Mathematical conjectures and theorems are most often of the form P(x) ? Q(x), meaning ?x,P(x) ? Q(x). The hidden quantifier ?x is crucial in understanding the implication as a statement with a truth value. Here P(x) and Q(x) alone are only predicates, without truth values, since they contain unquantified variables. But standard textbook…

This paper explored the authors' concerns about students enrolled in their introductory accounting course. Anecdotal evidence suggested that students struggle with basic arithmetic concepts that underlie basic business transactions even though their math placement and ACT scores are high. A survey of 125 students in a first accounting course was…

There is a paucity of evidence supporting the use of curriculum-based mathematics measures (M-CBMs) at the middle school level, which makes data-based decisions challenging for school professionals. The purpose of this study was to examine the relationships among three existing M-CBM indices: (a) basic facts, (b) concepts/application, and (c)…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

This study provides empirical evidence of a highly specific use of games in education--the assessment of the learner. Linear regressions were used to examine the predictive and convergent validity of a math game as assessment of mathematical understanding. Results indicate that prior knowledge significantly predicts game performance. Results also…

The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

Users of logistic regression models often need to describe the overall predictive strength, or effect size, of the model's predictors. Analogs of R[superscript 2] have been developed, but none of these measures are interpretable on the same scale as effects of individual predictors. Furthermore, R[superscript 2] analogs are not invariant to the…

We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

The computation, concept, and application subtests of the Stanford Achievement Tests (SAT) were administered to a student sample during grades 3, 5, and 7. The efficiency of earlier scores and Otis Lennon Mental Ability Test scores in predicting seventh-grade SAT math scores was examined and found to be weak. (SJL)

TWO METHODS OF RESPONSE DESCRIBED BY PIAGET AND INHELDER FOR DRAWING APPROPRIATE BOUNDARIES AND SELECTING APPROPRIATE PREDRAWN BOUNDARIES FOR HYPOTHETICALLY CUT, SOLID GEOMETRIC FIGURES WERE INVESTIGATED TO SEE WHETHER SECONDARY SCHOOL STUDENTS COULD RESPOND IN APPROPRIATELY TO THE MATHEMATICAL TASKS. THE RESPONSES OF 8TH-, 10TH-, AND 12TH-GRADE…

This experiment investigated the significance of spontaneous occurrence of number symbols in the drawings of 86 (23 male pairs and 20 female pairs) kindergarten children. A comparison was made of first grade achievement on the Piaget Number Concept Test of students who used alphabetic and numeric symbols in the Draw-a-Classroom Test in…

The suppressor variable, a variable wholly uncorrelated with a criterion, but which nevertheless improves prediction because of its relationship with a predictor, is critically examined. For a suppressor so defined, formal identities are shown with part, partial, and multiple correlational procedures. It is demonstrated that if maximum prediction…