Explores the nature of language from a linguistic viewpoint and describes how mathematics can be seen to be a foreign language by students. Describes how natural language reading strategies provide language-specific problems to mathematics teachers. (MDH)

To clarify what it means to teach mathematics for understanding and to learn mathematics with understanding, an interactional analysis of video recordings of two lessons in elementary school classrooms is presented. The two classrooms illustrate two distinct classroom traditions, in which mathematics was learned with and without understanding,…

Reacts to Ohlsson, Ernst, and Rees' paper by initially discussing the costs of methodology that utilizes artificial intelligence (AI) to model cognitive processes. Raises three concerns with the paper: insufficient clarification of the meaning of conceptual versus procedural understanding of base-10 subtraction; realism of the learning model; and…

Clarifies the benefits of having students write about their understanding and dispositions toward mathematics. Discusses ways to manage journal writing and incorporate it into existing classes. Suggests 19 assignments students can respond to in their journals. (MDH)

Academically talented high school students (n=239) evaluated a three-week individualized, flexibly paced precalculus summer course as more challenging than their ensuing school placement course. Results support the use of such courses, followed by appropriate placement, as a means of meeting the special academic needs of talented students. (DB)

An introductory preservice teacher activity from a typical college geometry course is presented. This activity leads the preservice teachers to specific goals, including increased geometric awareness within the everyday environment, appreciation for mathematical modeling techniques, and awareness of methods for teaching geometric concepts to…

Included are probability models for various strategies that contestants on the television game show, "Let's-Make-a-Deal," might use when given the option to stick with their original choice of three unopened doors or switch to the unopened door after one of the other two doors has been opened. (JJK)

Curriculum-based measurement (CBM) is recommended as an efficient, objective, flexible, and reliable way to compose ability-based instructional groups in both regular and special education settings. Steps for using CBM and specific applications for grouping in reading and mathematics instruction are offered. (DB)

Investigates the question concerning the maximum number of lines of symmetry possessed by irregular polygons. Gives examples to illustrate and justify the generalization that the number of lines of symmetry equals the largest proper divisor of the number of sides. Suggests related classroom activities. (MDH)

Presents a method blending ideas from logic, algebra, and operators to devise discrete functions that yield the same truth values as the truth tables associated with specific logic statements. Introduces mechanisms that encourage students to discover examples of discrete functions, approximately represent logic statements, and provides examples of…

Proposes lessons for algebra students using the context of tax calculations to learn about the concepts of slope, split functions, averages, rates, marginal rates, and percents. Students explore ramifications of possible tax revisions. (MDH)

Considers innumeracy, the unfamiliarity with mathematical concepts and methods, as being significantly pernicious to the evolution of technological societies. Proposes that the teaching of mathematics through culturally intimate, practical examples and models can profoundly contribute to the confidence necessary to encourage and sustain widespread…

Presents a calculator method to investigate the effects of varying parameters within mathematical functions in relationship to the accompanying changes in the family of their graphical representations. Suggests that the popularity of this activity makes it equally suitable for high school second-year algebra classes, preservice mathematics…

Described is an activity that categorizes a two-digit number as "sneaky" if the continued process of taking the difference of the squares of its digits leads to a difference of zero. Other categorizations are determined by whether the difference process ends in a one-digit number or continues in a loop of numbers. (MDH)

Presents activities in problem solving for levels K-2, 3-5, and 6-8 for each week of the month of March. Activities include open-ended problems and games that engage students' intellect and interest while working individually and cooperatively. (MDH)