Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving. Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found…

Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

In the era of multi-tiered system of support approach to learning, identifying mathematical interventions that have been found to be effective for students who are struggling academically is imperative. Given the divide between instructional approaches in general and special education mathematical teaching approaches, it is important to bridge the…

This paper proposes an hypothsis describing how some college students incorrectly view semantically laden letters and provides both clinical and written data that supports that hypothesis. Several word problems were given to nine college math students. These students were then interviewed as they attempted to solve these problems. In addition to…

Given are several examples of seemingly unrelated problems that nevertheless can be solved with a single mathematical idea--the proportion. It is hoped that as students see how a variety of problem contexts can be modeled by a proportion, they will use proportions more frequently in problem solving. (MNS)

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)

Describes how Suzuki's methods of teaching young pupils to play the violin can be combined with Polya's ideas on problem solving to teach mathematics to elementary school pupils. Six references are listed. (YP)

Four teaching ideas are discussed: a "giant" math problem designed to motivate students to use library sources, calculators, computers, and textbooks; a different way of finding fractional equivalents; a task-card project designed to encourage mathematics students to use libraries; and journal writing in a mathematics class. (MP)

Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

Presents four investigations involving geometric sequences and series: folding a sheet of paper in half 8 times, stacking pieces of paper cut in half 50 times, snapping your fingers at intervals doubled in length for 1 year, and summing time intervals continuously cut in half. (MDH)

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

A number for which the number of digits categorizes the number is called a star number. A set of star numbers having a designated property is called a constellation. Discusses nature and cardinality of constellations made up of star square, star prime, star abundant, and star deficient numbers. Presents five related problems for exploration. (MDH)

How children give meaning to problems solved by multiplying or dividing is considered. After showing two cases of children's understanding of multiplication problems, six recommendations for classroom practice are presented. (YP)

Concepts from cognitive psychology are presented as an alternative framework to arithmetic instruction for students with disabilities. The approach, which emphasizes reasoning, communication, and problem solving, is applied to addition, division, multiplication, subtraction, and word problems. The purpose of arithmetic instruction is asserted to…

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…