Creativity, dogmatism, and arithmetic achievement.

This dissertation addresses Danish students’ use and development of mental strategies in single-digit addition in the first years of school and relates it to teaching practices, later mathematical achievement and teachers’ perspectives on teaching and learning of number and arithmetic. The work builds on data from a study of 147 students’ development of strategy use from year one to four, and a study of six year one classes (83 students, six teachers) assessed twice (October/November, April/May) in year one. The latter study also included data from teacher interviews, classroom observations, and students’ achievement in arithmetic, fraction knowledge and word problem solving in year four. From year one to year four, students’ use of counting strategies decreased, and their use of fact-based strategies increased, but with substantial individual variation. On average boys, were two years ahead of girls in strategy use development. Strategy use patterns varied little between classes and did not develop differently across classes in year one. It follows that differences in teaching practice did not result in any traceable differences in the pace of development of strategy use during year one. Measures of strategy use in year one explained variation in mathematical achievement in year four that could not be explained by other year-one variables, achievement test measures included. The results indicate that habits of strategy use are deeply rooted within the individual child and seem to establish either before or at the outset of formal schooling, after which it develops slowly over time. The results highlight the relevance of students’ early understanding of number and arithmetic (i.e. strategy use) both as indicators of later achievement and as a focus for intervention and targeted teaching to support student development in all cases.

Until rather recent years home study or home work has been an integral part of the school program. Simultaneous with the increase in the complexities of our modern social life, the school curriculum of today has been undergoing a gradual change. Such outstanding social occurrences of modern times as industrialization, urbanization of our people, and newer methods in transportation and communication have been greatly accountable for the transfer of so many of the early responsibilities of the home to the school. The purpose of this study is to evaluate the effect of homework on seventh and eighth grade achievement in arithmetic; to give a quantitative expression as to the nature and extent of the variations in achievement existing in grades s even and eight of St. Joseph's Parochial School, Hays, Kansas.

To determine the efficacy of assessment and selection procedures used by a private, eight-grade, elementary school in suburban New York, the records of the 43 SS, 22 boys and 21 girls, who remained in the school until graduation were studied. Clarification of some basic questions was sought: Is it feasible to identify scholastic aptitude before first grade entrance? How stable and consistent is the pattern of achievement? Which factors, intellective, familial, and noncognitive, are associated with academic achievement? The selection and classification prediction composite was based on: the Stanford-Binet; a five-point personality assessment, derived from a clinical impression of such achievementrelated features as drive, social maturity, independence, stability, and adjustment; and educational level of the home. The criterion variable was the Stanford Achievement Test, which was administered to each student in May of each year. Third and Sixth grade group Otis IQ scores were also available for correlation with both the Binet and achievement scores. The following are some of the principal findings; supporting tables have been filed with the American Society for Information Sciences.' First, all three mean IQ scores were at least 17 points above the assumed mean IQ of 100, indicating that the school is atypical. Second, 23 of the 24 correlations between IQ and reading achievement were significant ( p = .01) as were 19 of the 24 correlations between IQ and arithmetic achievement. Third, educational level of the home was significantly correlated with reading achievement ( p = .01) for Grades 1 and 2 and with arithmetic achievement for Grades 2 and 4. Fourth, no single correlation between the personality predictor and reading achievement reached the .O1 level, but the rs between personality and arithmetic achievement were significant ( p = .01) for Grades 1 and 2. Fifth, the correlations among the three IQ tesa were consistently high. Sixth, achievement performance was consistent through the grades. Thus, it does seem feasible to identify scholastic productivity before entrance to first grade. A pattern of achievement is set before formal schooling begins and remains fairly consistent through the eighth grade. This pattern is related to the educational level of the home, suggesting that cultural factors and education-mindedness may be the determining features of academic achievement.

Research in children points to aerobic fitness as a source of individual differences in academic achievement. By examining the indirect effects of executive functions (EF) and intelligence on the relationship between aerobic fitness and academic achievement, the present study provides novel insight about the cognitive mechanisms underlying this relationship. 218 children (8–10 years) completed the following assessments: (i) a VO2max test to assess aerobic fitness; (ii) four tasks tapping components of EF (i.e., inhibition and cognitive flexibility); (iii) sub-tests of the Kaufman Brief Intelligence Test to assess fluid and crystallized intelligence; and (iv) sub-tests of arithmetic, spelling, and reading achievement (WRAT 3rd edition). Structural equation modeling (SEM) was conducted to examine the indirect role of EF and intelligence on the relationship between aerobic fitness and sub-domains of academic achievement. Covariate analyses included age, pubertal timing, and socio-economic status. Preliminary analysis via linear regression showed a direct effect of aerobic fitness on arithmetic achievement, whereas no effect was observed on spelling and reading achievement. Importantly, multiple mediation SEM revealed the direct effect of aerobic fitness on arithmetic achievement disappeared after accounting for the indirect effects of EF, whereas intelligence did not contribute significantly on this complex mediation process. Moreover, among EF components, cognitive flexibility, was the main driver of the relationship between aerobic fitness and arithmetic achievement. Unpacking which components of EF and intelligence affect the link between aerobic fitness and academic achievement, holds the promise of better understanding the heterogeneity still present in the literature.

Complexity of Abilities in Arithmetic,—In all attempts at measurement the primary problem is that of defining the ability, quality, or factor to be measured. In this respect the abilities in arithmetic offer no exception. When the question is raised as to the exact meaning of that which we call arithmetical ability the most capable student of the psychology of arithmetic must “side-step” with a statement which attempts to state the various directions in which the abilities in arithmetic function. One does not need to be a careful student of Education, Psychology or Mathematics to be aware of the fact that it is impossible to point out a particular mental activity or mental product and say, “This alone is arithmetic or the exercise of arithmetical ability.”

"A Comparison of the Mother and Father Schemata of Achievers and Under-Achievers: A Study of Primary Grades and Achievement in Arithmetic." The Journal of Social Psychology, 78(2), pp. 295–296

For the convenience of the reader, the format and much of the information published in Dr. Buswell's presentation has been incorporated in the following article.

An Experimental Study of the Relation of Homework to Achievement in Arithmetic

The progress in arithmetic learning of elementary-school children has always been of concern to teachers, parents, and the lay public. The recent crash program in the sciences has led to even greater interest in children's arithmetic achievement. Our colleges and universities have also been demanding a science- and mathematics-orientated student.

Numerical processing profiles in children with varying degrees of arithmetical achievement

This study involved the construction of a social desirability (SD) scale for children and an investigation of intercorrelations among SD, anxiety, lie scales, and reading and arithmetic achievement. The SD scale was empirically derived from an item pool on the basis of strength of agreement as to SD response among children responding under the SD-set. SD correlated moderately and negatively with two of the three anxiety scales, positively with one of two lie scales, and was uncorrelated with achievement. A factor analysis of the intercorrelations among the eight tests defined three rotated, nonorthogonal factors labeled anxiety, achievement, and SD.

Differences in measures of self-esteem and anxiety between children from three ethnic subgroups in each of three upper elementary grades, who had been divided by placing high or low on scores on tests of reading achievement, arithmetic achievement, and scholastic aptitude, were studied. In contrast to previous findings by Frerichs (1971), no self-esteem differences were noted in high vs. low reading achievement groups of Black children. Self-esteem and anxiety differences between subsamples of high vs. low achievement and of high vs. low scholastic aptitude were inconsistent across ethnic groups. Sample characteristics, differences in conditions for instrument administration, and varying child-adult relationships were suggested as possible sources of influences upon the findings.

Examining the relevance of basic numerical skills for mathematical achievement in secondary school using a within-task assessment approach

A comparison was made between the performance at eight years of age of 63 children who were born after elective induction of labour, and 29 spontaneously born children. The children had been tested previously at five years of age. Tests of reading and arithmetic achievement, visuomotor coordination, aural-visual coordination, auditory discrimination, and behavioural rating scales were administered. On two of the 12 measures (reading comprehension and euroticism) the induced children performed better than the spontaneously born. On all other measures there were no significant differences. There appeared to be no evidence of specific learning disabilities or behavioural problems among the induced children.

The use of manipulative materials and visual aids in teaching arithmetic is widely accepted by teachers and those concerned with the teaching of arithmetic. The Nationa Defense Education Act is an expression on the national level of a belief in the value of manipulative materials for instruction. While most modern arithmetic programs contain suggestions on the use of visual aids and manipulative materials, much remains to be done in evaluating the effectiveness of selected materials. Cost of materials varies considerably. One main concern of school systems is the cost of materials. Are inexpensive materials as effective as more expensive ones?