Discussed is the use, importance, and availability of programmed algebraic manipulation packages. The general power summation formula is presented and an example using a programed numerical verification package is provided. (KR)

Explained is the effect produced by an optics toy which uses two concave mirrors to produce an illusion. Formulas and calculations used in the explanation are detailed. (CW)

A class of 32 fourth graders, who studied inverse operations in grades 1-3, was given 3 written tests, each followed by an interview, to see how well they could simplify computations using inverse operations. Most could not evaluate 28 + 75 - 75, for example, without performing all operations. (GW)

This study analyzed relations between student achievement in the domain of fractions and the extent to which classroom practices are aligned with principles recommended by current reform frameworks. Hierarchical linear-model analyses revealed that alignment of classroom practices with reform principles was related to student achievement in problem…

A literature search to identify and analyze mathematics interventions for students with mild-to-moderate mental retardation found the focus of instruction has shifted since 1989 from basic skills instruction to computation and problem-solving instruction. Techniques such as constant-time delay, peer tutoring, time trials, and direct instruction…

Responses of 138 third and fourth graders to failures and successes in mathematics computation were studied in 4 experimental conditions varied by social learning context and modeling. The collaborative learning context increased student persistence after failure and dynamism after success, and modeling increased persistence and dynamism in an…

This article connects three disciplines while exploring how students computed tons of food consumed by both locusts and people. Included with this article are two worksheets "How Much Does a Locust Eat?" and "Can You Eat Those Locusts?". (Contains 3 figures.)

In this article, we formulate a nonlinear structural equation model (SEM) that can accommodate covariates in the measurement equation and nonlinear terms of covariates and exogenous latent variables in the structural equation. The covariates can come from continuous or discrete distributions. A Bayesian approach is developed to analyze the…

The learning difficulties for new entrant chemistry students from a multi-national, regional, tertiary education institution in the South Pacific were investigated using a purpose-designed diagnostic instrument. The instrument contained 25 items distributed across three themes: scientific reasoning, numeracy and scientific language literacy. The…

This study compared the involvement of American and Chinese mothers in their 5- and 7-year-old children's number learning in their everyday experience and during mother-child interaction on mathematics tasks pertaining to proportional reasoning. Results indicated that Chinese mothers of both the 5- and 7-year-old children were more likely to teach…

This article presents an in-class Monte Carlo demonstration, designed to demonstrate to students the implications of multicollinearity in a multiple regression study. In the demonstration, students already familiar with multiple regression concepts are presented with a scenario in which the "true" relationship between the response and…

This paper proposes a methodology to calculate both the difficulty of the basic problems and the difficulty of solving a problem. The method to calculate the difficulty of problem is according to the process of constructing a problem, including Concept Selection, Unknown Designation, and Proposition Construction. Some necessary measures observed…

What is an adequate education and how much does it cost? In 1989, Kentucky's State Supreme Court found the entire system of education unconstitutional--"all of its parts and parcels". The Court called for all children to have access to an adequate education, one that is uniform and has as its goal the development of seven capacities,…

Problem solving continues to be a major focus of K-12 mathematics education reform. This case study shows how a teacher's middle school mathematics instruction evolved from teaching problem solving as computation exercises to teaching how to select and implement combinations of problem solving strategies. The teacher's thinking about problem…

This article defines "higher level mathematical skills" and details an important class: that of "constructing instances" of mathematical objects satisfying certain properties. Comment is made on the frequency of higher level tasks in undergraduate work. We explain how such questions may be assessed "in practice" without the imposition on staff of…