Mathematical Attainment Research Articles

The Teaching of Mathematics in Japan: an English perspective

Abstract The difference between the education systems of Japan and England are briefly summarised, together with the evidence for mathematical attainment of secondary school pupils. The identification of factors related to the relative success of Japanese pupils as measured by international tests of mathematical attainment is attempted: these are categorised as cultural, organisational, pedagogical and process factors. Mathematics education in England is considered in relation to each of these groups of factors. Much of the ethnographic material is based on personal observation of classes in a number of Japanese secondary schools, presented from the perspective of a secondary school mathematics teacher in England. The practice of mathematics teaching in Japan is in marked contrast in many ways to that prevailing in English secondary schools and is presented as a mirror for English teachers to consider their own practice.

Gender, Ethnic and Socio‐economic Differences in Attainment and Progress: a longitudinal analysis of student achievement over 9 years

AbstractThe size and stability of gender, ethnic and socio‐economic differences in students' educational achievement are examined over a 9 year period. Both absolute differences in cognitive attainment and relative differences in progress are considered. The study, which is part of a follow up of an age cohort originally included in the ‘School Matters’ research, utilises multilevel modelling techniques. Attainment in reading and mathematics is reported at primary school (Year 3 and 5), secondary transfer (Year 6) and in the General Certificate of Secondary Education (GCSE) (Year 11). Whilst differences in achievement related to gender and socio‐economic factors remained consistent and generally increased over time, greater change was found in patterns of ethnic differences. Possible explanations for the findings are discussed, particularly in relation to the debate concerning performance assessment and equity. The importance of adequate control for socio‐economic background in the analysis of ethnic differences is noted.

A Response to Sainsbury, Schagen & Whetton

British Educational Research JournalVolume 21, Issue 2 p. 241-242 A Response to Sainsbury, Schagen & Whetton Julie Davies, Corresponding Author Julie Davies School of Education, ManchesterDepartment of Education, University of Manchester, Oxford Road, Manchester M13 9PL, UKSearch for more papers by this authorIvy Brember, Corresponding Author Ivy Brember School of Education, ManchesterDepartment of Education, University of Manchester, Oxford Road, Manchester M13 9PL, UKSearch for more papers by this author Julie Davies, Corresponding Author Julie Davies School of Education, ManchesterDepartment of Education, University of Manchester, Oxford Road, Manchester M13 9PL, UKSearch for more papers by this authorIvy Brember, Corresponding Author Ivy Brember School of Education, ManchesterDepartment of Education, University of Manchester, Oxford Road, Manchester M13 9PL, UKSearch for more papers by this author First published: April 1995 https://doi.org/10.1080/0141192950210209AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume21, Issue2April 1995Pages 241-242 RelatedInformation

The First Mathematics Standard Assessment Tasks at Key Stage 1: issues raised by a five school study

AbstractThis paper assesses the value parents can put on the mathematical Standard Assessment Task (SAT) score as an indicator of what children are achieving in mathematics. The results of a study of a sample of all the Year 2 children (176) from five randomly selected primary schools within one Local Education Authority (LEA) are presented. Pupils' scores on Mathematics 7, a standardised mathematics test for 7 year‐olds (National Foundation for Educational Research INFER], 1987a), are compared to the mathematics Standard of Assessment Task (SAT) score elicited by them in the previous half term. Results show that children with the same NFER 7 score may be designated Level 1, 2 or 3 on the mathematics SAT. No child in social class three (unskilled, manual) or four (unemployed), comprising 50% of the sample, attained Level 3. Conclusions, based on such a small study, are tentative. There is a need to be aware that measuring a child's attainment in mathematics may be more complicated than simply looking at the SAT results.

A chronometric study of mental addition in profoundly deaf children

AbstractIn attempting to account for inferior mathematical attainment among deaf children of all ages, some researchers have proposed that observed deficits may be partly the result of an absence of vocalization and subvocalization in the acquisition and execution of arithmetic by the deaf. When performing mental arithmetic, hearing children, it is claimed, rely on covert counting mechanisms based on internalized speech, while their deaf counterparts, due to a lack of articulatory prowess, are unable to utilize such mechanisms and instead are forced to adopt other less effective methods based on associative retrieval of arithmetical facts from long‐term memory. The present study sought to throw light on these assertions. Ten prelingually profoundly deaf 12‐13‐year‐olds, and 10 hearing controls were required to solve the 100 simple addition combinations. Analysis of response times revealed strong similarities between the two groups, with all children appearing to employ mechanisms based on covert counting. Implications of the present results are discussed in the light of previous findings.

Gender Differences in Mathematics Attainment of Singaporean Pupils

Abstract This study compares the performance of Singapore boys and girls in Ordinary (‘O’) level Mathematics (Syllabus D). A sample of 88 boys and 88 girls was used to identify some areas of concern as regards gender and Mathematics attainment. The findings of the study were as follows: (i) Boys performed better than girls on Paper I questions. (ii) For the compulsory questions on both papers boys did significantly better than the girls on the following topics – mensuration, statistics, arithmetic, geometry and probability while the girls out-performed the boys on algebra and graphs. (iii) Boys also surpassed girls on the compulsory questions which tested spatial ability. (iv) In Paper II, section B, girls showed a marked preference for questions on algebra and graphs, and vectors in two dimensions while the boys' only marked preference was the question on mensuration. The pupils' grades in Mathematics were also compared with those of the other subjects they took in the English medium examination and it was found that grades in Physics, Science (Chemistry, Physics) and Metalwork – the so called Mathematics-related subjects – did not correlate to the same degree for the two sexes. The Mathematics results of the Singapore candidature in ‘O’ level Mathematics examination revealed that on the whole boys performed better than girls.

Mathematics attainment at inner-city schools: Establishing the need for systematic formative evaluation practices

Recently there has been a great amount of research and professional educator interest in at-risk, poor academically attaining students, especially low socioeconomic status students at U.S. inner-city schools. A major factor that has been hypothesized in the research literature as being associated with poor academic attainment is the lack of critical and timely instructional feedback or formative evaluation. Using a sample of 130 inner-city senior high school students, the perceived quality and quantity of formative evaluation received by these students at their elementary and secondary school levels were assessed. in addition, each student was given a mathematics (pre-algebra) assessment using both a one and two-dimensional format (recognition plus confidence) to determine present levels of mathematics attainment. Finally data were collected from the cumulative grade-level folders of a subset of these students, especially norm-referenced data (NRT) in mathematics, to examine their relationship to scores on the Scholastic Aptitude Test-Quantitiative portion. The study finds that in addition to extremely poor mathematics attainment and poor formative evaluation practices there is little association between SAT (quantitative) scores and the grade-level (mathematics) NRT scores. These findings suggest that parents cannot depend on traditional norm-referenced measures to indicate actual mathematics attainment as these students are progressing through the schools. These findings also challenge urban school administrative personnel to reassess the use of NRT measures to monitor student progress and to develop more comprehensive and systematic formative evaluation procedures and practices for individual students as they progress through each grade level.

The influence of graphic calculator use on translation from graphic to symbolic forms

This article reports a study comparing the mathematical performance of upper secondary school mathematics students for whom a graphic calculator is a standard mathematical tool, with that of students of similar background without regular access to graphing technology. Students were tested on two types of item: symbolisation items, calling for an algebraic description of some cartesian graph; and interpretation items, calling for the extraction of information from some verbally contextualised graph. The findings illustrate that, under appropriate conditions, access to information technology can have an important influence both on the mathematical approaches employed by students and on their mathematical attainment. On the symbolisation items, use of graphic calculators was associated not only with markedly superior attainment by all students, but with greatly enhanced relative attainment on the part of female students.

Language and counting: Some recent results

It has long been recognised that the language of mathematics is an important variable in the learning of mathematics, and there has been useful work in isolating and describing the linkage. Steffe and his co-workers at Georgia, for example, (Steffe, von Glasersfeld, Richardson and Cobb, 1983) have suggested that young children may construct verbal countable items to count objects which are hidden from their view. Although there has been a surge of research interest in counting and early childhood mathematics, and in cultural differences in mathematics attainment, there has been little work reported on the linkage between culture as exemplified by language, and initial concepts of numeration. This paper reports on some recent clinical research with kindergarten children of European and Asian background in Australia and America. The research examines the influence that number naming grammar appears to have on young children’s understandings of two-digit numbers and place value. It appears that Transparent Standard Number Word Sequences such as Japanese, Chinese and Vietnamese which follow the numerical representation pattern by naming tens and units in order (“two tens three”), may be associated with distinctive place value concepts which may support sophisticated mental algorithms.

Gender Differences in Mathematical Attainment at 16 +

Summary Much is made today of ‘equal opportunities’ between the sexes in education. Yet, in mathematics in 1984 there were still only 10 girls achieving good grades to every 15 boys (DES statistics). A study group of one thousand 16+ mathematics scripts revealed that there are certain topics on which boys and girls differ significantly in performance. Comparisons are made with a similar study of GCE Ordinary Level papers in 1973/74 by Robert Wood. The object was to find the precise concepts that give the widest discrepancy between the sexes. These concepts were found to be concerned with scale or ratio, spatial problems, space‐time relationships or probability questions. It was found that there was little relative improvement and that the gap is now just as wide as it was in 1973/74. The areas of difficulty experienced by the girls are essentially the same despite recent ‘equality’ drives.

Father-daughter emotional relationships and mathematical attainment in primary schools

Father-daughter emotional relationships and mathematical attainment in primary schools

Length of preschool hospitalization, multiple admissions and later educational attainment and behaviour.

Differences in educational performance and behaviour at age 10 years between 2900 hospitalized and 11,000 non-hospitalized children in the 1970 British Births Cohort were described previously. In the present analysis associations were found between the length of time children spent in hospital before the age of 5 years and performance on vocabulary tests at age 5 and age 10. Children whose first admission occurred between 2 and 5 years of age were particularly likely to show this association. There was also a relationship between the length of preschool hospitalization and reading and mathematics attainment at age 10. It was the number of times a child was admitted to hospital before the age of 5, rather than the length of stay, which was associated with antisocial and anxious behaviour at age 5. The association was evident when the first admission occurred between 2 and 5 years of age and not before age 2. There was no association with such behaviour at age 10 once social and family factors and readmission between ages 5 and 10 were taken into account. There was a strong association between admission between ages 5 and 10 and behaviour scores at age 10. The results are interpreted as providing evidence for a need to develop the hospital educational service to ameliorate these associations and to review schemes which reduce the anxiety-provoking aspects of hospitalization for young children.

The Second IEA Mathematics Study

Education systems throughout the world place high importance on the teaching and learning of mathematics, and a high level of resource allocation is devoted to maintaining and improving efficiency and effectiveness in these activities. It is, therefore, not surprising that there was widespread interest in and support for a study that was to examine each system's curricula, teaching practices, and student outcomes in mathematics in relation to those of a variety of other systems. In the early 1960s, the IEA conducted the First International Mathematics Study (FIMS), a cross-national study involving 12 countries.' The subsequent 2 decades saw extensive and, in the case of some systems, radical curriculum innovation in school mathematics. A further motive

Factors associated with reading-plus-spelling retardation and specific spelling retardation.

Factors associated with reading-plus-spelling retardation and specific spelling retardation were investigated in a large sample of Dunedin children who were studied longitudinally between the ages of three and 11 years. Those with reading-plus-spelling retardation showed poor performance on WISC-R Verbal subtests relative to non-retarded children, but superior performance on Picture Completion and Object Assembly subtests. The group with reading-plus-spelling retardation also had poor speech articulation but no significant language, motor or neurological dysfunction. Their educational attainment in reading, writing and mathematics was consistently poor. Specific spelling retardation was associated with deficits on WISC-R Arithmetic and Coding subtests, teacher ratings of low attentiveness and poor achievement in writing and mathematics. No language, motor or neurological deficits were apparent in this group.

MATHEMATICAL LOW ATTAINERS CHECKLIST

Summary. To assess the frequency of 24 statements often associated with low attainers in mathematics, a checklist was devised and completed for each of 215 mathematical low attainers aged 9–10 years. Differences between the frequencies of association of the statements with mathematical low attaining boys and girls were tested for significance.

A longitudinal study of children's school mobility and attainment in mathematics

A longitudinal study of children's school mobility and attainment in mathematics

A longitudinal study of children's school mobility and attainment in mathematics

This paper reviews and examines the data on the mathematical attainment of geographically mobile children from a major study recently carried out by the National Children's Bureau (NCB). This investigation was designed to determine whether changes of school, apart from those normally occurring in the British education system, adversely affect children's attainment. The data used was contained in the National Child Development Study, collected over the last 26 years on a cohort of roughly fifteeen thousand children, to investigate whether the educational attainment of mobile children differs from non-mobile children of similar initial ability and socio-economic background. In this paper the data on mathematics attainment contained in the original report have been analysed and considered with the possible implications for schools and classrooms in mind.

Affective Variables and Mathematics Education

to general feelings such as liking/disliking of mathematics, nor is it meant to exclude perceptions of the difficulty, usefulness, and appropriateness of mathematics as a school subject. There are several ways affective variables are related to mathematics learning. It is likely that a student who feels very positive about mathematics will achieve at a higher level than a student who has a negative attitude toward mathematics. It is also likely that a high achiever will enjoy mathematics more than a student who

Learning BASIC programming: a course evaluation

The computer language BASIC is very simple and has achieved widespread acceptance. The demand for teaching BASIC to nonprofessionals is on the increase. The object of this paper is to find what sort of people would be successful in learning BASIC programming. After defining the language and the method of instruction I describe the experiment. Two groups of students are compared in terms of their ability to learn BASIC. The findings indicate that attainment in English language and mathematics play a big role in learning BASIC language or any other programming language.

Rules without reasons?: Some evidence relating to the teaching of routine skills to low attainers in mathematics

Evidence gathered by the Schools Council Low Attainers in Mathematics Project and from HMI surveys of schools suggests a high priority is being placed on the practice of routine skills, especially for low attainers, in both primary and secondary schools. Data from the Concepts in Secondary Mathematics and Science Project, in the form of results from both individual interviews and large‐scale testing programmes, is reviewed to suggest that this policy is not an effective one. Reasons for this, relating to children's levels of conceptual understanding, are discussed.