Differences between Flemish and Chinese primary students’ mastery of basic arithmetic operations

The present paper investigates differences in the process of mastering the four basic arithmetic operations (addition, subtraction, multiplication and division) between Flemish and Chinese children from Grade 3 till Grade 6 (i.e. from 8 to 11 years old). The results showed, firstly, that Chinese students outperformed Flemish students in each grade but that difference in addition, subtraction and division skills between the groups decreased as grade increased. Secondly, the levels of mastery of the four skills varied between Chinese and Flemish students. Multiplication was relatively easier for Chinese students than for their Flemish peers as compared to the other skills (that is, the gap was larger). Third, low achievers experienced comparable learning difficulties in both countries, and higher achievers demonstrated their greater ability early on.     

Chapter 3 Learning style factors and mathematics performance: Sex-related differences

This study examined the relationships among (a) sex; (b) grades in Algebra I, Geometry, and Algebra II; (c) mathematics learning styles and interests; and (d) scores on the PSAT-M, in a sample of high school students enrolled in Algebra II. The average grade in Algebra I was significantly higher for females than for males. Females reported significantly less interest in technical hobbies or careers than did males, less confidence in their ability to excel on mathematical tasks involving cognitive restructuring or applications, and a greater desire for structure when learning mathematics. In a sub-sample, males scored significantly higher than females on the PSAT-M. Scores on the PSAT-M were significantly related to grades in geometry but not algebra.     

Does grading affect educational attainment? A longitudinal study

The purpose of the study was to investigate how grading in primary school affected students’ achievement measured by grades in 7th, 8th and 9th Grade and educational attainment in upper secondary school (12th Grade), and how the effect varied as a function of students’ cognitive ability, gender and socio-economic status. The data derived from the Evaluation Through Follow-Up (ETF) longitudinal project containing information on students who received grades in Grade 6 and students who did not. The subjects were 8558 students born in 1967. A quasi-experimental design was applied where multiple growth and logistic models were fitted to data. The result showed a main significant negative effect of grading on subsequent achievement (Grade 7–9) and there were important differential effects: graded low-ability students received lower subsequent grades through Grades 7–9 and had lower odds to finish upper secondary education, compared to ungraded low-ability students. The gender difference seems to increase over time: graded girls achieve higher grades throughout Grades 7–9 and had higher odds to finish upper secondary education, compared to ungraded girls and graded and ungraded boys.     

Calculation and word problem-solving skill profiles: relationship to previous skills and interest

Abstract

The current study focuses on the calculation and word problem-solving skill profiles at the end of middle school and their relationships to previous skills and interest in math. The sample included 818 (48% boys) Estonian students from 31 schools. Math skills, reasoning, text comprehension, and interest in math were assessed in Grade 8. Latent profile analysis was used to identify latent profiles of calculation and word problem-solving skills in Grade 9 (age 15 years). Five latent profiles were found. Results indicated that students had significantly different math and cognitive skills; however, the interest level for average and lower-achieving students was quite similar. Students with the highest skills had an exceptionally high interest in math, showing that enhancing students’ interest together with academic skills might help to reach a high level of math skills by the end of middle school.     

Learning from comparison in algebra

Mastery of algebra is an important yet difficult milestone for students, suggesting the need for more effective teaching strategies in the algebra classroom. Learning by comparing worked-out examples of algebra problems may be one such strategy. Comparison is a powerful learning tool from cognitive science that has shown promising results in prior small-scale studies in mathematics classrooms. This study reports on a yearlong randomized controlled trial testing the effect of an Algebra I supplemental comparison curriculum on students’ mathematical knowledge. 141 Algebra I teachers were randomly assigned to either implement the comparison curriculum as a supplement to their regular curriculum or to be a ‘business as usual’ control. Use of the supplemental curriculum was much less frequent than requested for many teachers, and there was no main effect of condition on student achievement. However, greater use of the supplemental curriculum was associated with greater procedural student knowledge. These findings suggest a role for comparison in the algebra classroom but also the challenges of supporting teacher integration of new materials into the curriculum.     

Science Process Skills and Cognitive Preference Styles

The study examined the differences in cognitive styles between two comparable groups of students at the Grade 9 (Secondary 3) level, namely the LSS (Lower Secondary Science) group who had been exposed to the practical-based, inquiry-oriented type of science and the non-LSS group of students who had studied the more traditional type of science in the “old” science curriculum. Their differences in science achievement are measured by the common IEA Science Paper-Pencil, Multiple Choice Criterion Test and also, by the Science Process or Practical Test (which measured three levels of process skills, such as the observation/manipulation, reasoning and investigation skills). Variance in science achievement thus measured is examined against the 4 cognitive preference styles of the students, (measured by the Combined Cognitive Preference Inventory) namely the “recall”, “principles”, “applications” and “questioning” modes of thinking. The findings indicated that (a) the attainment of the science process or practical skills was characterised by the type of science curriculum (LSS or non-LSS) and it was significantly associated with the achievement level of students, (b) the cognitive preference pattern covaried according to the students' level of science achievement and the type of curriculum and (c) the weak but significant relationship between performance in the science practical skills and the students' modes of cognitive style have important implications for teachers who are concerned about the intended effects of changes in the science curriculum on the consequent learning behaviour or cognitive outcome of their students.     

The effect of being graded on later achievement: evidence from 13-year olds in Swedish compulsory school

The purpose of the study was to investigate how grading of students in primary school affected achievement measured by grades one year later, and how the effect varied as a function of cognitive ability, gender and socio-economic status. The data derive from The Evaluation Through Follow Up longitudinal project. Through a national curriculum change one group of students received grades and one group of students did not receive grades in the 6th Grade, while both groups of students received grades in the 7th Grade. A quasi-experimental design was thus created, with two comparable groups of students. The subjects were 8558 students born in 1967. Several multiple regression models were fitted to the data. The results showed no main effects of grading on subsequent achievement, but there were important differential effects: graded students with low cognitive ability received lower subsequent grades. The results also showed interaction effects between gender and grading and between gender and cognitive ability.     

A comparison of cognitive skills between completes and dropouts in a college physics course

Separate tests of mathematics skills, proportions and translations between words, and mathematical expression given the first week of class were correlated with performance for students who completed a college physics course (completes) and students who dropped the course (drops). None of the measures used discriminated between completes and drops as groups. However, the correlations between score on the test of math skills and on both of the measures involving mathematical reasoning (proportions, and translations) were dramatically different for the two groups. For the completes, these correlations were slightly negative, but not significant. For the drops, the correlation was positive and signficant at the p < 0.01 level. This suggests the possibility that the students who complete the course tend to have independent cognitive skills for the “mechanical” mathematical operations and for questions requiring some degree of reasoning, while, in contrast, the same skills for students at high risk for dropping overlap significantly. The study also found that when students are given the results of mathematics skills tests in a diagnostic mode, with feedback on specific areas of weakness and time to remediate with self study, the correlation between mathematics and physics is lower than previously reported values.     

The development of science process skills in authentic contexts

Instructional strategies and curriculum sequences aimed at teaching process skills have received considerable attention in science education. On the other hand, the teaching of domain-independent, context-free skills has been subject to criticism on the ground that important aspects of cognitive activities are functions of meaningful contexts. The intent of this study was to examine the development of integrated process skills in the context of open-inquiry laboratory sessions. The data-collection approach was qualitative and included videotapes of laboratory sessions, laboratory reports of students, and the reflective journals kept by the two teachers involved in the study. Forty-eight students from the Grade 11 introductory physics course, 29 students from the Grade 12 physics course, and 60 students from the Grade 8 general science course from an all-boys private school participated in the study. An interpretive research methodology was adopted for construction of meaning from the data. Students worked in collaborative groups during all of the open-inquiry laboratory sessions. Findings from the study indicate that students develop higher-order process skills through nontraditional laboratory experiences that provided the students with freedom to perform experiments of personal relevance in authentic contexts. Students learned to (a) identify and define pertinent variables, (b) interpret, transform, and analyze data, (c) plan and design an experiment, and (d) formulate hypotheses. Findings of this study suggest that process skills need not be taught separately. Integrated process skills develop gradually and reach a high level of sophistication when experiments are performed in meaningful context.     

Cognitive skills among children in Senegal: Disentangling the roles of schooling and family background

We use unique data to estimate the determinants of cognitive ability among 14–17-year olds in Senegal. Unlike standard school-based samples, tests were administered to current students as well as to children no longer – or never – enrolled. Years of schooling strongly affects cognitive skills, but conditional on years of school, parental education and household wealth, as well as local public school quality, have surprisingly modest effects on test performance. Instead, family background primarily affects skills indirectly through its impacts on years of schooling. Therefore closing the schooling gaps between poor and wealthy children will also close most of the gap in cognitive skills between these groups.     

Long-term outcome of the early identification and intervention of reading disabilities

This study examined the longitudinal effects of an early literacy intervention in Kindergarten. A group of children completed reading and cognitive measures between Kindergarten (5–6 years old) and Grade 7 (12–13 years old). Our results showed that 22 % of children were identified as at-risk for reading deficits in Kindergarten, but only 6 % of children had reading difficulties in Grade 7. In Kindergarten, at-risk groups scored lower than not-at-risk groups on measures of word and letter recognition, phonological processing, rapid naming, working memory, and language. We also examined a small group of children who were not-at-risk in Kindergarten, but had a reading disability in Grade 7; these children did not obtain lower scores than average readers on any of our Kindergarten measures. Finally, we illustrated that the trajectory of word reading skills was generally stable, such that most children scored within the average range between Grade 1 and 7. Our results provide evidence for the long-term positive outcomes of early literacy instruction.     

The foundational math skills of Indian children

We leverage data on learning for 101,084 public-school students in grades 4, 6, and 8 across 19 Indian states to diagnose their mathematic skills. These data allow us to diagnose their achievement on less frequently assessed skills. We use a novel approach to estimate the share of students who can meet fourth-grade standards. We find that the foundational skills of children are even lower than previously documented: 52% mastered frequently assessed skills, but only 27% mastered typically unassessed skills. These children also make less progress than believed. Gender gaps in these skills emerge between grades 4 and 6 and persist.     

Effects of the SOLVE Strategy on the Mathematical Problem Solving Skills of Secondary Students with Learning Disabilities

This study examined the effects of explicit instruction in the SOLVE Strategy on the mathematical problem solving skills of six Grade 8 students with specific learning disabilities. The SOLVE Strategy is an explicit instruction, mnemonic‐based learning strategy designed to help students in solving mathematical word problems. Using a multiple probe across participants design, results suggested a functional relation between explicit instruction in the SOLVE strategy and increase in strategy use and computation scores on grade level mathematical word problems for all participants. Additionally, all participants generalized the SOLVE Strategy to other mathematic topics and concepts, and the teacher and students felt the intervention was socially acceptable. Finally, limitations, implications for practice, and suggestions for future research are discussed.     

Translating words into equations: a cognitive load theory approach

The conditions under which explicit instruction in checking, combined with worked examples, may be beneficial in learning how to translate sentences into algebraic equations was examined from the perspective of cognitive load theory. In two experiments it was shown that Grade 8 and 9 students were initially disadvantaged by the inclusion of a checking method. However, after a more substantial period of acquisition, students with a low level of mathematical knowledge performed significantly better after receiving checking instructions than those who did not receive checking instructions. In contrast, higher knowledge students were continually disadvantaged by the inclusion of a checking method. The positive effect of checking for lower knowledge students and the negative effect for higher knowledge students in this domain is a further example of the expertise reversal effect.     

Mathematics achievement and gender: A longitudinal study of selected cognitive and affective variables [grades 6–12]

This study examined the relationship of selected cognitive and affective variables to mathematics achievement for a random sample of 60 students as they progressed through 6th, 8th,10th and 12th grades. A consistent gender difference was found for stereotyping mathematics as a male domain. No consistent significant gender difference between means was found for spatial skills, verbal skill or mathematics achievement. Confidence, verbal skill and spatial visualization were each consistently positively correlated with mathematics achievement for both males and females. No gender difference was found for these correlations. However, spatial skills alone were found to be consistent significant predictors of mathematics achievement for females each year of the study, but not for males. Verbal skill was a consistent significant predictor of mathematics achievement for males, but not for females. The results of this study could lead to a reevaluation of the hypothesis that spatial skills help boys achieve in mathematics.     

Children's cognitive effort and fluency in writing: Effects of genre and of handwriting automatisation

This study investigated the cognitive effort of 5th and 9th graders while writing a text. We manipulated genre (narrative text vs. argumentative text) and tested how level of handwriting automatisation contributes to cognitive effort and fluency in writing. The participants were 23 students from Grade 5 and 21 from Grade 9, who wrote two texts differing in genre while performing a secondary reaction time task. The results showed that cognitive effort interacted with genre. Cognitive effort decreased between Grades 5 and 9 only for writing argumentative text. Handwriting did not contribute to fluency in writing, but contributed to cognitive effort only in 5th-graders' writing of narrative text. The findings are discussed in light of the factors contributing to cognitive effort and fluency in writing.     

Transfer of reading-related cognitive skills in learning to read Chinese (L1) and English (L2) among Chinese elementary school children

This study investigated transfer of reading-related cognitive skills between learning to read Chinese (L1) and English (L2) among Chinese children in Hong Kong. Fifty-three Grade 2 students were tested on word reading, phonological, orthographic and rapid naming skills in Chinese (L1) and English (L2). The major findings were: (a) significant correlations between Chinese and English measures in phonological awareness and rapid naming, but not in orthographic skills; (b) significant unique contribution of Chinese and English rapid naming skills and English rhyme awareness for predicting Chinese word reading after controlling for all the Chinese and English cognitive measures; (c) significant unique contribution of English phonological skills and Chinese orthographic skills (a negative one) for predicting English word reading after controlling for all the English and Chinese cognitive measures; and (d) significant unique contribution of Chinese rhyme awareness for predicting English phonemic awareness. These findings provide initial evidence that developing reading-related cognitive skills in English may have facilitative effects on Chinese word reading development. They also suggest that Chinese orthographic skills or tactics may not be helpful for learning to read English words among ESL learners; and that Chinese rhyme awareness facilitates the development of English phonemic awareness which is an essential skill predicting ESL learning.     

Leveraging the power of peer-led learning: investigating effects on STEM performance in urban high schools

The Peer Enabled Restructured Classroom (PERC) is an instructional innovation developed to address gaps in science, technology, engineering, and math (STEM) in urban high schools. The PERC model changes instruction from teacher led to peer led by bringing peer students into the classroom to lead small-group work. Our study sought to provide empirical evidence in support of the peer-led model as a means of improving STEM learning for tutored students in urban schools. We used propensity score matching to evaluate the innovation's impact on students’ achievement on standardized end-of-course tests in two 9th-grade courses – Integrated Algebra and Biology. Results suggest that by the 2nd year of implementation, enrolment in PERC Biology increased the likelihood of passing. Similar effects were not observed for PERC Integrated Algebra, but when comparing cohorts, we found that the 2nd year was twice as likely to pass as the 1st year. We discuss implications for programme improvement.     

Gender differences in reading achievement and enjoyment of reading: The role of perceived teaching quality

The authors examined the extent to which classroom-specific relationships between students’ gender and their reading achievement and enjoyment of reading are associated with student-perceived teaching quality. Based on a sample of 10,543 ninth-grade students from 427 classrooms, multilevel analyses revealed that effective classroom management, adequate pacing, and a strong focus on language competencies were related to a less pronounced increase of girls’ advantage in reading achievement during Grade 9. High levels of teacher support and focus on language competencies were related to smaller gender differences in enjoyment of reading at the beginning of Grade 9, though not associated with change of these differences over the school year. Our findings suggest that high teaching quality is not only related to higher reading achievement and reading enjoyment in classrooms as a whole, but may also help to mitigate the increase of gender gaps in reading achievement and motivation commonly observed in secondary school.