Educating Teachers to Teach Multiplicative Structures in the Middle Grades

The middle-grades mathematics related to multiplicative structures has undergone careful scrutiny over the past decade. Researchers have identified the types of reasonings involved; the difficulties students have with the concepts and why these difficulties might occur; and the interconnections within this content area. On the basis of this research we make four recommendations for the preparation and professional development of teachers. The recommendations deal with different but related forms of reasoning: quantitative reasoning, multiplicative reasoning, proportional reasoning, and reasoning with rational numbers. Problematic issues that follow from the recommendations are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Publication productivity in selected School Psychology Journals: 1985-1991

This study examines the institutional affiliations of authors who have published in the three major journals of School Psychology and two additional journals started recently in the field between January, 1985, and July, 1991. The specific journals examined were Psychology in the Schools, Journal of School Psychology, and the School Psychology Review. These journals comprise the primary research outlets in School Psychology. In addition, papers published in Professional School Psychology and the Journal of Psychoeducational Assessment were also included in the analysis because these represent relatively new publication outlets for School Psychology. Findings regarding institutional productivity are compared with those obtained from previous studies in this area.     

Performance of Nonrecursive Latent Variable Models under Misspecification

A problem central to structural equation modeling is measurement model specification error and its propagation into the structural part of nonrecursive latent variable models. Full-information estimation techniques such as maximum likelihood are consistent when the model is correctly specified and the sample size large enough; however, any misspecification within the model can affect parameter estimates in other parts of the model. The goals of this study included comparing the bias, efficiency, and accuracy of hypothesis tests in nonrecursive latent variable models with indirect and direct feedback loops. We compare the performance of maximum likelihood, two-stage least-squares and Bayesian estimators in nonrecursive latent variable models with indirect and direct feedback loops under various degrees of misspecification in small to moderate sample size conditions.     

Effects of Item Wording on Sex Bias

This study examined the effects of gender-related item-wording changes on the performance of male and female examinees. Mathematics word problems and English language items were created in neuter, male, and female versions. Items were administered to randomly equivalent samples of about 300 high school juniors and seniors. Loglinear analysis was used to assess the impact of item gender and its interaction with examinee sex on the difficulty and discrimination of each item in each context. No items were found to have sex bias in either context. Mathematics items did not have different difficulty or discrimination in the three gender versions. Neither mathematics nor English items had different discrimination levels in the three gender-related versions. Some English items, however, were found to have different difficulty levels in the three gender-related versions. These difficulty differences were not systematic." none of the three gender versions appeared consistently more or less difficult than the others.     

Mapping a complex system: what influences teacher learning during initial teacher education?

Despite a growing body of knowledge about what content, processes and arrangements for learning may result in more effective initial teacher education, there remains a problem with the variability of outcomes from teacher education programmes. This paper reports on a multi-perspective exploration of what influences learning to teach in valued ways during initial teacher education. Framed by complexity theory, which emphasises the non-linear nature of social phenomena, the paper presents an analysis of 76 maps of influences on learning to teach (made by teacher candidates, teacher educators, mentor teachers and policy makers), looking for differences and patterns that might point the way to explanations about teacher candidates’ varying ability to enact practice that improves outcomes for all learners.     

ATTITUDES TOWARD MATHEMATICS,LEVEL OF MATHEMATICAL COMPETENCY,AND RELATIVE GAINS IN COMPETENCY IN TWO‐ AND FOUR‐YEAR COLLEGES: A COMPARISON

An attitude toward mathematics questionnaire indicated no real difference in attitudes between two‐ and four‐year colleges. No differences in mathematical competencies, as measured by the Beckmann‐Beal Mathematical Competencies Test for Enlightened Citizens, existed between two‐ and four‐year colleges. The gain in mathematical competency due to taking one precalculus mathematics course was only 1.48 questions, or an increase of only 4.1%.