Presents a problem that describes a real-world situation from World War II that tries to estimate the number of German tanks, half-tracks, and aircraft, and a simulation of that problem in which the selection of a suitable estimate is less apparent. (ASK)

This study examined effects of teacher characteristics (gender, teacher education and certification, class management skills and job satisfaction) and teaching styles on indicators of good classroom practice in mathematics classes in secondary education by means of multilevel analysis. The study reveals that the presence of effective classroom…

This article describes connections between chess and mathematics, including examples of activities that connect chess with set theory, patterns, algebra, geometry, combinatorics, and Pascal's triangle. The author observes that competitive games play a dual purpose in advancing the work of mathematics educators: to reinforce a specific skill and to…

This article describes TI-73 calculator activities appropriate for middle school students. It was found that the use of the calculator allowed for higher-level thinking and a richer exploration of mathematical ideas by students. [Included with this article are "Dice Roll Worksheet" and "Transforming Tree Worksheet".] (Contains 9 figures.)

This article illustrates students' efforts to resolve an apparent discrepancy between their self-generated solutions and the answer obtained using the division algorithm for fractions. (Contains 5 figures.)

This article describes the pitfalls of using key words to support students when problem solving, and provides an alternative way (quantitative analysis) to support students' sense-making. (Contains 1 table and 2 figures.)

This article describes ways in which students develop schemas as they generalize and formalize patterns when solving related algebraic problems that involve size, shape, growth, and change. (Contains 7 figures and 3 tables.)

Working from Carolyn Kieran's categorization of "arithmetic" and "algebraic" thinkers, the article describes one eighth-grade "arithmetic" thinker's progress as she attempts to solve one- and two-step equations.

The NAEP testing over the past decade shows gradual improvement of test scores at the eighth-grade level, contrary to what many say about stagnant scores. However, by 2000, only one-fourth of eighth graders performed at the proficient level. (Contains 2 tables and 6 figures.)

Algebraic thinking in the middle grades involves constructing generalizations, moving beyond the focus of specific calculations in elementary school. This creates exciting opportunities to examine the validity of general arguments. Creating rich mathematical tasks and asking questions related to justification encourages students to examine what…

Worthwhile mathematical tasks not only prompt students to learn mathematics, they also prompt teachers to learn and improve their teaching in their own mathematics classrooms. When teachers use worthwhile tasks, they have to learn "what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask…

Many students have traditionally found the processes of algebraic manipulation, especially factorisation, difficult to learn. This study investigated the value of introducing students to a Vedic method of multiplication of arithmetic numbers to algebra that is very visual in its application. This research considered a possible role of the…

Three issues about students' reasoning, proving and understanding proof in number patterns are investigated in this paper. The first is to elaborate the features of junior high students' reasoning on linear and quadratic number patterns. The second is to study the relationships between 9th graders' justification of mathematical statements about…

Emphasis on problem solving and mathematical modeling has gained considerable attention in the last few years. Connecting mathematics to other subjects and to the real world outside the classroom has received increased attention in mathematics programs. This article describes an application of simple differential equations in the field of…

This short note introduces an interesting random walk on a circular path with cards of numbers. By using high school probability theory, it is proved that under some assumptions on the number of cards, the probability that a walker will return to a fixed position will tend to one as the length of the circular path tends to infinity.