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)

In this article, we analyze the complexity of using instructional dialogues in the teaching of mathematics. We trace a 10-lesson unit on functions and their graphs taught by Magdalene Lampert to a 5th-grade classroom. We use this trace to help analyze and systematize the complexity of the classroom discourse. Analysis shows that Lampert's…

Many years ago, Arons pointed out the incomprehension science students exhibit of the basic mathematical operations multiplication and division and the need to address the problem in physics classes to assure student understanding of the physical world. McDermott et al.'s Physics by Inquiry program does address this need directly and in detail (by…

Few things capture the spirit of spring like flying a kite. Watching a kite dance and sail across a cloud spotted sky is not only a visually appealing experience it also provides a foundation for studies in science and mathematics. Put simply, a kite is an airfoil surface that flies when the forces of lift and thrust are greater than the forces of…

This article analyses the modeling approach used by one student in a business problem. It is argued that if we use previous frameworks we are not able to classify the students' approach to modeling as purely theoretical or empirical. Instead the student used a theoretical approach when constructing a real model, but abandoned it when she had to…

This article discusses the role of the commutative, associative, distributive, and identity properties of addition and multiplication in preparing children for future success in algebra. (Contains 3 figures.)

This article, in honor of the 100th anniversary of "Mathematics Teacher," touches briefly on mathematics and the history of mankind.

Confidence intervals (CIs) give information about replication, but many researchers have misconceptions about this information. One problem is that the percentage of future replication means captured by a particular CI varies markedly, depending on where in relation to the population mean that CI falls. The authors investigated the distribution of…

Innovative teachers can make writing as an integral part while teaching math to students. The teachers will have to implement the math instruction that enables students to organize and consolidate their mathematical thinking through communication, analyze and evaluate the mathematical thinking of others, and use the language of mathematics to…

Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for the students' learning, the mathematical tasks that will be used to promote student learning, and hypotheses about the process of the students' learning.…