Optimizing Early Mathematics Experiences for Children from Low-Income Families: A Study on Opportunity to Learn Mathematics

Both the National Council of Teachers of Mathematics and the National Association for the Education of Young Children recognize that well-designed opportunity to learn mathematics can help improve mathematics achievement of students from low-income families and from minority backgrounds. Using data from a nationally representative sample, the Early Childhood Longitudinal Study-Kindergarten cohort, this study empirically examined a subset of children from low-income families to determine whether African American and Caucasian students have differential opportunity to learn mathematics and the extent to which opportunities to learn predict gains in mathematics achievement at kindergarten. Results indicated African American kindergartners have differential opportunity to learn mathematics than their Caucasian peers from low-income families. African American students were found to have received, on average, more reported instructional time spent on mathematics, higher use of math manipulatives, worksheets, textbooks and chalkboard work than their Caucasian peers. Moreover, greater opportunity to learn mathematics predicted higher mathematics achievement for both African American and Caucasian students from low-income families, specifically, opportunity to learn skills such as telling time, using measurement tools accurately, estimating quantities, and knowing the value of coins and cash.     

Effects of a Learning Information System on Mathematics Achievement and Classroom Structure

Abstract

The authors examined the effects of implementing an instructional system that automates application of evidence-based components of effective instruction on student mathematics achievement and on classroom behaviors known to be related to overall student achievement outcomes. A treatment group of 157 4th- and 5th-grade students used the intervention in conjunction with the Everyday Math curriculum. Student performance was compared with a within-school control group of 61 4th- und 5th-grade students, as well as all 4th- and 5th-grade students in the district (N = 6,385). The students in the control groups received only the Everyday Math curriculum. Results indicate that the implementation of the instructional management system as an enhancement to Everyday Math resulted in an increase in the amount of time spent on classroom activities that researchers have identified as contributing to positive academic outcomes. Furthermore, students who used the Accelerated Math program demonstrated greater mathematics achievement gains than did the control groups.     

The Relation Between Executive Functions,Fine Motor Skills,and Basic Numerical Skills and Their Relevance for Later Mathematics Achievement

Research Findings: This study examined the interrelations between fine motor skills, executive functions, and basic numerical skills in kindergarten as well as their predictive value for mathematics achievement in 2nd grade in a sample of 136 children. Structural equation modeling techniques were used to uncover the unique predictive value and mediation of 4 predictors. The results indicated that each of these factors made a unique contribution to the prediction of later mathematics achievement; when estimated simultaneously, basic numerical skills were the strongest predictor, which suggests that domain-specific factors have a greater impact on mathematics achievement than domain-general factors. A strong direct and indirect predictor was updating. Nevertheless, indirect effects of fine motor skills and an inhibition/switching factor indicated that domain-general skills have a direct impact on early domain-specific precursors and through them an indirect effect on mathematics achievement. Practice or Policy: These findings suggest that the relationship between motor skills, executive functions, and mathematical skills is more complex in its nature. Therefore, to achieve the best outcome, all skills should be promoted if a child has difficulties with mathematics.     

Teaching Preschoolers to Count: Effective Strategies for Achieving Early Mathematics Milestones

Attention to early childhood mathematics instructional strategies has sharpened due to the relatively poor mathematics performance of U.S. students in comparison to students from other countries and research evidence that early mathematics skills impact later achievement. Early Childhood counting skills form the foundation for subsequent mathematics learning. In this article, we discuss the milestones of counting development and examine preschool classroom mathematics observations through the lenses of two CLASS Dimensions, Concept Development and Instructional Learning Formats. Recommendations for effective instructional strategies around counting and suggestions for incorporating mathematics instruction into storybook reading are provided.     

Mathematics achievement,language and cognitive development: Classroom practices in Papua New Guinea

A case study was conducted of mathematics instruction at five sites in Papua New Guinea. Trial instructional materials were developed, teachers received inservice training and implementation was carefully monitored for a six-week period. English and mathematics achievement instruments and eight measures of cognitive development were administered to a sample of 201 students in grades two, four and six. Mathematics and language achievement varied significantly among the five sites. Students at all grade levels exhibited poor application of problem solving skills while showing computation, measurement and mathematical language abilities superior to results previously reported. English reading and measures of conservation and classification competence were highly correlated with mathematics achievement. Correlations between memory measures and mathematics achievement decreased from grade two to grade six while correlations between measures of language and cognitive development and mathematics achievement tended to increase. The results indicated that the non-consumable student textbooks ameliorated to some extent the problems associated with non-native language instruction for the students involved in the study. It was concluded that locally developed textbooks with an appropriate language load would enhance mathematics learning, particularly in remote-rural areas where current teaching conditions and lack of materials interact with poor English skills to create an imbalance in achievement.     

Student learning emotions in middle school mathematics classrooms: investigating associations with dialogic instructional practices

Emotions are central to how students experience mathematics, yet we know little about how specific instructional practices relate to students’ emotions in mathematics learning. We examined how dialogic instruction, a socially dynamic form of instruction, was associated with four learning emotions in mathematics: enjoyment, pride, anger, and boredom. We also examined whether these associations differed by student gender and prior mathematics achievement. The sample consisted of 1307 sixth through eighth grade students (51.6% female, 59.0% White, 30.8% African American, and 10.3% other race; 42.3% receive free/reduced price lunch) from 70 mathematics classrooms. Results indicated that teachers who used more dialogic mathematics instruction had students who reported more enjoyment and pride, and less anger and boredom. Males and low-achieving students reported more positive and fewer negative emotions with greater dialogic instruction compared to their female and high-achieving counterparts.     

Mathematics education and learning disabilities in Spain

In the first part of this article, we describe the basic objectives of the math curriculum in Spain as well as the basic contents, teacher resources, and obstacles perceived in mathematics instruction. Second, we briefly describe the concept of learning disabilities (LD) as they are currently defined in Spain. As stated in the recent educational reform, a student with LD is any student with special educational needs. The emphasis is placed on the educational resources that these students need in order to achieve the curricular objectives that correspond to their age group or grade. Third, we comment specifically on the educational services model and the evaluation and instructional procedures for students with math learning disabilities. Finally, we describe some lines of research that have appeared in the last few years in Spain that have led to the development of new evaluation and intervention procedures for students with LD in computation and problem solving.     

Designing Curriculum-Based Mathematics Professional Development for Kindergarten Teachers

This study examines the influence of a year-long mathematics professional development program on Kindergarten teachers’ beliefs, content knowledge, instructional practices, and their students’ achievement. The professional development program is grounded in the theoretical construct of learner-centered professional development and focuses on supporting teachers’ integration of standards-based pedagogies aligned with the Common Core State Standards in Mathematics. Data analysis included examining 15 Kindergarten teachers’ mathematics content knowledge, their beliefs about mathematics, their enactment of student-centered pedagogies, and student achievement on curriculum-based assessments. Findings indicated that teachers adopted more student-centered pedagogies and embraced more student-centered beliefs about mathematics teaching during their time in the project. Further, Kindergarten teachers also demonstrated gains in their mathematical content knowledge, and those content knowledge gains were linked to gains in student achievement.     

Exploring the relationship between teacher enjoyment of mathematics,their attitudes towards student struggle and instructional time amongst early years primary teachers

In this study we explored the relationship between teacher enjoyment of teaching mathematics, their attitudes towards student struggle, and the amount of time teachers spent teaching mathematics. Ninety-eight primary educators were surveyed regarding their attitudes and behaviors towards mathematics instruction. Hierarchical regression analyses revealed that teacher enjoyment of teaching mathematics explained variance in both teacher attitudes towards student struggle and instructional time spent on mathematics, even after relevant educator characteristics were accounted for. Findings suggest that teacher enjoyment of teaching mathematics in the early primary years has important implications for both the quality and quantity of mathematics instruction students receive.     

The impact of alternative authentic assessment outcomes in Palestinian fourth grade math classrooms

Focusing on evaluating students’ performance in basic math classrooms, the researchers in this study examined the impact of alternative assessments on learning outcomes in fourth grade Palestinian classrooms. Representing a large sector of education in the Palestinian territories, fourth grade students were randomly selected to participate in the study in which they participated in various math instructional and assessment activities throughout multiple lessons and cycles. Alternative assessment approaches were used including student self- assessment, peer assessment, and teacher assessment in terms of three main achievement levels to measure the extent to which students learned the math concepts by recall and remembrance, ability to apply, and making inferences. Mixed Design ANOVA measures were used to analyze and interpret the results which showed significant trends and correlations across the four cycles of math instruction and indicated that alternative authentic assessment methods have had a positive impact on students’ learning and application of math. Implications for integrating authentic assessment measures as well as peer and self- assessments were drawn in light of the promising outcomes of augmenting student motivation and developing critical life-long skills.     

The relation between classroom management and mathematics achievement: A multilevel structural equation model

The impact of teachers on their students’ academic achievement continues to be an area of inquiry. One area not fully explored is the relation between teachers’ behavior and classroom management (CM) skills, student motivation, and student achievement. We examined these relations using a multi‐level structural equation model. Data included Behavior Management subscale scores of the Classroom Assessment Scoring System for 247 fourth and fifth grade teachers, indicators of academic motivation, and end‐of‐year state standardized mathematics assessment results for 4,847 students from the National Center of Teacher Effectiveness Main Study. The results indicate teachers’ CM skills have a significant direct effect on student motivation and a significant indirect effect on students’ math achievement, suggesting that students in classrooms of teachers with better CM are more motivated to learn math and have higher math achievement scores. This underscores the importance of helping teachers increase their use of evidence‐based classroom management techniques.     

The Growth and Nature of Research Interest in Arithmetic and Reading

ABSTRACT

The author examined whether mathematics instruction provided by kindergarten teachers is related to children's mathematics learning during the kindergarten year based on the children's socioeconomic status and race. Hierarchical linear modeling was employed using a large sample of kindergarten students to estimate relationships between the teacher's instructional approach (e.g., concrete-spatial, interpersonal, linguistic) and children's mathematics skills. Results showed that the teacher's instructional approach was selectively related to children's mathematics learning. Students in classrooms where teachers frequently employed a concrete-spatial instructional approach learned more during the kindergarten year. Students from lower socioeconomic backgrounds benefitted more from teachers who often employed an interpersonal approach, and Black/African American students benefitted less from classrooms where teachers relied more on a linguistic approach. The findings suggest that kindergarten teachers’ instruction needs to employ varied methods that take into account students’ mathematics skills and background characteristics.     

Factors that Differentiate Mathematics Students in Cyprus,Hong Kong,and the USA

The purpose of this study was twofold: to examine how attitudinal and instructional variables differentiated 4th-grade students in Cyprus, Hong Kong, and the USA; and to determine how those variables were related to math performance on the TIMSS test. A discriminant analysis was performed to examine how those variables differentiated the students in the 3 countries. The most striking result was that the students from all 3 countries, who were similar to the average students in Cyprus, had the highest achievement within their countries. Thus, 4th-grade students who liked math, who thought it was important to do well in math for their friends, who did not need private instruction, and who had not been taught using computers or small group procedures, tended to be the better students. However, students who were similar to the average USA student had the lowest achievement within each of the 3 countries.     

Selecting Students and Services for Compensatory Education: Lessons from Aptitude--Treatment Interaction Research

In this keynote review, we draw from recent theory and research on individual differences, learning, and instruction to answer questions about the selection of students and the provision of services in compensatory education. In addressing the question regarding provision of services to Chapter 1 students, we focus on five issues: (a) fragmentation versus integration of what is to be learned, (b) time as a variable, (c) the provision of direct instruction and possible alternatives to direct instruction, (d) compensatory education for aptitude processes, and (e) instructional grouping decisions. Current Chapter 1 services may promote fragmentation rather than integration of the academic content for the student. Moreover, Chapter 1 services focus more on teaching basic skills than on promoting higher-order thinking in reading and mathematics. We discuss problems associated with current selection procedures such as misclassification and "labeling" of Chapter 1 students. We conclude with recommendations for educational researchers and policymakers.     

Teachers’ use of class time and student achievement

We study teachers’ choices about how to allocate class time across different instructional activities, for example, lecturing, open discussion, or individual practice. Our data come from secondary schools in England, specifically classes preceding GCSE exams. Students score higher in math when their teacher devotes more class time to individual practice and assessment. In contrast, students score higher in English if there is more discussion and work with classmates. Class time allocation predicts test scores separate from the quality of the teacher's instruction during the activities. These results suggest opportunities to improve student achievement without changes in teachers’ skills.     

Classroom instructional quality,exposure to mathematics instruction and mathematics achievement in fifth grade

This study examined the quality of teacher–child interactions and exposure to mathematics instruction as predictors of 5th grade student’s mathematics achievement. The sample was a subset of the children involved in the NICHD–SECC longitudinal study (N = 657). Results indicate that, even after controlling for student demographic characteristics, more exposure to mathematics instruction was related to increased fifth grade mathematics achievement for both calculations and applied problems assessments, but there was no main effect for improved instructional quality. Findings also indicate that, in classrooms where lower instructional quality was observed, greater exposure to mathematics instruction predicted improved mathematics achievement. Findings are discussed in terms of differing aspects of mathematics instruction and the possible compensatory role of exposure to instruction in classrooms of lower quality.     

Motor Skills and Executive Function Contribute to Early Achievement in East Asia and the Pacific

Research Findings: This study examined the contributions of motor skills and executive function (EF) to early achievement. Participants were 7,797 children (3,889 girls) between 36 and 72 months of age from 6 countries in East Asia and the Pacific. Fine and gross motor skills, EF, language and literacy achievement, and mathematics achievement were evaluated using the East Asia-Pacific Early Child Development Scales, a tool that assesses child development in 7 domains. Children’s caregivers provided demographic information. There were 3 salient findings. First, gross and fine motor skills predicted both language and literacy and mathematics achievement. Second, in general, fine motor skills contributed more to the prediction of early achievement than gross motor skills. However, there were no differences between the contributions of fine and gross motor skills to the prediction of early language and literacy in Papua New Guinea or early mathematics in Timor-Leste. Third, EF partially mediated the relation between both early achievement and gross and fine motor skills in the overall sample, Cambodia, and Timor-Leste and fully mediated the association of gross motor skills and early achievement in China, Mongolia, Papua New Guinea, and Vanuatu. Practice or Policy: Implications of the findings for early childhood education are discussed.     

Developing a Multi-Dimensional Early Elementary Mathematics Screener and Diagnostic Tool: The Primary Mathematics Assessment

There is a critical need to identify primary level students experiencing difficulties in mathematics to provide immediate and targeted instruction that remediates their deficits. However, most early math screening instruments focus only on the concept of number, resulting in inadequate and incomplete information for teachers to design intervention efforts. We propose a mathematics assessment that screens and provides diagnostic information in six domains that are important to building a strong foundation in mathematics. This article describes the conceptual framework and psychometric qualities of a web-based assessment tool, the Primary Math Assessment (PMA). The PMA includes a screener to identify students at risk for poor math outcomes and a diagnostic tool to provide a more in-depth profile of children’s specific strengths and weaknesses in mathematics. The PMA allows teachers and school personnel to make better instructional decisions by providing more targeted analyses.     

Using a Curriculum-Based Instructional Management System to Enhance Math Achievement in Urban Schools

More than two-thirds of students living in U.S. low-income urban areas have not demonstrated basic levels of math achievement. Teachers are confronted with a difficult task of meeting the needs of an increasingly academically diverse population of urban students. There is a well-confirmed knowledge base on effective instruction, but teachers need massive amounts of information for effective, sustainable improvement and data-driven decision making. The bottleneck to improving teaching and learning is a lack of systematic, usable information on individual student performance and progress at the classroom level.

We examined the effect of adding a computerized curriculum-based instructional management system as an enhancement to ongoing math instruction. Two math tests were used to contrast performance gains for students in the treatment group in comparison to two control groups: a same-school math instruction-only group, and a randomly selected district-wide math instruction-only group. Teachers in our experimental group implemented the treatment with varying degrees of fidelity, so we examined the impact of the level of implementation on student performance. We also examined the extent to which the treatment worked differently for high, middle, and low achieving students.

There were positive outcomes for students in classrooms in which teachers used the instructional management system (Accelerated Math [AM]). In fact, students enrolled in classrooms where teachers implemented the AM intervention to a greater degree benefitted the most. Gains in math performance were consistent for high, middle, and low performing students. Use of a computerized instructional management system enabled teachers to differentiate instruction, make instructional adaptations for students of all ability levels, and provide students with relevant practice and immediate informed feedback. It also resulted in significant gains in math achievement.