is orderly, predictable, and safe as procedures are effectively estab- lished. Transitions during the day are effectively handled to minimize disruption and maximize time for instruction.

3. Student behavior is closely monitored to ensure each child remains on task, whether working independently or in small groups. Misbehavior is handled effectively and consistently.

4. Instruction is characterized by providing quality feedback that expands children’s comprehension of a topic and by engaging students in higher order cognitive skills such as analysis and problem solving (Allen et al., 2013; Kane, Taylor, Tyler, & Woo- ten, 2011).

These classroom features correspond to material discussed earlier in the text. How might a safe, inclusive, respectful climate promote learning in the classroom? Evidence indicates that a positive emotional climate in the classroom promotes children’s interest and effort in school (Reyes, Brackett, Rivers, White, & Salovey, 2012). Interest and effort are, of course, signs of

Section 11.2Learning to Read

motivation. Recall in Chapter 10 that we discussed links between low motivation and poor test performance both in the classroom and on standardized intelligence tests. We also saw in Chapter 10 how anxieties related to stereotypes can compromise cognitive performance. Presumably a respectful climate is one that reduces such anxieties.

More generally, features #1 and #2 in the previous list remind us of the importance of reduc- ing stress in the classroom. Over time, stress-inducing environments can adversely impact cognitive development (Blair, 2010).

Chapter 3 emphasized the relationship between the EFs and academic performance. Children’s instructional needs are directly met by minimizing disruptions and distractions that tax executive functioning and interfere with time devoted to teaching (see #2 in the previous list). Given the limitations of young children’s EFs, we can also appreciate the value of a directive, nonpassive approach to keeping children on task (#3).

Finally, classrooms are most effective when teachers engage students and provide feedback rather than spend their time handling multiple disruptions (#3 and #4). The importance of feedback was featured in our discussion of children’s developing problem-solving skills in Chapter 8. Feedback is also a form of scaffolding in which the teacher helps the student reach a correct solution to a problem the child could not solve indepen- dently (Chapter 7).

11.2 Learning to Read Reading is a remarkable skill. It allows us to form a permanent record of our thoughts and the thoughts of others, to explore imaginary worlds, and to acquire a vast amount of information. Learning to read lays the foundation not only for children’s academic success, but also for life success in most circumstances. Although formal instruction in reading typically begins in kindergarten or first grade, the reading process actually begins much earlier. In this section, we examine emergent literacy, instructional practices for teaching reading, reading problems, and learning disabilities such as dyslexia.

Emergent Literacy Reading is a complex cognitive ability that requires the coordination of many cognitive and perceptual skills described in the previous chapters. Table 11.1 provides an overview of four stages of reading development (as first detailed by Chall, 1996).

Questions to Consider

1. We saw how teacher prompts and ques- tions promote memory development. How could prompts and questions pro- mote other domain-general features of cognition, such as inhibition and language?

2. What are some obstacles a teacher might face in providing the effective classroom features listed in this sec- tion? What evidence provided in this section, or elsewhere in the text, might be useful in devising solutions to those obstacles?

Section 11.2Learning to Read

Table 11.1: Stages of reading development

Stage Age Skill

0. Prereading 3 years to kindergarten Letter discrimination; recogni- tion of some words

1. First year of instruction Kindergarten or first grade Phonological recoding skills; learn letter–sound correspondence

2. Reading fluently Second to third grade Learn to read fluently; compre- hension is generally limited

3. Reading to learn Fourth to eighth grade Comprehend the material that is read

As the table describes, the process of learning to read—stage 0—begins before a child can even sound out a letter on a page. However, this description of the prereading stage does not capture the richness of the many reading-related skills that develop prior to actual reading. Emergent literacy refers to those skills, knowledge, and attitudes that are precursors to con- ventional forms of reading and writing, as well as the environments and activities that sup- port these developments (Whitehurst & Lonigan, 1998). The emergent literacy framework views the development of literacy and reading as a continuum (Whitehurst & Lonigan, 1998). It replaced the “reading readiness” approach, which viewed prereading and formal reading as more distinct abilities.

The National Institute of Child Health and Human Development Early Child Care Research Network and the National Center for Family Literacy (2008) emphasize the importance of emergent literacy reading and writing achievement in their policy statements. Numerous studies support the predictive relationship of emergent literacy to later reading achievement (Cabell, Justice, Konold, & McGinty, 2011; Wagner & Torgesen, 1987).

Emergent literacy consists of two broad skill domains shown in Table 11.2: oral language skills and code-related skills (Whitehurst & Lonigan, 1998). Oral language skills include the production and comprehension (understanding) of the structure of language through narratives, syntax, and the meaning of language through vocabulary. Code-related skills help children understand the alphabetic nature of language. They include skills such as print con- cepts, knowledge of alphabets, phonological awareness, and writing. Although these two domains are separate, they are related and show different relationships to later reading abili- ties (Hipfner-Boucher et al., 2014; Lonigan, Burgess, & Anthony, 2000; Storch & Whitehurst, 2002). We will review some of these skills in more detail below.

Section 11.2Learning to Read

Table 11.2: Components of emergent literacy

Component Definition

Oral language skills

Language Semantic, syntactic, and conceptual knowledge

Narrative Comprehending and producing narrative or stories

Print conventions Right-to-left reading, or left-to-right reading, recognizing common words, such as McDonald’s

Emergent reading Pretending to read

Code-related skills

Graphemic knowledge Letter-name knowledge

Phonological awareness Rhyme, manipulation of syllables and phonemes

Syntactic awareness Correcting grammatical errors of self and others

Phoneme–grapheme relationship Letter–sound correspondence

Emergent writing Invented spelling (attempting to spell)

Other factors

Phonological memory Short-term memory for phonologically coded information

Rapid naming Rapidly naming sequences of colors, letters

Print motivation Interest in shared print-book reading

Source: Adapted from Whitehurst, G. J., & Lonigan, C. J. (1998). Child development and emergent literacy. Child Development, 69, 848–872.

Oral Language Oral language abilities involve communicating effectively with others and first emerge around age 2 to 3 years (Roskos, Tabors, & Lenhart, 2004). Two of the more crucial oral language skills are creating narratives and establishing a vocabulary. Constructing narratives or stories ulti- mately contributes to understanding written text (Kendeou, Van den Broek, White & Lynch, 2009; O’Neill, Pearce, & Pick, 2004). The comprehension of both narratives and text “requires referential statements (that is, memory for the story or what happened), contextual informa- tion (orientation statements, such as when, where and who) and evaluative statements (why something happened or a character’s internal states or reactions)” (Reese, Suggate, Long, & Schaughency, 2010, p. 381). Semantics, or vocabulary development, (reviewed in Chapter 9) also contributes to reading achievement, particularly comprehension (Bradfield et al., 2014). In order to understand a text they are reading, children need a good vocabulary.

Children differ in their oral language skills. These idiographic differences partially relate to different parental and educational practices (Wood, 2002). Many children are at risk for not

Section 11.2Learning to Read

learning how to read because their environments do not provide emergent literacy activities, such as joint book reading, exposure to oral narratives, or stories. Thus, children may enter kindergarten with very little experience with books and emergent literacy skills. They may not be familiar with letters or print concepts, such as reading from left to right.

Teachers and parents can facilitate children’s narrative construction and vocabulary by read- ing stories, engaging in pretend or fantasy play, and discussing previous events. One of the most effective parent-child activities in promoting early literacy is joint book reading, which occurs when children and adults read a book together. Joint book reading contributes to chil- dren’s oral language skills, such as narrative construction and vocabulary (Mol & Bus, 2011; Sénéchal, LeFevre, Thomas, & Daley, 1998; Skwarchuk, Sowinski, & LeFevere, 2014). This strategy is similar to social-constructivist approaches to cognitive development described in Chapter 7.

Dialogic reading is a specific type of joint book reading intervention designed to foster chil- dren’s meaningful interaction with a text by asking questions about the story (Whitehurst & Lonigan, 1998). This includes asking “wh-” questions (who, what, when, where, and why), using open-ended questions, expanding on what the child says, and encouraging and praising children’s participation (Lever & Sénéchal, 2011). It is quite similar to the elaborative nar- rative style of memory talk described in Chapter 4 for facilitating autobiographical memory.

Numerous studies demonstrate that emergent literacy skills correlate with later reading skills, such as comprehension, in both the short and long term. Intervention studies that teach parents or teachers how to engage in dialogic reading boost children’s narrative skills (Lever & Sénéchal, 2011; Reese, Sparks, & Leyva, 2010). Dialogic reading also enhances vocabulary development in bilingual preschoolers who have language delays (Tsybina & Eriks-Brophy, 2010). Figure 11.1 illustrates dialogic strategies used in a picture book reading context to boost vocabulary in 3-year-olds.

In one intervention study focused on vocabulary, kindergarten children from low-income families (who were at risk for both language and reading delays) were randomly assigned to either a dialogic reading group or an alternative intervention group. In the dialogic reading group, small groups of children were read a story using the questions and responses charac- teristic of dialogical reading. The alternative treatment group was provided training in pho- nemic awareness. Each intervention type consisted of two 20-minute sessions per week for 8 weeks (Lever & Sénéchal, 2011).

The dialogic group improved on narrative assessments involving both structure and content compared to the other intervention group. Asking questions and other engagement strategies increased children’s ability to both produce fictional narratives and to comprehend story nar- ratives. The dialogic group also gained more expressive vocabulary compared to the control group (Lever & Sénéchal, 2011). Other nondialogical intervention programs target different emergent literacy skills, such as print concepts (Lonigan, Purpura, Wilson, Walker, & Clancy- Menchetti, 2013). Generally speaking, all intervention studies help improve those skills that are specifically targeted (Reese, Sparks, & Leyva, 2010).

Section 11.2Learning to Read

Figure 11.1: Dialogic reading strategies for children

These are strategies parents could use to boost vocabulary in a dialogic reading. Notice how the parent attempts to elicit the child’s response to questions.

Establish Joint Attention “Look” + Point at a picture

Wh–question Prompt: “What’s this?”

Pause Wait for child to respond

Child does not respond

Child responds e.g., “Cat!”

Praise “Good job!”

Recast “Yes, a big cat!”

Model “A cat!”

“What’s this, again?” Establish new joint attention referent

Source: Tsybina, I., & Eriks-Brophy, A. (2010). Bilingual dialogic book-reading intervention for preschoolers with slow expressive vocabulary development. Journal of Communication Disorders, 43(6), 538–556. Reprinted with permission from Elsevier.

Code-Related Skills Code-related skills contribute to analyzing the relationship between sounds and letters (Cabell, Justice, Logan, & Konold, 2013). Table 11.2 listed several code-related skills. Phono- logical awareness is the ability to recognize and manipulate the sound segments of language (Skibbe, Behnke, & Justice, 2004). We focus on its development in this section because it has been the most extensively studied and is strongly related to reading. Phonological aware- ness develops during the preschool years and includes phoneme and syllable deletion, as well as rhyming (Anthony & Francis, 2005; Goswami & East, 2000). Phonological awareness measures range along a continuum of complexity, beginning with rhyming, progressing to segmenting and blending syllables, and ending with segmenting and blending phonemes.

Section 11.2Learning to Read

Performance on these tasks is related to reading skill. As described in Chapter 9, phonemes are the smallest unit of sounds, which are combined to produce words.

We consider two measures of phonological awareness that reflect the segmentation (elision) and blending of syllables and phonemes. In an elision task, children repeat a part of a spoken word by deleting a unit of sound. For instance, in a syllable elision task, children are asked to “say ‘baseball’ but don’t say ‘base.’” The correct response is “ball.” In a phoneme deletion task—which is more difficult because it is a smaller unit—children are told to “say ‘table’ but don’t say ‘ta.’” The correct response is “ble” (Tyler, Osterhouse, Wickham, Mcnutt, & Shao, 2014). The ability to manipulate sounds (phonemes, syllables) indicates recognition of the speech units that make up words and contributes to reading.

The blending task requires a child to combine different sounds to make a word. It can include the formation of compound nouns by combining words, such as “foot” + “ball”, combining syl- lables, such as tel+e+phone, or individual phonemes, such as b + i + r + d. For both the elision and blending tasks, as the unit becomes smaller (that is, moves from syllable to phoneme), the task becomes more difficult. Typically, it is not until kindergarten or first grade that chil- dren are able to manipulate phonemes in this intentional or conscious manner (Lieberman, Shankweiler, Fischer, & Carter, 1974). In spontaneous speech, children blend sounds even as infants and toddlers, but this is not done consciously.

Emergent Literacy and Reading As listed in Table 11.2, a number of different skills make up emergent literacy. We have cov- ered representative examples of both oral language and code-related skills that have been identified as particularly important to reading success. It needs to be noted, however, that the other skills contribute to reading success (Brunswick, Martin, & Rippon, 2012). For instance, cognitive achievements, such as phonological memory and visuospatial skills, are associated with reading (Brunswick et al., 2012).

The National Literacy Panel reviewed all evidence from studies of emergent literacy and its predictive relationship with conventional literacy skills (that is, code-related skills, fluency, text comprehension, writing and spelling) in kindergarteners and first graders. Six factors of emergent literacy were particularly important in predicting later literacy measures:

1. alphabet knowledge (AK): knowledge of the names and sounds associated with printed letters

2. phonological awareness (PA): the ability to detect, manipulate, or analyze the audi- tory aspects of spoken language (including the ability to distinguish or segment words, syllables, or phonemes), independent of meaning.

3. rapid automatic naming (RAN) of letters or digits: the ability to rapidly name a sequence of random letters or digits.

4. RAN of objects or colors: the ability to rapidly name a sequence of repeating random sets of pictures of objects (e.g., “car,” “tree,” “house,” “man”) or colors.

5. writing or writing name: the ability to write letters in isolation on request or to write one’s own name.

6. phonological memory: the ability to remember spoken information for a short period of time. (Lonigan & Shanahan, 2008, p. 3)

Section 11.2Learning to Read

Thus, learning to read begins before kindergarten and consists of both specific emergent lit- eracy skills and more general language and cognitive processes. As we review in the next section, a variety of instructional strategies for teaching children to read in kindergarten and first grade have been used.

Teaching Children to Read Do you remember how you learned to read? Becoming a successful reader requires at least two fundamental skills—reading or recognizing the words and extracting meaning from text. In this section, we consider different approaches to formally teaching children to read: the phonics method and whole-language method. The process of teaching children to read has generated heated political debate and even reached the halls of Congress. Parents, educators, and politicians often have strong feelings about this topic (Chall, 1996; Tunmer, 2014). This debate is partly attributed to the lack of studies conducted in a scientifically sound manner (McGuinness, 2004).

In the phonics method, children are taught to decode words by learning the letter-to-sound regularities of written language (McGeown & Medford, 2014). To read fluently requires know- ing sound–letter correspondences (the sound that goes with each letter) and knowing how to blend the sounds together to make a word, similar to the blending task described earlier. This strategy is particularly useful when unfamiliar words are encountered.

The phonic approach reflects both bottom-up and top-down processes, which is character- istic of the information-processing perspective. Bottom-up processes involve the lower level skills of coding words into their sounds, which involves phonemic awareness and sound–let- ter correspondence, to word recognition, which leads to the determination of meaning. Top- down processes are involved in identifying meaning by considering the overall context in which a word appears (Faust & Kandelshine-Waldman, 2011). Thus, reading involves interac- tions between these two processes.

The whole-language method focuses on recognizing whole words and determining the mean- ing of words and text (Foorman, 1995). It emphasizes the entire reading experience and the reading strategies that can be used to abstract meaning from text. The whole-language approach adopts a top-down, constructivist perspective in which children construct meaning from the text (Meyer & Manning, 2007). This approach emphasizes reading engaging stories from the very beginning of learning to read. There is less emphasis on phonics and phono- logical awareness, which is believed to be automatically acquired via the process of learning to read.

Many advocates of the whole-language approach characterize the phonics approach as a bor- ing, repetitive drill conducted via worksheets that fail to engage children in the enjoyment of reading. Furthermore, the basic alphabetic nature of written English is too irregular to guar- antee reading success. That is, there is not a straightforward relationship between letters and sounds because of the many exceptions (Strauss & Altwerger, 2007). In contrast, the phonics approach argues that the whole-language approach ignores the importance of phonological awareness to reading and does not have strong scientific support for its view (see Meyer & Manning, 2007).

Section 11.2Learning to Read

Although both approaches incorporate some elements of the other, there is clear evidence that instruction in code-related skills, such as phonological awareness, improves reading (Carson, Gillon, & Boustead, 2013). It allows children to identify novel words by breaking down the letters into sounds and then blending them together. As children become more flu- ent readers, they do not need to break down words into phonemes, which would be a labor- intensive exercise; instead, they can recognize words by sight.

Reading skills in first grade have been linked to long-term reading and academic success. A longitudinal study of 54 children assessed first-grade reading skills (reading, vocabulary, lis- tening comprehension, and spelling), along with IQ. Their reading skill level, including their vocabulary and comprehension skill, was reassessed when the children were in 5th grade and then again in 10th (Sparks, Patton, & Murdoch, 2014). Early reading skill in childhood was found to be related to their 5th- and 10th-grade reading level and knowledge. This rela- tionship held even when the effects on intelligence (IQ) were controlled. This indicates that these relationships were not due to intellectual differences between the children, but rather to early reading differences (Sparks et al., 2014). Other longitudinal studies have also demon- strated the long-term effects of early reading skill on later reading and academic achievement (Wagner & Torgesen, 1987).

Early literacy and reading ability are linked not only to later reading skills, but to the acqui- sition of knowledge (Duncan et al., 2007). This makes perfect sense. Initially, children are learning to read through third grade, but by fourth grade, they should be reading to learn (Chall, 1996). Thus, good readers are more likely to be academically successful than poor readers because they can use reading to further their understanding of academic concepts. This achievement gap between good and poor readers may become magnified with develop- ment, although it is not always found (Pfost, Hattie, Dörfler, & Artelt, 2014). The general link between reading, knowledge, and academic achievement is well established.

Reading Difficulties and Dyslexia Chapter 9 described how children are universally successful at acquiring their first lan- guage, unless there is extraordinary deprivation or neurological difficulty. Unfortunately, the same cannot be said about becoming a successful reader. According to the National Center for Learning Disabilities and the Association for Supervision and Curriculum Development, reading is not a natural process that spontaneously emerges, but rather needs to be taught (http://ascd.org).

Many children struggle to learn to read. Longitudinal surveys indicate that about 20 percent of U.S. children have some type of reading disability. In representative assessments of reading proficiency, 10 percent of fourth graders were classified as having severe reading difficul- ties, and 37 percent did not reach basic reading proficiency (see Lonigan & Shanahan, 2008). Children from all backgrounds can have reading problems, although their risk increases for children of low socioeconomic status, racial minorities, and nonnative speakers of English (Lombardino, 2012; Lonigan & Shanahan, 2008).

Section 11.2Learning to Read

Most children with a learning disabil- ity also have reading disabilities (Lom- bardino, 2012; Lyon, 1999). Children who primarily have a reading disabil- ity show different profiles of strengths and weaknesses (Kim & Lombardino, 2013). The causes of reading difficul- ties can vary depending on the type. Reading difficulties can be attributed to both environmental and biological causes. As discussed previously, many children enter kindergarten with few emergent literacy skills because of their environmental circumstances, in which parents are less likely to provide children with the experiences needed to develop those skills (Korat, Klein, & Segal-Drori, 2007). Intervention strat-

egies, such as dialogic joint book reading and phonological awareness training, can help com- pensate for the absence of these early experiences (Lever & Sénéchal, 2011).

There are also biological risk factors for reading impairments. Dyslexia is a learning dis- ability that has a clear biological basis and affects about 10% of children in the United States (Lombardino, 2012; Lyon, Shaywitz, & Shaywitz, 2003). Dyslexia is defined as a learning dis- ability characterized by problems with the phonological component of language. This pro- duces difficulties with fluent word recognition, poor spelling and decoding ability (Shaywitz, Gruen, Mody & Shaywitz, 2009). Despite good listening comprehension and normal intelli- gence, these difficulties negatively impact academic achievement (Vellutino, Fletcher, Snowl- ing, & Scanlon, 2004).

There are a number of misconceptions associated with dyslexia that should be dispelled early in our discussion. All of the following are accurate descriptions of dyslexia:

• Dyslexia is not strictly a reading disorder. • Dyslexia is not related to intellectual ability. • Dyslexia is not primarily characterized by letter reversal. • Dyslexia is not a visual problem.

At its core, dyslexia is primarily a deficit in phonological processing. Phonological process- ing refers to the wide range of skills, including speech perception, speech production, and short-term memory (Shaywitz, Mody, & Shaywitz, 2006). Many of the code-related skills discussed in the emergent literacy section involve phonological processing, which emerges before reading begins. Once reading instruction begins, individuals with dyslexia have dif- ficulty acquiring the alphabetic principle. This principle involves the recognition that words can be broken down into smaller units, such as syllables and phonemes (Lyon et al., 2003). Thus, individuals with dyslexia may struggle sounding out the sounds associated with letters, such as converting the word “d-o-g” to “d-oh-guh.” These individuals expend so much effort reading words that reading is a laborious process.

Goldyrocks/iStock/Thinkstock There are many causes of reading difficulty, which affects children both academically and emotionally and often leads to frustration and discouragement.

Section 11.2Learning to Read

Dyslexia is also linked to broader language abilities not directly involved in reading, such as word retrieval and rapid naming (Lombardino, 2012). Word retrieval is recalling a name of a picture or object. Rapid naming is the ability to quickly retrieve words or sounds. In a typical task, children are instructed to name rows of colored circles or names of letters as rapidly as possible (Araújo, Pacheco, Faísca, Petersson, & Reis, 2010).

Although dyslexia is not associated with deficiencies in intelligence, students with dyslexia often struggle in school, which affects their academic expectations. For example, one study found that adolescent boys with dyslexia have lower GPAs and lower expectations about their future education than boys without dyslexia. The parents of these boys had similar beliefs about their son’s academic futures. These effects were not found for girls. The gender differ- ences may be related to the general finding that girls as a group tend to perform better aca- demically and are more motivated to achieve. Further, boys with dyslexia may be more impul- sive and hyperactive than girls, which might affect parental expectations (Rimkute, Torppa, Eklund, Nurmi, & Lyytinen, 2014).

Neuroscience and Dyslexia Much of recent research has focused on identifying the neural basis of dyslexia. It is well established that the left hemisphere is actively involved in numerous language tasks, including reading, for typically developing children. The left hemisphere is less active in children with dyslexia (Hoeft et al., 2006).

There are also anatomical or structural differences in the brain (see Figure 11.2). For instance, the arcuate fascicu- lus is a brain region in the left hemisphere that is smaller in adults with dyslexia. The arcuate fasciculus connects Bro- ca’s and Wernicke’s areas of the left hemisphere. Broca’s area is associated with speech production, while Wer- nicke’s area, also in the left hemisphere, is associated with speech comprehension. Similarly, kindergarten children who had yet to receive much formal reading instruction but performed poorly on a measure of phonological aware- ness, had a smaller arcuate fasciculus. This result indicates that these neural deficits are likely a cause of dyslexia rather than a consequence, since it was present before reading began (Saygin et al., 2013).

Dyslexia tends to run in families, indicating a genetic com- ponent (Carrion-Castillo, Franke, & Fisher, 2013). These genetic influences appear early before reading begins. Kindergarten children with a family history of reading problems performed significantly worse on phonological awareness, rapid naming, and letter knowledge, and were more likely to be diagnosed with dyslexia in third grade (Bergen, Jong, Maassen, & Leij, 2014). These phonological deficits can show up as early as age 2 months and are associated with a later diagnosis of dyslexia (Van Zuijen, Plakas, Maassen, Maurits, & Van der Leij, 2013).

Figure 11.2: Brain activation patterns in a phonological memory task in typical children and children with dyslexia

Brain regions associated with dyslexia. The arcuate fasciculus (yellow) branches into the temporal cortex to facilitate communication between Broca’s and Wernicke’s areas of the left hemisphere.

Source: Xu, M., Yang, J., Siok, W. T., & Tan, L. H. (2015). Atypical lateralization of phonological working memory in developmental dyslexia. Journal of Neurolinguistics, 3367–3377. Reprinted with permission from Elsevier.

Section 11.3Learning Mathematics

It is important for teachers to understand the nature of children’s reading disabilities because the interventions are different. Children who have reading problems because of inadequate environmental stimulation can benefit from some of the intervention procedures discussed earlier such as dialogic reading. Children with dyslexia, however, need more intensive, spe- cialized, and long-term interventions and should be referred to a specialist. Being aware of a family’s history can help identify children who may be at risk. More broadly, there are many activities that teachers of preschool to grade school children can use to increase reading suc- cess in their students (Lombardino, 2012).

Questions to Consider

1. In developing emergent literacy activities for children in preschool (ages 3 to 4 years) what would you recommend? What activities would you suggest for parents to prepare their children for reading success?

2. Which strategy—phonics or whole language—do you believe is most effective in teaching children with dyslexia to read? Support your answer with evidence.

11.3 Learning Mathematics Effective mathematics education is a national priority in the United States (National Math- ematics Advisory Panel, 2008). At a time of growth in math-intensive occupations such as engineering and science, student math achievement in the United States lags behind peers’ achievement in many countries throughout the world (National Mathematics Advisory Panel, 2008). Understanding the development of cognitive processes that underlie and contribute to math skill can inform educational practices intended to optimize children’s math learning.

Children’s math knowledge in the United States is characterized by wide variability (Ramani & Siegler, 2014; Siegler, 2003). Although many children experience success and even excel at math, others perform very poorly. Such differences tend to be very stable throughout child- hood, which means that young children who lag behind their peers in early childhood tend to stay behind (Duncan et al., 2007). This stability is an example of continuity in idiographic development.

One way to address large discrepancies in achievement is to make sure all children possess sufficient mastery of the foundations of math success upon entering school (Geary, 2013). In this chapter, we discuss two widely studied foundations of mathematics: understanding numerical magnitude and counting (Geary, 2013). We place these foundations in the context of learning to add, a focus of math instruction in early grade school. We then discuss fractions, a topic that is a focus in later grades. As we will see, mastery of fractions is a precursor to math achievement in high school. The section concludes with an overview of learning disability and a consideration of best practices in math education.

Counting Learning to count provides a foundation for early math achievement as children enter grade school (Aunola, Leskinen, Lerkkanen, & Nurmi, 2004). At root, basic arithmetic operations

Section 11.3Learning Mathematics

like addition and subtraction presume counting knowledge (counting forward in the case of addition, backward for subtraction).

We discussed in Chapter 2 how infants can detect differences in magnitudes. Although that early ability is certainly impressive, the onset of counting marks a leap forward in the under- standing of numbers. As children learn to count, they are explicitly learning the order of number words (“one, two, three…”), connecting those words with corresponding objects, and understanding that the last number word in a sequence represents the total number of objects in the set that was counted (Clements & Sarama, 2014). We discuss the development of these counting features in this section.

The process of learning to count is variable at first, as toddlers and preschoolers (ages 2 to 5) practice learning number words and their correct sequence (Baroody & Price, 1983; Gelman & Gallistel, 1978). Opportunities for counting begin early in life in the nursery rhymes (“This old man, he played one…”) and games (simple card games) many children encounter. Tod- dlers also hear parents and others talk about, and count with, numbers (Levine, Suriyakham, Rowe, Huttenlocher, & Gunderson, 2010).

A 3-year-old’s hardy trial-and-error attempts at counting to eleven demonstrate the challeng- ing process:

One, two, three, four, eight, ten, eleben. No, try dat again. One, two, three, four, five, ten, eleben. No, try dat again. One! two! threeee- four, five, ten, eleben. No. … [finally] … One, two, three, four, five, six, seven, eleven! Whew. (Gelman & Gallistel, 1978, pp. 93)

Learning how to count involves mastering counting principles (Gelman & Galistel, 1978). The one-to-one principle is the awareness that a single number or word (or other symbol) is uniquely assigned to a single item in an array or set of items. The stable order principle of counting is understanding that counting words are sequenced in a consistent order (“one”, “two”, “three”, etc.).The cardinality principle is understanding that the last number in a sequence represents the number of items in a set (Gelman & Galistel, 1978). For instance, if a child is counting his pennies, the last number he utters represents all of the pennies he counted.

By their third birthday many children demonstrate awareness of the one-to-one principle; for instance, they detect double-counting and skipping errors when watching someone else count (Gelman & Meck, 1983). They also detect obvious violations of the stable order prin- ciple (for example, “2, 1, 5…”). The ability to detect such errors improves during the preschool years (Frye, Braisby, Lowe, Maroudas, & Nicholls, 1989).

Beginning counters can recite numbers in correct sequence without always recognizing that the last word they utter in the counting sequence represents the quantity of the set (that is, the cardinality principle). Cardinality is assessed in toddlers by asking them to give a par- ticular number of items to someone (Wynn, 1990). If a child is asked to give a puppet “three” items, the child demonstrates an understanding that the number word specifies numerosity by handing over exactly three items.

Children ages 2½ to 3 years tend to correctly respond to requests for up to three or four items. Larger numbers pose more difficulty for them. The toddlers experience difficulty fulfilling

Section 11.3Learning Mathematics

requests for more than three or four items even when they can count up to ten (Le Corre, Van de Walle, Brannon, & Carey, 2006; Sarnecka, Goldman, & Slusser, 2015). Their performance— counting in sequence—does not necessarily encompass an underlying competence with the principle of cardinality.

By age 3½ many children demonstrate knowledge of the cardinality principle (Wynn, 1992b). This knowledge coincides with overcoming the earlier limitation in identifying sets larger than three or four. Once children begin to correctly identify sets greater than “4” (for example, correctly handing “6” to the puppet) they appear to have figured out that any number, not just “1” through “4”, refers to a specific quantity. Thus, they can correctly link the value of a set to number words already in their counting repertoire.

Recall the role of language in facilitating cognitive development in social-constructivist theo- ries (Chapter 7). Consistent with such theories, children’s understanding of cardinality may be boosted by the degree to which they are exposed to language that expresses number concepts.

In one study, parental “number talk” included references to age (“when you turned one”), counting (“one, two, three”), and amount (“one truck”) directed toward children ages 14 to 30 months (Levine et al., 2010, p. 1312). The frequency with which children were exposed to parental number talk predicted their knowledge of cardinality at age 46 months. That is, when shown two displays containing different amounts, children were more proficient at pointing to the correct display—for example, “point (to the display) with six” (Levine et al., 2010, p. 1312)—if they had received greater exposure to number talk approximately two years earlier.

Just as environments differ in providing emergent literacy activities, there is also variation in providing exposure to number talk. Children from low-SES backgrounds tend to lag in their understanding of number words, which places them at risk for later difficulties with math (Jordan & Levine, 2009). Later in this section we will review an intervention effort that famil- iarizes low-SES children with foundational knowledge of numerical magnitude.

Counting and Strategies for Addition By kindergarten nearly all children (over 90%) can count to at least 9 (LeFevre et al., 2006). Recall from earlier chapters that IP theories focus on the discovery of strategies as a mecha- nism of cognitive development. Counting, which is a focus of kindergarten curricula, is an early strategy for children as they learn to add numbers (see Table 11.3).

The strategies described in Table 11.3 are used in varying amounts from preschool through second grade (Siegler & Jenkins, 1989; Siegler, 1996). Note in Table 11.3 that the min strategy is a clear advancement over the sum strategy. Adding by counting from the larger addend is the quicker and more efficient strategy because it involves less counting. For instance, using the min strategy to solve 6 + 2 involves starting from 6 and only counting two fingers (“7,” “8”) while the sum strategy is counting from “1” to “8.”

Section 11.3Learning Mathematics

Table 11.3: Children’s strategies for adding numbers

Strategy Use when solving 3 + 5

Sum Put up 3 fingers, usually counting “1, 2, 3”; put up five fingers, usu- ally counting “1, 2, 3, 4, 5”; continue counting (“1” through “8”) to arrive at the sum.

Shortcut sum Say, “1, 2, 3, 4, 5, 6, 7, 8,” possibly accompanied by putting up fingers while counting.

Min Say “5, 6, 7, 8” or “6, 7, 8,” possibly accompanied by putting up fingers for each count.

Count from first Count from the first addend, “3, 4, 5, 6, 7, 8” or “4, 5, 6, 7, 8.”

Retrieval Simply respond with the answer. A sample explanation for the answer is “I just knew it.”

Source: Adapted from Shrager, J., & Siegler, R. S. (1998). SCADS: A model of children’s strategy choices and strategy discoveries. Psychological Science, 9(5), 405–410.

Generalizations with respect to the discovery of addition strategies include:

• the min strategy is discovered through practice; • the min strategy is usually preceded by the shortcut sum strategy; and • children continue to use the earlier, familiar strategies even after discovering the

min strategy (Shrager & Siegler, 1998).

Children’s strategies do not typically develop in a stage-like manner in which the acquisition of a more advanced strategy means abandoning the less advanced strategy. The development of strategies is better characterized by continuity rather than discontinuity. The overlap- ping waves model depicts children’s strategy use as highly variable, with different strategies employed within a given period (Siegler, 1996).

During the same practice session a child might first use the sum strategy, then switch to the min strategy for other problems, before reverting back again to the sum strategy. The over- lapping nature of strategy use is a characteristic found in many domains ranging from tod- dlers trying to stay upright when walking to high school students learning to design scientific experiments (Siegler, 2000a).

Children use multiple approaches when solving addition problems, and gradually, the more effective and efficient strategies “win” and predominate (Siegler, 1996). For instance, the min strategy is used about a third of the time by kindergarteners, with the retrieval strategy occurring much less frequently. By first grade, children sometimes still use the min strategy, but not as much as the retrieval strategy (Siegler, 1996). As use of the more advanced strate- gies increases, the less efficient ones (like the sum strategy) decrease and gradually disappear from use.

Children discover more advanced strategies when difficulties prompt them to seek out new ways to approach a task (Siegler, 2000a). Other times they discover new strategies through practice (Siegler, 2000b). Once a new strategy is discovered, one way to prompt children to

Section 11.3Learning Mathematics

continue using it instead of reverting to earlier strategies is to present relatively challenging problems. For instance, the problem 2 + 21 is easier for children to solve with the min strat- egy (“21”, “22”, “23”) than with the sum strategy (“1”, “2”, “3”, etc.) (Shrager & Siegler, 1998). Reverting to an earlier less advanced strategy is ineffective for the more challenging problem.

With practice, counting strategies become unnecessary as basic arithmetic facts are memo- rized and automatically retrieved (the last stage in Table 11.3). During the early grade school years, increasing reliance on retrieving single-digit math facts from memory is associated with neural maturation that strengthens connections between the hippocampus and the neo- cortex (Qin et al., 2014). The hippocampus is a part of the brain generally associated with memory (see Chapter 4).

Numerical Magnitude Mathematical operations, whether basic or advanced, distinguish between more and less. In this section, we discuss the development of children’s knowledge that entities do in fact differ in amount, or magnitude. Magnitude can be represented symbolically (for example, numer- als) and nonsymbolically (for example, dots). Both types of representations are illustrated in Figure 11.3. Children demonstrate their understanding of magnitude by how accurately and quickly they discriminate between numerals (“Which is bigger?”) and between displays of different quantities (such as displays of dots).

Figure 11.3: Symbolic and nonsymbolic representations of magnitude

Numerals are symbols that represent magnitude (top). Nonsymbolic magnitudes (bottom) are illustrated spatially and visually; for example, by different quantities of dots.

Symbolic numerical magnitudes

Non-symbolic numerical magnitudes

Numerical magnitude can also be represented without symbols, as in these examples.

Numerals and number words are symbols that represent magnitude.

1, 2, 3, 4, 5 . . . I, II, III, IV, V . . . One, Two, Three, Four, Five . . .

Section 11.3Learning Mathematics

Nonsymbolic numerical magnitudes are quantifiable collections of entities typically arranged visually and spatially (Fazio, Bailey, Thompson, & Siegler, 2014). When a child looks at two groupings of pennies, their magnitude is presented nonsymbolically. Symbolic numerical magnitudes are notations, usually number words or numerals, mapped onto a quantity (Geary, 2013). The numeral “6” signifies the quantity of six objects or entities, “7” denotes seven entities, and so forth. We discuss the development of each of these understand- ings of magnitude in turn.

Nonsymbolic Numerical Magnitude The approximate number system (ANS) is the cognitive mechanism responsible for esti- mating and comparing nonsymbolic magnitudes (Piazza, 2010). The ANS is in operation when a child sees two gumball machines and judges which one contains more candy. It is associated with activity in the parietal cortex and, as we saw in Chapter 2, is evident in infants’ ability to discriminate between two displays of different magnitudes (Piazza, 2010).

By age 3 to 4 years, children can accurately discriminate between sets differing by a 3:4 ratio (Piazza, 2010). They notice the difference, for instance, between a display of six dots and another display of eight dots. In the early grade school years, discrimination becomes refined to a 4:5 ratio and eventually reaches a 7:8 ratio by adulthood. The gradual refinement of acu- ity in discriminating magnitudes during childhood is evidence of continuity in development.

We illustrate how the ANS operates and its possible relationship to math achievement by discussing a study conducted with 14-year-olds (Halberda, Mazzocco, & Feigenson, 2008). Over a series of trials, a display of intermixed blue and yellow dots was quickly flashed on a computer screen and the adolescents had to estimate which color was greater in number on each trial. The ratio between the two colors ranged from 1:2 to 7:8. Discriminations were most accurate when the difference between blue and yellow dots was largest (1:2 ratio) and then gradually decreased as the ratio between the different colors decreased.

There were also substantial individual differences in adolescents’ accuracy. The acuity of the ANS is measured by the fineness of the discriminations one makes. Some adolescents suc- ceeded at making discriminations when the difference between yellow and blue dots was quite small, while others struggled with ratios that were less than 2:3. The individual differ- ences were examined to determine whether they were associated with math achievement scores that had been gathered when the adolescents were in grade school (grades K-6). Those who were better able to make discriminations at age 14 were found to have had better math performance at each of those grades. This could not be attributed simply to general cognitive factors like IQ (Halberda et al., 2008).

It is not yet clear why, exactly, ANS acuity and math achievement might be linked (Feigenson, Libertus, & Halberda, 2013). One possibility is that symbolic magnitudes depend on ANS acu- ity (Hyde, Khanum, & Spelke, 2014). For instance, number words are acquired by mapping a term (“seven”) onto a magnitude. Precise representations of magnitudes (the ANS) may support this mapping process in preschoolers (Feigenson et al., 2013; vanMarle, Chu, Li, & Geary, 2014).

Another possibility is that individual differences in math achievement—differences in chil- dren’s learning about math—impact their ANS acuity (Halberda et al., 2008). That is, rather

Section 11.3Learning Mathematics

than the ANS impacting math achievement, the reverse relationship is possible. Yet another possibility is that a third factor, such as executive functioning, is responsible for the relation- ship between ANS acuity and math achievement (Fuhs & McNeil, 2013). In other words, dif- ferences in children’s executive functioning impact their performance on both ANS acuity and math achievement.

For now, the correlation between ANS acuity and math achievement in children remains under investigation (Inglis Attridge, Batchelor, & Gilmore, 2011). We discuss the link in this chapter because it helps expose the processes that underlie number understanding and math achievement. It also illustrates how a primitive ability rooted in early infancy may impact, or be impacted by, education and learning. In this sense, we see evidence of continuity in development.

Symbolic Numerical Magnitude For children to understand math in school, they must be able to understand the relationship between a numeral and the quantity it represents. Showing children numerals and asking them to judge which is bigger or which is closer to a target (for example, “Which number, 7 or 8, is closer to 9?”) are common ways to assess their understanding of symbolic numerical magnitude. Children’s accuracy and the speed with which they make their judgments when comparing numerals are consistently correlated to mathematics achievement (De Smedt, Noël, Gilmore, & Ansari, 2013). Grade school children’s knowledge of symbolic magnitudes is more strongly linked to math achievement than ANS acuity (Fazio et al., 2014).

Why would quickly and accurately accessing the meaning of numerals facilitate the develop- ment of mathematical skills (Holloway & Ansari, 2009)? To illustrate, consider a word prob- lem that asks children to add “three turtles to two turtles.” A beginner who knows the mean- ing of the words might count to himself on his fingers (as we saw in Table 11.3) to solve the problem. In contrast, a child who is unclear about the meaning of the number words would struggle without reminders or visual aids depicting three and two. The child who already knows the meaning of the words would, presumably, have a head start in eventually memoriz- ing 3 +2 as a basic math fact.

Linear Representations of Numbers Children’s understanding of the magnitudes of symbolic numbers can be measured by asking them to estimate where a number would go along a number line. The linear representation of numbers involves estimating numbers at equal rates along a continuum (Siegler & Booth, 2004). Magnitudes are spatially represented so they are spaced evenly between endpoints. As we will see in this section, competency in representing magnitudes along a number line is linked to children’s math achievement.

The ability to estimate where magnitudes belong on a number line emerges during the pre- school years. To illustrate, 4- and 5-year-old children were asked to estimate a number’s location by making a mark on an unmarked number line flanked by the numbers 1 and 10.

Section 11.3Learning Mathematics

Accuracy was determined by how closely the child’s mark corresponded to the actual value on the line. For instance, a child who marked “3” at an interval that actually corresponded to “9” would be less accurate than a child who marked “8” at that interval. Older children were more likely to accurately position a number than younger children. Accuracy was related to early numerical skills such as correctly ordering numerals 1 through 5 (Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, 2010).

In general, older children are more likely than younger ones to position their numbers linearly on the number line (Siegler & Lortie-Forgues, 2014). That is, older children are more likely to place numbers at relatively equal intervals such that, for instance, the distance between “5” and “7” is comparable to the distance between “5” and “3”. Younger children arrange their numbers by spreading the smaller numbers relatively far apart and then bunching, at much smaller intervals, the larger numbers. In other words, the distance between “2” and “3” would be much greater than the distance between “8” and “9.”

Evidence suggests the developmental pattern repeats itself during childhood as the number line range increases. For instance, 5-and 6-year-olds can arrange numbers linearly on num- ber lines ranging from 0-10 but not for number lines ranging from 0-100 (Siegler & Lortie- Forgues, 2014). Later, in the 0-1,000 range, 7- and 8-year-olds spread apart smaller numbers and use much smaller spacing for the largest numbers, whereas 9- and 10-year-olds arrange the numbers linearly (Siegler & Opfer, 2003).

Accuracy in number line estimation is strongly predictive of children’s mathematical achieve- ment (Booth & Siegler, 2008; Siegler & Lortie-Forgues, 2014). A number line is useful for concretely viewing mathematical operations (Ramani & Siegler, 2011). The math problem “2 + 4” can be visualized along a number line by starting at 2 and moving one’s finger 4 intervals before reaching 6. Subtraction problems can be visualized in a similar fashion. The number line represents whole numbers at equidistant lengths; accordingly, the answer to a problem like “3 + 3” can be recognized as literally doubling the first digit (“3”). Children without a con- ceptual basis for understanding numerical magnitude are left to rely solely on rote memoriza- tion of math facts (Ramani, Siegler, & Hitti, 2012).

Recall from Chapter 7 that the social-constructivist perspective draws our attention to con- crete objects serving as tools that transform a child’s cognitive development. A number line serves as a tool for learning about numbers. Other objects can serve a similar function.

For instance, the body can serve as a “tool” for connecting number words to objects (‘two hands” “five toes”, etc.) in a familiar and fun way (cf. Varol & Farran, 2006). Toys like blocks can also serve as tools for early number learning (Linder, Ramey, & Zambak, 2013; Ramani, Zippert, Schweitzer, & Pan, 2014). Four- and 5-year-olds actively talk about number and mag- nitude when constructing objects with blocks (for example, “We need more blocks on this side” and “Here’s two windows”; Ramani et al., 2014, p. 330). With guidance and prompt- ing from an adult (“show me how many windows you have”), playing with toys can be an opportunity for informal math lessons. In the Spotlight on Research, we see how playing board games can impact children’s early linear representations of numbers.

Section 11.3Learning Mathematics

Spotlight on Research: Early Math Learning With Linear Board Games There is substantial variability in children’s knowledge of math when they enter preschool and kindergarten. Children from low-income backgrounds tend to lag in knowledge of written numerals, counting, solving arithmetic problems, and in other math basics (Ramani & Siegler, 2014. In one training attempt to help children overcome such lags, low-income preschoolers (4 and 5 years old) were given experience playing a board game that emphasized counting and the linear representation of magnitude (Ramani & Siegler, 2011, Experiment 2).

The board game featured 10 horizontally arranged squares, each consecutively numbered from 1 to 10 (see Figure 11.4). The board game was similar to the commercially available game called “Chutes and Ladders.” Children used a spinner to determine the number of squares they should move their token. They were, essentially, counting numerals at equal intervals along a number line.

Figure 11.4: Linear board games help preschoolers understand numerical magnitude

A linear board game that gives children experience counting and using a number line. In the study discussed in the text, the game was played over four sessions, roughly 20 times total.

Source: Adapted from Ramani, G. B., Siegler, R. S., & Hitti, A. (2012). Taking it to the classroom: Number board games as a small group learning activity. Journal of Educational Psychology, 104(3), 661–672.

(continued)

Section 11.3Learning Mathematics

Spotlight on Research: Early Math Learning With Linear Board Games (continued) At the end of training, a posttest was administered to see if children’s number knowledge was positively impacted. Compared to control conditions that involved low-SES children in activi- ties like identifying numerals, children playing the board game showed significant improve- ment. Positive effects of playing the board game were evident in number line estimation, arith- metic (addition problems), and numerical magnitude comparison problems (for example, indicating which of two numbers is greater). The authors concluded that practice at linear board games positively impacts children’s ability to represent numbers in a linear fashion.

The children in the study from low-income backgrounds had less experience playing board games but more experience playing video games than children from middle-income back- grounds. More generally, it may be that children from all backgrounds who have less experi- ence with family activities involving numbers—activities such as board games, card games, and using simple recipes—may be relatively limited in their early knowledge of numbers (Ramani & Siegler, 2014. Interventions like extra practice playing linear board games can help make up for such differences.

Finally, the impact of practice playing linear board games appears to possess a degree of stabil- ity. In another study related to the one we just featured, the positive effects of playing linear board games on understanding numbers were evident after 2 months even though there was no further intervention (Ramani & Siegler, 2008).

Critical-Thinking Question

Design a concept for your own board game that would help children practice another early math skill, such as magnitude estimation. Which skill would you choose, and how would the game incorporate it?

Fractions Understanding fractions is critical for mastering math concepts like algebra that appear later in a child’s math education. For instance, fifth graders’ knowledge of fractions predicted their mathematics achievement in high school even after accounting for other predictors like work- ing memory and IQ (Siegler et al., 2012).

Real-World Application: Recommendations for Helping Children Master Fractions http://ies.ed.gov/ncee/wwc/practiceguide.aspx?sid=15

The role of mastering fractions in children’s math achievement is so crucial that the U.S. gov- ernment has created a website summarizing five instructional recommendations for improv- ing children’s understanding of fractions in K through 8th grade. The recommendations are organized in sequence. Do you think the order of the instructional techniques is more consis- tent with a continuous or discontinuous view of fraction knowledge development? Why?

Section 11.3Learning Mathematics

Instruction in fractions begins in third or fourth grade in the United States, but many children have difficulty mastering the subject (Siegler, Fazio, Bailey, & Zhou, 2013). To illustrate, in one study children at the end of fifth grade had difficulty understanding the magnitudes that fractions represent; for instance, they incorrectly assumed that three-digit decimal fractions (for example, .274) were larger than two-digit decimal fractions (for example, .83) and/or they neglected the 0 in the tenths position and equated .07 with .7 (Rittle-Johnson, Siegler, & Alibali, 2001; Siegler et al., 2013).

Fractions pose difficulties in part because children incorrectly apply the properties they have learned about whole numbers to fractions (Siegler et al., 2013). In the example in the previ- ous paragraph, .274 will be judged as greater than .83 if a child treats the fractions as whole numbers (that is, 274 > 83). This line of reasoning is evident in the following examples:

Child 1: 0.5 < 0.25, “because 25 is bigger.”

4.7 < 4.08, “because the zero does not matter and 8 is bigger than 7.”

Child 2: 4.8 < 4.63, “since 63 is bigger than 8.” (Resnick et al., 1989 pp. 20)

Note how studying fractions draws on the EFs. Children need to maintain rules in working memory (for example, “the first place to the left of the decimal is tenths, the second place is hundredths” etc.). Similarly, multistep problems like subtracting fractions or reducing them require the child to keep information in mind from earlier steps while effectively processing and solving each new step in the problem (Cragg & Gilmore, 2014; Raghubar, Barnes, & Hecht, 2010). Working memory and classroom attentiveness measured when children were in the fourth grade predicted their mastery of fractions at the end of their fifth grade year (Hecht & Vagi, 2010). This evidence informs efforts to help children master fractions.

An attempt to improve fourth graders’ understanding of fractions illustrates the importance of targeting domain-general cognitive processes like working memory as well as specific knowledge about fractions (Fuchs et al., 2013a). The intervention was directed at children who were at risk for lower levels of math learning (determined by standardized test perfor- mance). It involved 36 lessons that principally focused on ordering and comparing fractions along a 0 to 1 number line. To illustrate, one lesson involved ordering three fractions along a number line from least to greatest. The intervention also accounted for domain-general fac- tors such as relatively limited working memory capacity; for instance, children were taught strategies for measuring fractions that reduced working memory demands.

At the end of training, children were tested in areas such as understanding fraction values (for example, comparing the magnitudes of different fractions) along with adding and subtracting fractions. Children who received the intervention outperformed children in the control group whose instruction in fractions did not focus on the number lines but relied instead on a stan- dard textbook. Moreover, children with relatively low working memory capacity were able to benefit from the intervention (Fuchs et al., 2013a).

Mathematical Learning Disability As we noted at the outset of this section, children with relatively low math competencies upon school entry are at-risk for continued low mathematics achievement. Deficits in math

Section 11.3Learning Mathematics

competency can have long-lasting consequences that are evident well after schooling ends. Poor math skills are linked to increased rates of employment in relatively low-paying occupa- tions as well as increased rates of unemployment (Geary, 2011).

Children identified as having a mathematical learning disability (MLD) score at the bottom 10% on standardized math tests for two consecutive academic years (Geary, 2011). Their intelligence test scores are above the 15th percentile (that is, higher than at least 15% of the population), meaning that they do not meet the criteria for a more general intellectual dis- ability. Developmental dyscalculia, mentioned in Chapters 2 and 8, can be considered synony- mous with MLD (Mazzocco, Feigenson, & Halberda, 2011). Approximately 7% of children are identified as having an MLD (Geary, Hoard, Nugent, & Bailey, 2012).

The intraparietal sulcus (IPS) is a region of the brain located in the parietal lobe (behind the frontal cortex) and it is associated with learning new math facts and representing magni- tudes. Neural abnormalities in the IPS have been observed in individuals diagnosed with MLD (Butterworth, Varma, & Laurillard, 2011).

For instance, 10-year-olds with low performance on a magnitude estimation and a number line task had less gray matter in the IPS compared to higher performing children (Lubin et al., 2013). Gray matter in the brain is generally associated with information processing. The presence of neural abnormalities in a region of the brain associated with basic numeral pro- cessing implies that math interventions for children with MLD might initially focus on basic, fundamental concepts such as practice in discriminating between magnitudes (Butterworth et al., 2011).

Twin studies find that MLD is more likely to co-occur in identical twin pairings compared to fraternal twins (Oliver et al., 2004). The genetic influence on MLD also overlaps to an extent with other learning disabilities (Kovas & Plomin, 2007). Estimates of the frequency with which reading and math learning disabilities co-occur in individuals range from 30% to 70% (Willcutt et al., 2013). This overlap likely reflects a shared genetic source.

The heritability of MLD may help explain why it tends to co-occur with ADHD, which is also heritable (DuPaul, Gormley, & Laracy, 2012; Geary, 2011). Observational studies illustrate how math learning is adversely impacted by symptoms of ADHD. In one such study, 7- and 8-year- old children completed a math worksheet while inattentive behaviors were coded (Antonini, Narad, Langberg, & Epstein, 2013). Symptoms of inattention that were coded included look- ing away from the math sheet for two or more seconds, doodling, or counting how many prob- lems remained before finishing the worksheet. The ADHD group had significantly less on-task behavior than the control group. As expected, poor performance on the math assessment was associated with inattentive behavior.

Cognitive Influences on MLD MLD is characterized by specific and general cognitive deficits. A deficit specific to math is evident in the operation of the ANS. Children with an MLD tend to less accurately discrimi- nate between magnitudes compared to typically developing peers (Feigenson et al., 2013; Geary, 2013). They also exhibit a domain-general deficit in working memory and typically score below average on intelligence tests (Geary, 2013).

Section 11.3Learning Mathematics

In addition to working memory limitations, children with MLD experience difficulty retriev- ing basic arithmetic facts from long-term memory (Geary et al., 2012). Memory problems result in overreliance on rudimentary counting strategies, like the min strategy discussed earlier, even into the early grade school years (Geary et al., 2012).

The retrieval problems of children with MLD are associated with weakness in inhibiting incorrect math answers that are associated with the correct answer to a problem (Barrouil- let, Fayol, & Lathulière, 1997; Geary, Hamson, & Hoard, 2000). For instance, in the early grade school years, children with an MLD tend to err on addition problems by retrieving a number associated with the counting sequence of one of the addends. This means that when a child is given a problem such as 5 + 3, a number associated with the counting sequence of “5” (that is, “5, 6…”) interferes with the correct answer. Consequently, a common retrieval error for a problem such as 6 + 3 would be answering with “7” (a counting associate of “6”) rather than “9” (Geary et al., 2000).

According to IP theory, development occurs when information is retrieved quickly and automatically rather than slowly and deliberately. Speeded practice on arithmetic prob- lems imposes a time limit for completing all trials and was a featured component of tutor- ing sessions for first graders identified as at risk for poor math achievement (Fuchs et al., 2013b). The 16-week tutoring program facilitated fast and automatic retrieval of basic math facts (for example, number values, counting by tens) and resulted in effective gains in math performance.

As we mentioned earlier, there is a genetic influence on math competency (Geary, 2011). Returning to our nature–nurture theme, even though a characteristic is heritable, it can still be impacted by the environment (as we discussed in Chapter 10). The effectiveness of the tutoring program above illustrates how the environment can modify characteristics that are related to genes.

Procedures or Concepts First? We conclude our discussion with a fundamental question about math education. Throughout much of the 20th century, educators debated between two approaches for teaching mathemat- ics (Baroody, 2003). On the one hand, some advocated for mastery of basic skills through rote memorization. Others, similar to Piaget, felt children should first be encouraged to actively explore and discover by themselves underlying concepts of math such as the independence of sum and order (that is, regardless of how one orders the numbers, 3 + 5 or 5 + 3, the product is the same). Today psychologists frame the debate by investigating children’s acquisition of procedural and conceptual math knowledge.

Procedural knowledge in math is the awareness of how to solve problems by correctly fol- lowing rules and steps when completing a task (LeFevre et al., 2006). A math teacher may ask children to “show their work” in order to determine if their procedural knowledge is sound. Conceptual knowledge is knowledge of math facts and principles that impact understand- ing of how and why a mathematical procedure leads to a correct outcome (LeFevre et al., 2006). The cardinality principle is an example of conceptual knowledge, while the ability to count is procedural knowledge.

FlairImages/iStock/Thinkstock Requiring that students show the steps involved in calculating a math problem is an example of assessing procedural knowledge.

Section 11.3Learning Mathematics

In addition to working memory limitations, children with MLD experience difficulty retriev- ing basic arithmetic facts from long-term memory (Geary et al., 2012). Memory problems result in overreliance on rudimentary counting strategies, like the min strategy discussed earlier, even into the early grade school years (Geary et al., 2012).

The retrieval problems of children with MLD are associated with weakness in inhibiting incorrect math answers that are associated with the correct answer to a problem (Barrouil- let, Fayol, & Lathulière, 1997; Geary, Hamson, & Hoard, 2000). For instance, in the early grade school years, children with an MLD tend to err on addition problems by retrieving a number associated with the counting sequence of one of the addends. This means that when a child is given a problem such as 5 + 3, a number associated with the counting sequence of “5” (that is, “5, 6…”) interferes with the correct answer. Consequently, a common retrieval error for a problem such as 6 + 3 would be answering with “7” (a counting associate of “6”) rather than “9” (Geary et al., 2000).

According to IP theory, development occurs when information is retrieved quickly and automatically rather than slowly and deliberately. Speeded practice on arithmetic prob- lems imposes a time limit for completing all trials and was a featured component of tutor- ing sessions for first graders identified as at risk for poor math achievement (Fuchs et al., 2013b). The 16-week tutoring program facilitated fast and automatic retrieval of basic math facts (for example, number values, counting by tens) and resulted in effective gains in math performance.

As we mentioned earlier, there is a genetic influence on math competency (Geary, 2011). Returning to our nature–nurture theme, even though a characteristic is heritable, it can still be impacted by the environment (as we discussed in Chapter 10). The effectiveness of the tutoring program above illustrates how the environment can modify characteristics that are related to genes.

Procedures or Concepts First? We conclude our discussion with a fundamental question about math education. Throughout much of the 20th century, educators debated between two approaches for teaching mathemat- ics (Baroody, 2003). On the one hand, some advocated for mastery of basic skills through rote memorization. Others, similar to Piaget, felt children should first be encouraged to actively explore and discover by themselves underlying concepts of math such as the independence of sum and order (that is, regardless of how one orders the numbers, 3 + 5 or 5 + 3, the product is the same). Today psychologists frame the debate by investigating children’s acquisition of procedural and conceptual math knowledge.

Procedural knowledge in math is the awareness of how to solve problems by correctly fol- lowing rules and steps when completing a task (LeFevre et al., 2006). A math teacher may ask children to “show their work” in order to determine if their procedural knowledge is sound. Conceptual knowledge is knowledge of math facts and principles that impact understand- ing of how and why a mathematical procedure leads to a correct outcome (LeFevre et al., 2006). The cardinality principle is an example of conceptual knowledge, while the ability to count is procedural knowledge.

FlairImages/iStock/Thinkstock Requiring that students show the steps involved in calculating a math problem is an example of assessing procedural knowledge.

In general, should math education focus more on procedures or con- cepts? The answer has practical implications for how math is taught in schools, affecting everything from curriculum development to teachers’ classroom practice. Research indicates gains in procedural knowledge sup- port conceptual knowledge, and vice versa; however, the interrelationship between the two is not completely equivalent (Rittle-Johnson & Schnei- der, 2015). In some studies, instruction on concepts has a stronger influence on procedural knowledge than does procedural instruction on conceptual knowledge.

To illustrate procedural and conceptual knowledge, we examine a study demonstrating how one influences the other. Multistep addition problems (for example, 3 + 4 + 5 = 3 + ___) were given to grade school children. Typically, math problems are presented to children so that the equals sign (“=“) indicates the answer (for example, 4 + 5 = 9). Early grade school children tend to interpret the equals sign as “give the answer” instead of interpreting it as an indication that both sides of the sign are identical (Chesney et al., 2014). Understanding equivalence is a precursor to algebra, which means that training to help children solve and understand equiv- alence problems like the one above has potential implications for future math achievement.

Some children received training on procedural knowledge (for example, “add 4 +5 to get the answer”) to help them overcome procedural errors such as simply putting a “5” in the blank spot. Training in procedural knowledge improved children’s conceptual knowledge of addi- tion; for instance, children with procedural training made gains when asked what it means for two sets of objects to be equal. For other children, conceptual training (instruction on the meaning of the equal sign) improved their ability to solve the math problems (that is, procedural knowledge). In other words, conceptual and procedural knowledge influenced each other (Rittle-Johnson & Alibali, 1999). Effective math education integrates both forms of knowledge (Baroody, 2003).

Questions to Consider

1. We discussed findings that children can count up to 10 before mastering the car- dinality principle. How does this finding relate to the performance–competence theme of our book?

2. Apply what you learned about math learning in this section to develop a possible intervention strategy for children at risk for poor math competency.

Section 11.4Teaching Children at Risk

11.4 Teaching Children at Risk There are numerous reasons why children can be at risk for academic problems. We pre- viously discussed learning disabilities associated with reading and ADHD. In this section, we focus on risk factors associated with poverty, and on dual language learners because of the large number of children impacted. We will briefly review the education and academic achievement of both groups, as well as Head Start as a representative intervention program designed to boost academic success.

Head Start Children from impoverished environments often perform worse than children from higher SES families on a wide range of cognitive tasks, including emergent literacy, reading, math- ematics, and EFs. Intervention programs have been developed to overcome some of these deficits, and programs vary in their level and form of intervention.

A well-known federal program is Head Start, designed to facilitate school readiness of 3- and 4-year-olds from low-SES families. The School Readiness Act of 2007 states:

• “The Head Start and Early Head Start programs provide comprehensive services to support the mental, social, and emotional development of children from birth to age 5. … Head Start services are responsive to each child and family’s ethnic, cultural, and linguistic heritage.

• Head Start encourages the role of parents as their child’s first and most important teachers. Programs build relationship with families that support positive parent- child relationship, family well-being, and connections to peers and community” (http://www.acf.hhs.gov/programs/ohs/about/head-start).

According to the Head Start Child Development and Early Learning Framework, school readi- ness is assessed in five domains: 1. Language and Literacy; 2. Cognition and General Knowl- edge; 3. Approaches to Learning; 4. Physical Development and Health; and 5. Social and Emo- tional Development.

Head Start serves over a million children and their families every year with a yearly invest- ment of $7 billion. (Note, however, that many children from low-SES environments are not enrolled in Head Start or other high quality preschools.) Head Start typically serves children from ages 3 to 4 years. We will focus on the effectiveness of attempts to improve the first three aspects of school readiness, which are directly linked to cognitive development.

Several studies have demonstrated associations between high quality center-based preschool programs and later academic abilities (Ansari & Winsler, 2011; Burger, 2010). High-quality preschool programs emphasize academic skills and have the appropriate teacher–student ratio, although they can vary widely in their instructional strategies and the types of families they serve. Studies that compare the effectiveness of Head Start to other prekindergarten programs and to parental care have often reported that children in Head Start have smaller academic gains than those children in prekindergarten. They perform better than children in parental care do, however. Other studies reported that children in Head Start do not perform better in school readiness (Forry, Davis, & Welti, 2013).

Section 11.4Teaching Children at Risk

One of the criticisms of many of the studies comparing the effectiveness of different preschool programs, particularly Head Start, is that they have either small sample sizes or do not involve controlled studies in which children are randomly assigned to a Head Start group or a control group. Congress recently mandated that Head Start conduct an evaluation study to determine whether it was an effective program in both the short and long term. To this end, more than 4,600 3- and 4-year-olds were randomly assigned to either a Head Start group or a control group consisting of either another prekindergarten program or family care. Both a 3-year-old and 4-year-old cohort were followed and assessed on a number of academic skills at several time points through third grade. The report, released in 2010, stated:

• Children in the 4-year group showed gains in language and literacy by the end of their first year in Head Start. Specifically, vocabulary, letter-word identification, preacademic skills, color identification, letter naming, and parent-reported emer- gent literacy improved.

• The 3-year-old group had gains in all four domains. In addition to literacy, there were improvements in math, parental interactional styles with their child, and chil- dren’s social behavior.

• However, by the end of first grade, only language ability still demonstrated an effect of Head Start. The 4-year-old cohort showed stronger vocabulary, and the 3-year-old cohort showed stronger oral listening, compared to the control groups.

• By the end of third grade, the 4-year-old cohort showed an impact of Head Start on reading, compared to the control groups. On the other hand, Head Start for the 3-year-old cohort had a negative impact on likelihood of grade promotion (U.S. Department of Health and Human Services, 2010).

The summary of findings reflects outcomes for the entire sample of children. The impact study also examined subpopulations and identified stronger effects of Head Start. In particu- lar, children from the 3-year-old cohort who came from high-risk households showed positive impacts on reading assessments, letter-word identification, and teacher reports of reading and language abilities in third grade.

Overall, the effects of Head Start on language and cognitive performance mostly disappeared by early elementary school, whereas for the high-risk group the effects are more lasting—at least to 3rd grade. Similar findings have been reported in smaller scale studies of Head Start effectiveness (Ludwig & Phillips, 2008). Interestingly, Head Start is associated with more long lasting effects that appear later in adolescence and adulthood. For instance, children who participated in Head Start were more likely to go further in school, have higher incomes, and were less involved in criminal activities (Garces, Thomas, & Currie, 2002). The process by which early effects disappear while long-term effects emerge is unknown at this time. In many ways though, these outcomes might be more important than the loss of academic gains.

In evaluating the effectiveness of Head Start, it is important to recognize that the interven- tion itself is relatively brief compared to children’s overall academic experience. Although many of the academic effects quickly dissipate, if intervention was more long lasting, then the academic effects may be as well. Thus, providing additional instruction and support as these children progress through school should be beneficial, although inadequate resources may limit the availability.

Section 11.4Teaching Children at Risk

Dual Language Learners Dual language learners (DLLs) are children who are not fluent in English and speak a differ- ent language in their home. As you may recall from Chapter 9, we discussed bilingualism primarily in the context of language acquisition and its cognitive benefits. In this section, we focus on DLLs whose native language is not English but who are enrolled in schools where primary academic instruction is provided in English. Thus, DLLs are a subset of bilingual chil- dren. In school settings, this often puts them at risk for academic achievement. According to the Foundation for Child Development, the proportion of DLLs has increased by 200% from

1990-2010. In some communities as much as half of the prekindergarten population is made up of DLLs (Espi- nosa, 2013).

DLLs as a whole often lack proficiency in English and have poorer academic achievements. They demonstrate an achievement gap compared to Cau- casian students. For instance, the National Center for Education Statis- tics reported in their Nation’s Report card that DLLs scored 20-26 percent- age points lower on mathematics and reading achievement (Hemphill, Vanneman, & Rahman, 2011). As ado- lescents, they are more likely to drop out of school (Espinosa, 2013). There are several reasons for these out-

comes, including coming from low-SES families and being on the receiving end of educational strategies that are not always effective at simultaneously teaching English and providing aca- demic instruction.

There are several different teaching approaches used for DLLs. Immersion programs gen- erally provide all-English instruction to DLLs. Transitional bilingual programs provide instruction in their native language in high amounts during the early grades, slowly transi- tioning to English over grade levels. For instance, in one school district, kindergartners who were native Spanish speakers received 75% of the instruction in Spanish, 70% in first grade, 40% in second grade, and 20% in fifth grade. Dual language programs provide equal training in both languages during the week. These programs can vary in how they are implemented in different schools. A recent instructional approach is two-way immersion (TWI) in which both DLL and monolingual children are provided education in both languages.

How effective are these programs in facilitating academic success? In a review of multiple pro- gram studies, bilingual programs (and TWI) were more effective than immersion programs, although there were limitations. Academic outcomes in children’s native language particu- larly showed benefits, where the benefits for English reading skills were mixed across studies (Rolstad, Mahoney, & Glass, 2005). For instance, DLLs in some form of Spanish- English bilin- gual education program in kindergarten had lower scores on English assessments of reading comprehension and oral language in third grade, although they did perform better on compa- rable Spanish measures (Nakamoto, Lindsey, & Manis, 2012). Although it does make intuitive

Monkeybusinessimages/iStock/Thinkstock Dual language learners are not fluent English speakers. Adolescent DLLs tend to have difficulty in school and are at greater risk of dropping out.

Summary and References

sense that children perform better in their native language, it demonstrates that their difficul- ties are not competence-based but performance-based.

These broad based intervention programs are helpful in knowing how to structuring aca- demic instruction. A key element to being a successful learner in U.S. schools is to develop pro- ficiency in reading English (Castro, Páez, Dickinson, & Frede, 2011). We previously discussed the oral language and code-related skills that are important to reading success in monolin- gual children. These same strategies can be effective for DLLs. However, the National Reading Panel (2000) points out that that by themselves these skills are not adequate for guaranteeing success in reading. To enhance the likelihood of success, DLL children need more oral instruc- tion to produce better proficiency in English oral language beyond what is typically provided. Continuing exposure to their native language actually enhances proficiency in English (Castro et al. 2011).

Instructional and educational strategies known to sup- port DLLs’ academic progress include: (a) assessing DLLs English acquisition proficiency on a regular and frequent basis; (b) providing small group interventions for DLLs who may have math or reading difficulty; (c) building vocabulary through direct teaching using both the children’s native language and English; and (d) focusing on development of academic English (Castro et al., 2011). Additional research is needed to identify the best educational practices for DLLs, and all children. Those approaches that incorporate research findings from developmental studies of cognitive development and neuroscience show the most potential for enhanc- ing children’s development.

Summary and References

Chapter Summary

• The experience of formal schooling promotes children’s cognitive development in areas like memory and categorization.

• Especially effective classrooms are characterized by minimal disruptions, respect for all children, and cognitive engagement through feedback and use of higher order skills like problem solving and memory.

• Emergent literacy during the preschool years lays the foundation for reading devel- opment and consists of both oral language and code-related skills.

• Oral language skills include the construction of narratives and stories. • Code-related skills consist of abilities to manipulate speech sounds, such as elision,

deleting a syllable or phoneme from a word, and blending, combining phonemes and syllables to make a word.

• Evidence suggests that dyslexia occurs due to a specific biological deficit in phono- logical processing. The left hemisphere is less active and certain brain regions are smaller in both children and adults with dyslexia.

• There has been considerable debate regarding whether the phonics or whole- language method is more effective in teaching reading. The phonics approach

Question to Consider

Some DLL children also live in an impoverished environment and are enrolled in Head Start programs. What types of additional educational interventions might these children need to learn in order to read and become academically successful?

Summary and References

stresses learning sound–letter correspondence. The whole-language approach focuses on reading for meaning, and sound–letter correspondence is believed to develop automatically.

• Children with a family history of reading disabilities are at increased risk for devel- oping dyslexia, which suggests a genetic basis.

• Children learn to count during the preschool years by mastering the principles of one-to-one, stable order, and cardinality.

• Numerical magnitude is represented symbolically and nonsymbolically. The ability to discriminate between magnitudes before formal schooling is associated with later mathematical achievement.

• Children’s use of counting as an early math strategy emerges in the preschool years, and the strategies are used by children in various ways.

• Evidence indicates mathematical learning disability has a genetic basis that overlaps with other learning disabilities.

• Mathematical learning disability is associated with cognitive deficits in working memory, retrieval, and discriminating between magnitudes.

• Procedural knowledge involves knowing how to solve a math problem, whereas con- ceptual knowledge involves understanding the underlying principles of the problem.

• Intervention programs such as Head Start are designed to compensate for children’s lack of school preparedness by providing academic enrichment. The immediate aca- demic benefits from Head Start programs typically disappear by third grade. How- ever, Head Start is associated with other long-term benefits such as higher income and completion of more school years.

• Dual language learners are also at risk for low levels of academic achievement because they are learning subject matter in their nonnative language.

• Studies show that dual language learners acquire academic content better in bilin- gual programs than in English immersion programs, whereas the results for acquir- ing English language skills are mixed.

Posttest Questions

1. Two individuals, one schooled the other unschooled, are asked to group the follow- ing items: banana, pear, and monkey. Based on evidence discussed in the chapter, which outcome is most likely?

a. Both individuals will use the category fruit to group banana and pear. b. The unschooled individual will have difficulty following directions and randomly

group the items. c. The unschooled individual will group by function (monkeys eat bananas), and the

schooled individual will group by an abstract category (pears and bananas are both fruits).

d. Both individuals will use a concrete feature, color, to group pear and banana together because both are yellow-green in appearance.

Summary and References

2. Which of the following is NOT a feature of classroom effectiveness discussed in the chapter?

a. The environment is inclusive. b. The teacher proactively handles disrespectful interactions among peers. c. The environment is left unstructured so that children can learn independence by

monitoring their own behavior. d. Teacher feedback plays an important role in engaging students in higher order

analysis.

3. Which of the following is NOT a component of code-related skills in emergent literacy?

a. rhyming b. elision c. phonological memory d. sound–letter correspondence

4. What is one the strongest early predictors of later reading ability?

a. IQ b. phonological awareness c. whole-language reading instruction d. executive function

5. Which of the following is true of dyslexia?

a. It develops because of poor early literacy experiences. b. It is associated with lower IQ. c. It is more likely to occur in children from low-SES backgrounds. d. It is a learning disorder not limited to reading.

6. refers to the relationship between a numeral (such as 5) and the exact quan- tity of items the numeral signifies.

a. Nonsymbolic magnitude b. The ANS cognitive mechanism c. The stable order principle d. Symbolic magnitude

7. A 3-year-old counts five pieces of candy one at a time by saying, “1, 2, 3, 4, 5.” When asked how many pieces of candy she has just counted, the child shrugs her shoulders and says, “I don’t know.” She does not yet grasp the counting principle of .

a. stable order b. cardinality c. nonsymbolic magnitude d. one-to-one correspondence

Summary and References

8. Samuel is a preschooler who uses his fingers to solve 4 + 4. He puts up four fingers for each hand and begins counting “1, 2, 3…” until he reaches “8.” Which of the fol- lowing statements is most accurate?

a. Samuel is using the sum counting strategy. b. Samuel has committed answers to single-digit addition problems to memory. c. Samuel is using the min counting strategy. d. Samuel likely has a learning disability in math.

9. Remembering how to reduce fractions by finding the least common denominator is an example of .

a. procedural knowledge b. the min strategy c. conceptual knowledge d. the shortcut sum strategy

10. Studies of the effectiveness of Head Start find that children who go through the pro- gram demonstrate all of the following EXCEPT .

a. immediate gains in language skills b. increased likelihood of graduating from high school c. long-term improvement in intelligence d. higher income as adults

11. Dual language learners need additional instructional support in which aspect of language to reach reading proficiency?

a. oral language exposure in their native language and English b. phonological awareness c. phonics reading method d. letter–sound correspondence

Critical-Thinking Questions

1. Do you think homeschooling would have the same benefits on cognitive develop- ment as formal schooling? Why or why not? What aspects of cognitive development might you assess to answer this question? What differences in the experiences of formal schooling and homeschooling would you need to take into account?

2. In a preschool classroom, one teacher emphasizes practice in how to count by helping children count to 100. Another teacher emphasizes the concepts underly- ing numbers by teaching children about number lines and the cardinality prin- ciple. Each teacher thinks the other’s approach is wrong. What would you tell each teacher? Why?

3. What are some of the challenges that a child who is deaf and has hearing par- ents might face in learning to read? In what ways would you need to modify the approaches recommended in this chapter for enhancing emergent literacy and read- ing instruction?

4. Describe how research into how mathematics or reading are learned supports a particular theory of cognitive development described in earlier chapters, as well as one of our four core themes.

Summary and References

Key Terms

alphabetic principle The recognition that words can be broken down into smaller parts.

approximate number system (ANS) A cognitive mechanism for estimating and comparing quantities.

arcuate fasciculus A brain region in the left hemisphere that has been associated with dyslexia. It connects Broca’s area and Wer- nicke’s area.

blending A phonological awareness task that requires the combination of sounds of phonemes or syllables to produce a word.

Broca’s area A region in the brain’s left hemisphere associated with the production of speech.

cardinality principle The principle that the total number of items in a set is repre- sented by the last number counted in the set.

code-related skills Skills of understanding of the written component of language, such as sound–letter correspondence.

conceptual knowledge The understanding of principles and ideas that underlie math- ematical procedures.

dialogic reading A specific type of joint book reading involving elaborative question- ing and expansion.

dual language learners (DLLs) Children who are not fluent English speakers and speak a different language at home.

dyslexia A learning disability character- ized by difficulties with the phonological component of language. This leads to prob- lems in reading, including difficulty recog- nizing words, spelling, and letter–sound correspondence.

elision A measure of phonological aware- ness in which children must repeat a word and then delete a unit of sound at different levels, from phonemes to syllables.

emergent literacy The skills developed prior to the development of skills in con- ventional reading and writing, as well as the environments and activities that support these developments.

Head Start A comprehensive federal intervention program designed to facilitate school readiness of prekindergarten-aged children from low-income families. It not only supports the cognitive and academic development, but also the social, physical, and emotional development of children from ages 3 to 5 years.

immersion programs Academic instruc- tion that provides instruction only in English to dual language learners.

intraparietal sulcus A region of the brain in the parietal lobe that is associated with mathematical learning disability.

linear representation The estimation of numerical magnitudes at equal intervals between endpoints.

mathematical learning disability (MLD)  A learning disability in which cognitive defi- cits lead to difficulty acquiring competency in math, as evidenced by math achievement scores at the bottom 10% of a standardized assessment for two consecutive academic years; intelligence scores are at least at the 15th percentile.

nonsymbolic numerical magnitudes  Quantities of entities displayed in a visual and spatial arrangement.

Summary and References

number talk Informal references to num- ber and number-related concepts directed toward infants and toddlers.

one-to-one principle The principle that each numeral or symbol is assigned to one and only one item when counting items in a set.

oral language skills The production and comprehension of spoken language through syntax and the meaning of language through vocabulary.

overlapping waves model The idea that variation exists in children’s strategy use, with multiple strategies potentially used within a given period.

phonics methods Reading instructional strategies in which children are taught to decode words by using the spell-to-sound regularities of written language.

phonological awareness The ability to understand and manipulate the sounds of language.

phonological processing The range of skills associated with understanding sounds of language, including both reading and language tasks.

procedural knowledge The awareness of how to successfully complete a math task by following prescribed rules and steps.

sound–letter correspondence Awareness of the sound associated with each letter.

stable order principle The principle that symbols such as number words are always sequenced in the same order.

symbolic numerical magnitudes Quanti- ties of entities represented through the use of number words and symbols.

transitional bilingual programs Academic instruction that provides dual language learners with instruction in their native lan- guage in high amounts at first, then slowly transitions to instruction in the target lan- guage as the learner becomes more fluent.

Wernicke’s area A region of the brain’s left hemisphere associated with understanding speech.

whole-language method A reading instructional strategy in which children are taught by focusing on the entire reading experience and reading strategies to abstract meaning from text.

Additional Resources Web Resources

Developing Early Literacy http://lincs.ed.gov/publications/pdf/NELPReport09.pdf This source provides helpful tips for fostering emerging literacy for preschool teachers, as well as basic information on literacy and reading.

Dyslexia http://dyslexia.yale.edu/whatisdyslexia.html From Yale University comes this excellent resource for students, parents, and teach- ers regarding dyslexia. It also provides strategies for coping with dyslexia, as well as individual stories.

Early Math Foundations http://www.du.edu/kennedyinstitute/media/documents/math-in-the-early-years.pdf The importance of early math learning for later math achievement. Policy implications are noted.

Summary and References

Teaching Children with ADHD http://www2.ed.gov/rschstat/research/pubs/adhd/adhd-teaching_pg3.html This website from the Department of Education provides numerous strategies for help- ing children with ADHD succeed in school.

Further Reading

Cole, M. (1990). Cognitive development and formal schooling: The evidence from cross- cultural research. In L. C. Moll (Ed.), Vygotsky and education: Instructional implications and applications of sociohistorical psychology (pp. 89–110). New York: Cambridge University Press. This is an influential overview of research, history, and theory addressing the conse- quences of schooling on cognition across different cultures.

Geary, D. C. (2013). Early foundations for mathematics learning and their relations to learn- ing disabilities. Current Directions in Psychological Science, 22(1), 23–27. This article contains an accessible presentation of the early competencies that are at the root of a math learning disability.

Meyer, R., & Manning, M. (2007). Reading and teaching. Hillsdale, NJ: Erlbaum. This book provides a series of real-world case studies of different ways of instructing children to read with teacher comments.

Opfer, J. E., & Siegler, R. S. (2012). Development of quantitative thinking. In K. Holyoak & R. Morrison (Eds.), Oxford handbook of thinking and reasoning (pp. 585–605). New York: Oxford University Press. The authors provide an extensive review of how infants and children represent magnitude.

Answers and Rejoinders to Chapter Pretest

1. False. Experiences in schooling, such as engaging in activities that engage memory, positively impact cognitive development.

2. True. Children can begin the process of learning to read before they enter kindergar- ten by participating in emergent literacy activities.

3. False. Reading is not a “natural” achievement but requires instruction. 4. Dyslexia primarily involves difficulty with phonological processing. 5. True. Studies find that individual differences in math knowledge tend to remain

stable over time. 6. False. The beneficial cognitive effects of Head Start frequently disappear by third

grade. However, there are long-term benefits, such as an increase in the likelihood of graduating from high school.

Answers and Rejoinders to Chapter Posttest

1. c. The unschooled individual will group by function (monkeys eat bananas), and the schooled individual will group by an abstract category (pears and bananas are both fruits). Schooling impacts how individuals categorize items.

Summary and References

2. c. The environment is left unstructured so that children can learn independence by monitoring their own behavior. Effective classrooms involve directive behavior from a teacher. Peer interactions, transitions, and on-task behaviors are closely monitored by the teacher rather than letting students “work it out themselves.”

3. c. phonological memory Phonological memory is the ability to remember spoken language and is not consid- ered a coding skill.

4. b. phonological awareness Phonological awareness reflects coding skills and is associated with later reading.

5. d. It is a learning disorder not limited to reading. Dyslexia can affect cognitive and general language skills in nonreading tasks such as rapid naming and word retrieval.

6. d. Symbolic magnitude Magnitudes are represented symbolically by numerals and number words.

7. b. cardinality The cardinality principle is the understanding that the last number in a counting sequence represents the value of the set.

8. a. Samuel is using the sum counting strategy. The sum counting strategy used by preschoolers involves counting from “one.”

9. a. procedural knowledge Procedural knowledge involves understanding the steps and rules used to solve math problems.

10. c. long-term improvement in intelligence The effects of Head Start on intelligence typically disappear by elementary school.

11. a. oral language exposure in their native language and English Although phonological awareness is important for DLLs, as it is for monolinguals, researchers have suggested that additional oral language exposure is needed.