Argues that a major difficulty in learning how to do mathematical modeling is in the first independent run through the modeling cycle. Reviews a case study (N=12) on mathematical modeling and presents the conclusions in three sections: (1) the choice of task; (2) the presentation of the task; and (3) tutor intervention and support. (ASK)

Defines ethnomathematics as the investigation of mathematical knowledge in small-scale, indigenous cultures. Puts ethnomathematics as one of five distinctive subfields within a general anthropology of mathematics, and describes interactions between cultural and epistemological features that have created these divisions. Reviews political and…

Describes several studies that challenge conventional wisdom regarding the teaching and learning of nonstandard and standard unit, rulers, and measurement sense. Discusses the educational implications of their results. (Author/CCM)

Prospective secondary teachers can explore mathematics at their own level by using the law of cosines to establish connections between topics that are usually taught separately such as cosine of the difference of two angles, Cauchy's inequality, determinants, sine of the difference of two angles, triangle inequality, and inner product of two…

Assessed the effectiveness of instruction in promoting sixth-grade students' conceptual understanding of the concept of averages using a leveling model and an open-ended problem-solving approach. Found that students were more capable of using the leveling approach and applying formal averaging algorithm to solve problems than using the open-ended…

Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)

Presents an activity that uses combinations of Cuisenaire rods of length one or two to make various lengths and trains. (ASK)

Introduces problems on rhombuses and dodecagons and their solutions. Emphasizes the angles and symmetric features of these geometric figures. (ASK)

Presents three activities on quadratic relationships, their graphs, and their formulas. (ASK)

Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)

Describes a method to combine two learning experiences--optical physics and matrix mathematics--in a straightforward laboratory experiment that allows engineering/physics students to integrate a variety of learning insights and technical skills, including using lasers, studying refraction through thin lenses, applying concepts of matrix…

Introduces the necessary game-theoretic background and explains how game-theoretic experiments of the Matching Pennies game can be used as a classroom activity to develop intuition about saddle points. (Author/ASK)

Reviews what is known of the student experience with mathematical proof at university level. Suggests that while the least well-qualified graduates may have the poorest grasp of mathematical proof, the most highly qualified students may not necessarily have the richest form of subject matter knowledge needed for the most effective teaching.…

Investigates the question, Can the mathematics students are taught be cast in such a form that it can be apprehended with the abilities they have and if so, how? Focuses on the language of student abilities, the nature of abilities, and individual differences. (MM)

Reports on a study designed to construct an understanding of two grade 6 students' proportional reasoning schemes. Finds that two mental operations, unitizing and iterating, play an important role in students' use of multiplicative thinking in proportion tasks. (Author/MM)