Acquisition and use of shortcut strategies by traditionally schooled children

This study aimed at analysing traditionally taught children’s acquisition and use of shortcut strategies in the number domain 20–100. One-hundred-ninety-five second, third, and fourth graders of different mathematical achievement levels participated in the study. They were administered two tasks, both consisting of a series of two-digit additions and subtractions that maximally elicit the use of the compensation and indirect addition strategy (, so the answer is 2 + 1 or 3). In the first task, children were instructed to solve all items as accurately and as fast as possible with their preferred strategy. The second task was to generate at least two different strategies for each item. Results demonstrated that children of all grades and all achievement levels hardly applied the compensation and indirect addition strategy in the first task. Children’s strategy reports in the second task revealed that younger and lower achieving children did not apply these strategies because they did not (yet) discover these strategies. By contrast, older and higher achieving children appeared to have acquired these strategies by themselves. Results are interpreted in relation to cognitive psychological and socio-cultural perspectives on children’s mathematics learning.

Learning to spell: variability, choice, and change in children's strategy use

We examined whether the overlapping waves model, originally developed to account for strategy choices in arithmetic, could also account for strategy choices in spelling. The contrast was of particular interest because arithmetic is an algorithmic domain (a domain that includes strategies that always yield correct answers if executed properly), whereas spelling is not. Thirty first-grade students spelled words under 2 conditions, and 23 of these students were retested in second grade. Trial-by-trial analysis of strategy use was used to identify which strategies first and second graders used, how adaptively they chose among them, how effective the strategies were, and what changes occurred from first to second grade along each dimension. The model proved useful for understanding the development of spelling, despite the fact that explicit use of backup strategies had a minimal impact on accuracy. Implications for understanding adaptive strategy choices in algorithmic and nonalgorithmic domains are discussed.     

Using a Think-Aloud with Diverse Students: Three Primary Grade Students Experience Chrysanthemum

Many struggling readers, students with English as a second language, and children with disabilities do not engage in the strategies that good readers use when reading for understanding. Reading comprehension depends upon the students’ ability to successfully use strategies to monitor and control their own comprehension. Teachers need to help students develop skills that will aid in reading comprehension. The think-aloud is one strategy that can help struggling readers improve fluency and comprehension. One of the most important components to determine the success of the think-aloud is the teacher’s ability to model and facilitate the think-aloud procedure. The teacher needs to have a basic understanding of what is meant to be accomplished using this method. This article profiles how three teachers model and facilitate a think-aloud with three struggling readers.     

So young and already victims of stereotype threat: Socio-economic status and performance of 6 to 9 years old children on Raven’s progressive matrices

The aim of this study was to verify whether children from low socio-economic status (SES) are victims of stereotype threat. Children in first grade (6 to 7 years old) and third grade (8 to 9 years old) performed Raven’s progressive matrices, an intellectual ability test commonly used by psychologists. The test was presented either with the (evaluative) instructions recommended by Raven et al. (1998) or with non evaluative instructions. Children’s SES and beliefs concerning differences of abilities at school as a function of SES were also assessed. The results indicated that, as early as first grade, participants believed that children from high SES are better at school than children from low SES. Furthermore, low SES participants’ performance on the Raven’s matrices was lower in the evaluative condition than in the non evaluative condition. The experimental instructions did not affect high SES participants’ performance. The discussion explores implications of these results in the use of standardized tests to assess the intellectual abilities of low SES children.     

Types of writings found in the early levels of basal reading programs: Preprimers through second grade readers

Eight leading basal reading programs, approved for adoption in California public schools in 1983, were analyzed to determine the array of the types of writing included in the program from preprimers to second grade readers. The Teacher’s Manuals were examined to determine whether provision was included for teaching children how to read a wide variety of discourse types. A third investigation was undertaken in this study to determine the array of discourse types in standardized reading tests and assessment tests included in the basal program. Data indicated that the majority of selections in all of the readers were narrative materials (56%), poems accounted for 25% of the total selections, and exposition accounted for 15% of the total selections. A second analysis of page allocation indicated narrative writings accounted for more than 80% of the total page allocation. Few differences by grade level or by individual programs were found. The Teacher’s Manual of each of these programs provided instruction for teaching children how to read various types of writing. Suggestions for reading narrative writing constituted the greatest percentage. An analysis of discourse types in standardized tests indicated two discrepancies between reading programs and standardized tests: (1) few “whole” texts were included in tests before the end of second grade; and (2) most texts were narrative. The analysis of the assessment tests within each of the programs indicated narrative materials were most often used for testing and poetry was not assessed in any program. Presented at the 33rd Annual Conference of The Orton Dyslexia Society, San Diego, California, November 1983.     

Strategy Self-Verbalization During Remedial Listening Comprehension Instruction

Abstract

This experiment investigated the effects of strategy self-verbalization on children’s self-efficacy and listening comprehension. Children with language deficiencies in grades two through four received instruction in listening comprehension. One-half of the children in each grade verbalized explicit strategies prior to applying them to questions. Strategy self-verbalization led to higher self-efficacy across grades, and promoted performance among third and fourth graders, but did not benefit second graders. Future research should apply strategy self-verbalization to other language skills and should explore the effects of covert fading.     

Measuring teachers’ content knowledge of language and reading

In the context of a longitudinal, four-year study of reading instruction in low-performing, high-poverty urban schools, we surveyed teacher knowledge of reading-related concepts, and established a modest predictive relationship between teachers’ knowledge, classroom reading achievement levels, and teachers’ observed teaching competence. There were significant associations among these variables at the third and fourth grade levels. To obtain this result, measures of teacher content knowledge in language and reading were refined in a three-stage process. Our purpose was to explore the type and level of questions that would begin to discriminate more capable from less capable teachers, and that would have a predictive relationship with student reading achievement outcomes. After experimenting with measurement of K-2 teachers’ content knowledge (Form #1), we piloted a Teacher Knowledge Survey with 41 second and third grade teachers in one study site (Form #2). We then refined and expanded the Survey (Form #3) and administered it to 103 third and fourth grade teachers in both project sites. Teachers’ misconceptions about sounds, words, sentences, and principles of instruction were pinpointed so that professional development could address teachers’ needs for insight and information about language structure and student learning.     

Strategic competence: Applying Siegler’s theoretical and methodological framework to the domain of simple addition

In this study we investigated the variability, frequency, efficiency, and adaptiveness of young children’s strategy use in the domain of simple addition by means of the choice/no-choice method. Seventy-seven beginning second-graders, divided in 3 groups according to general mathematical ability, solved a series of 25 simple additions in 3 different conditions. In the first condition, children could choose whatever strategy they wanted to solve each problem. In the second and third condition, the same children had to solve all problems with one particular strategy, respectively adding up to 10 and retrieval. The results demonstrate that second-graders as a whole choose adaptively between retrieval, decomposition, and counting strategies when solving simple additions, and that they use these strategies neither equally frequently nor equally efficiently. Furthermore, our results indicate that children with different mathematical ability use generally the same strategies to solve these problems, but differ in the frequency, accuracy and adaptiveness with which they apply these strategies. Finally, this study documents the value of the choice/no-choice method to assess the adaptiveness of young children’s strategy use in the domain of early arithmetic.     

The relation between metastrategic knowledge,strategy use and task performance: Findings and reflections from a numerosity judgement task

In the research literature several positions concerning the role played by metacognition in adaptive strategy choice can be distinguished. While many authors adhere so-called metacognitive models of strategy choice and strategy change, others have questioned the extent to which metacognitive factors are associated with strategy choice and task performance and have proposed alternative theoretical frameworks wherein strategy choices are described in terms of associative models. In the present article we report data coming from a larger research project on the development of children’s numerosity judgement strategies and skills. The experimental task involved judging numerosities of colored blocks presented in a rectangular grid. Participants were 59 second grade and 50 sixth grade children, whose strategic performance data — obtained by means of a systematic analysis of their response-time patterns — were compared with interview data collected at the end of the experiment. The major result of this comparison is that not only the children from the oldest age group, but also the children from the youngest age group showed clear evidence of metacognitive awareness and understanding of different aspects of their strategic performance.     

Perceptions of Learning: Interviews with First and Second Graders in a Hungarian Primary School

The paper discusses children’ attitudes towards school and learning soon after entering primary school in Hungary. First and second grade primary school students (N?=?33) were interviewed. The interviews explored the following questions: What are the teachers’ and the children’s roles in the classroom? What is learning? Where do children learn? What kind of learning strategies do students use in arithmetic and reading? How are students evaluated in the school? What do students like best about school? The data suggest that the children quickly adapt to the school environment and, on the whole, have a positive attitude towards school and learning but—with a few exceptions—their views on the role of schooling in life reflect traditional, school subject centred goals and values and little awareness of the learning process.     

Procedural and conceptual changes in young children’s problem solving

This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach, clinical interviews were conducted with ten 5–6-year-old children. The aim was to document how children combine knowledge of addition facts, calculation procedures and arithmetic concepts when solving a multiple-step task and how children’s application of different types of knowledge and overall solving approach changes and develops when children engage with solving the task in a series of problem solving sessions. The study documents children’s pathways towards developing a more effective and systematic approach to multiple-step tasks through different phases of their problem solving behaviour. The analysis of changes in children’s overt behaviour reveals a dynamic interplay between children’s developing representation of the task, their improved procedures and gradually their more explicit grasp of the conceptual aspects of their strategy. The findings provide new evidence that supports aspects of the “iterative model” hypothesis of the interaction between procedural and conceptual knowledge and highlight the need for educational approaches and tasks that encourage and trigger the interplay of different types of knowledge in young children’s arithmetic problem solving.     

Depth of lexical knowledge among bilingual children: the impact of schooling

The majority of studies examining the language and literacy skills of second generation immigrant bilingual children have focused on the breadth of lexical knowledge in populations with a low level of involvement in literacy activities. This study extends previous work in three ways. First, we focused on a sample of second generation immigrant bilingual children from favorable socio-cultural backgrounds. Second, we examined whether these children show lexical knowledge gaps in their second language on various measures of breadth and depth, as compared to their monolingual peers. Finally, we asked whether this gap tends to increase, remain stable, or decrease with formal schooling. Bilingual (n?=?70) and monolingual (n?=?55) children between the ages of 7 and 8?years were evaluated on measures of depth and breadth of lexical knowledge in the second language of the bilingual group. Both groups were tested twice: at the beginning of second grade and at the beginning of third grade. The findings indicate a significant gap between the target groups with respect to most measures of both depth and breadth at the beginning of second grade. However, after a year of schooling, the bilingual children showed significant progress in their lexical knowledge in their second language. The discussion addresses theoretical and clinical implications of these findings.     

Gender Differences in Arithmetic Strategy Use: A Function of Skill and Preference

This study was designed to examine whether first-grade boys' use of retrieval and first-grade girls' use of manipulatives reflected gender differences in their abilities to use these strategies or gender differences in preferences for strategy use. Eighty-four first-grade students, 42 boys and 42 girls, from two suburban elementary schools participated in this study. The children solved basic arithmetic problems under two conditions: a free-choice condition in which they were allowed to solve the problems any way they preferred and a game condition in which the children's strategy use was constrained so that all children used the same strategies on the same arithmetic problems. Strategy use during the free-choice session replicated the findings of earlier research indicating that girls tend to use strategies utilizing manipulatives and boys tend to use retrieval. During the game condition, when we controlled the types of strategies children used on different problems we found that boys were as able as girls to calculate solutions using manipulatives. Girls, however, were not as capable as boys in their retrieval of answers to arithmetic problems from memory. No differences were found in error rates or speed of retrieval. Gender differences were found in the variability of correct retrieval, with boys being significantly more variable than girls.     

Increasing explanatory behaviour,problem-solving,and reasoning within classes using cooperative group work

The present study builds on research that indicates that teachers play a key role in promoting those interactional behaviours that challenge children’s thinking and scaffold their learning. It does this by seeking to determine whether teachers who implement cooperative learning and receive training in explicit strategic questioning strategies demonstrate more verbal behaviours that mediate children’s learning than teachers who implement cooperative learning only. The study also sought to determine whether students who receive training in explicit questioning strategies demonstrate more explanatory behaviour than their untrained peers, and, as a consequence, do these same students demonstrate more advanced reasoning and problem-solving skills on follow-up reasoning and problem-solving tasks. The study involved 31 teachers in two conditions, the cooperative + strategic questioning condition and the cooperative condition, and two groups of students from each teacher’s classroom. The results show that the teachers in the cooperative + strategic questioning condition used significantly more mediating behaviours than their peers in the cooperative condition. The study also showed that the children in these teachers’ classes engaged in more elaboration and obtained significantly higher scores on the follow-up reasoning and problem-solving tasks. The study demonstrates the importance of explicitly teaching strategic questioning strategies to children during cooperative learning.     

THE CONDITIONAL AND INTERACTION EFFECTS OF EPISTEMOLOGICAL BELIEFS ON THE SELF-REGULATED LEARNING OF COLLEGE STUDENTS: Cognitive and Behavioral Strategies

This study examines the conditional and interaction effects of each of four dimensions of the epistemological beliefs of college students regarding the ability to learn, the speed of learning, the structure of knowledge, and the stability of knowledge on four measures of the cognitive components (elaboration, rehearsal, organization, metacognition) and four measures of the behavioral components (effort regulation, management of time and study environment, peer learning, help seeking) of self-regulated learning strategies. Students with more sophisticated beliefs about the nature of knowledge and learning were more likely than their peers to use educationally productive cognitive and behavioral strategies in their learning. Beliefs about one’s ability to learn had the most significant and substantial effects, and the structure of knowledge had the second most significant and substantial effects on students’ use of self-regulated cognitive and behavioral learning strategies. Although a student’s belief about the stability of knowledge by itself had a statistically significant effect on only one learning strategy, this belief served as moderator for six of the 11 statistically significant interaction effects of epistemological beliefs on the use of cognitive and behavioral learning strategies. Implications of these findings for theory, research, policy and practice are examined.     

PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS

Many factors influence a student’s performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils’ real-world knowledge, which support the construction of a ‘situation model’. In this study, we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process, and we assess the effects of the situation model on pupils’ problem solving performance. The sample is composed of 750 pupils of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec, Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem. Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem. The situation model influences pupils’ problem solving performance, but this influence depends on the type of information included in the problem statement, as well as on the arithmetic skills of each individual pupil.     

Supporting Oral Second Language Use: A Learning Experience in a First Grade German Immersion Class

This article describes a learning context in which the first grade classroom teacher creates a learning community where she uses different teaching strategies to encourage children’s second language use and learning. The first graders share, discuss, and learn both the second language (German) and content.     

Aggressor/victim subtypes and teacher factors in first grade as risk factors for later mental health symptoms and school functioning

In a sample of 244 first graders, we identified four subtypes of children based on multi-informant measures of victimization by peers and aggression toward peers: aggressive victims (AV), non-victimized aggressors, non-aggressive victims, and non-aggressive, non-victimized (i.e., normative) children. We examined the differences between the aggressor/victim groups concurrently and two years later in third grade in terms of both mental health symptoms (severity and directionality) and school functioning (academic competence and school engagement). AV showed the worst results for mental health, academic competence, and school engagement concurrently and two years later. The role of first-grade teacher experience and education in predicting third-grade outcomes was also the subject of examination. Significant interactional effects were found between both AV and teacher experience and education. Most notably, the education level of first-grade teachers interacted with AV status to predict school engagement, such that the least engaged students at third grade were AV whose first-grade teachers had no schooling beyond a bachelor’s degree.     

Interactive Homework: A Tool for Fostering Parent–Child Interactions and Improving Learning Outcomes for At-risk Young Children

The notion that parent involvement impacts student learning outcomes for children who are at risk for failing academically has been supported by prominent early childhood education experts. Recent attention has been given to specific ways parents can help increase student learning through their interactions with children as they complete home learning activities. It is important to note that the term parent is used interchangeably with the terms adult, guardian and family member. The term “at-risk reader” refers to readers who are at risk of failing school because of reading deficiencies. This report will examine whether parent training to increase parent–child interactions during the completion of second grade Interactive Homework Assignments (IHA) can facilitate increases in a student’s ability to draw inferences from reading selections, a skill closely aligned with proficiency in reading acquisition. The second grade level was chosen because these children were those whose teachers were concerned with preparing them to take the third grade SAT9. Third grade level was not selected because many of their professional development activities were prescribed due to their immediate concern with preparing students to take the SAT9. IHA, for the scope of this study, is homework designed to increase parent involvement and student achievement. The results indicate that specific parent training during a brief period of time, approximately four weeks, has the potential for improving academic performance for academically at-risk students.     

Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance

This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of working memory. Concurrent analyses indicated that mathematics anxiety represents a unique source of individual differences in children’s calculation skills and mathematical applications, but not in children’s geometric reasoning. Furthermore, we found that higher levels of mathematics anxiety in second grade predicted lower gains in children’s mathematical applications between second and third grade, but only for children with higher levels of working memory. Overall, our results indicate that mathematics anxiety is an important construct to consider when examining sources of individual differences in young children’s mathematical performance. Furthermore, our findings suggest that mathematics anxiety may affect how some children use working memory resources to learn mathematical applications.