Presents a framework to guide teaching and assessment procedures with particular emphasis on the importance of communication in learning mathematics. The Lesh translation model contains five modes of mathematical representation: manipulatives, real-life contexts, written symbols, verbal symbols, and pictures. Describes teaching scenarios. (MKR)

This study investigated the effects of various levels of secondary school calculus experience on performance in first-year college calculus, with focus on student performance on conceptual and procedural exam items. Students who had a year of secondary school calculus differed significantly in performance from those who had either no experience or…

Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…

Described is an activity that uses the techniques of integral calculus to determine the volume of a bundt cake. The cake is used as an example of a solid of revolution. Included are the procedures and assumptions used by students to solve this problem. (KR)

The absolute-value scale, a manipulative that students can construct from a sheet of ruled notebook paper, helps to promote conceptual connections between the number line and the notion of absolute value as distance. This manipulative technique is particularly suited to students who are struggling with transitional abstract cognitive development.…

Presents a nontechnical introduction to the field of statistics. Includes discussions on descriptive statistics, random variables, mean, standard deviation, standardized scores, and inferential statistics. Describes six statistical software packages available for IBM personal computers and compatibles. (KR)

Presents music education as a setting for teaching nonlinear dynamics and chaotic behavior connected with fixed-point and limit-cycle attractors. The aim is not music composition but a first approach to an interdisciplinary tool suitable for a single-session class, at either the secondary or undergraduate level, for the introduction of these…

Typically, the mathematical properties concerning the golden ratio are stated correctly, but much of what is presented with respect to the golden ratio in art, architecture, literature, and aesthetics is false or seriously misleading. Discussed here are some of the most commonly repeated misconceptions promulgated, particularly within mathematics…

Assessment of 121 nondisabled elementary boys and 107 boys with attention-deficit hyperactivity disorder (ADHD), ages 7 through 14 years, found significantly lower problem-solving scores in specific math concepts and slower computational performance for the boys with ADHD when reading and problem structure were held constant. Instructional…

Magnitude comparison, calculation verification, and short-term memory span experiments were conducted as a means of investigating number processing in 17 deaf college students with academic weaknesses. Deaf students' level of accuracy did not differ from that shown by their hearing peers; however, mean response times of deaf students were greater…

Presented is a proof where special attention is accorded to rigor and detail in proving the lemma that relates ruler-and-compass constructions to arithmetical operations. The idea that some angles cannot be trisected by a ruler and compass is proved using three different cases. (KR)

Presented is the theorem proposed by Volterra based on the idea that there is no function continuous at each rational point and discontinuous at each irrational point. Discussed are the two conclusions that were drawn by Volterra based on his solution to this problem. (KR)

It is difficult for students to unlearn misconceptions that have been unknowingly reinforced by teachers. The examples "multiplication makes bigger,""pi equals 22/7," and the use of counter examples to demonstrate the numerical property of closure are discussed as potential areas where misconceptions are fostered. (MDH)

In whole concept mathematics, students actually use math and understand the practicality of what they are studying. This learner-centered approach treats students with respect, uses real-life situations, encompasses a variety of learning styles, and involves cooperative learning techniques. (SK)

Focuses on literacy and mathematics and shows how fourth graders worked through "My Travels with Gulliver," an innovative unit that integrated literature, writing, and mathematics so that children could learn concepts across the curriculum. (MG)