The purpose of this study was to examine four pre-service middle and high school mathematics teachers' understanding of the directly and inversely proportional relationships presented through hands-on and real-world missing-value word problems. The problems included single and multiple proportions, and the PSTs were provided with plastic gears and…

The purpose of this paper is to propose an "operational" idea for developing algebraic thinking in the absence of alphanumeric symbols. The paper reports on a design experiment encouraging preschool children to use the associative property algebraically. We describe the theoretical basis of the design, the tasks used, and examples of…

This is an account of events in a real classroom when the notion that there is a distinction between calculation by counting, and calculation by structuring is a focus for learning. Pupils have "hands-on" experiences that support their understanding of "number". The teaching "aid" might be unfashionable in…

How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. "Hands-on Activities for Teaching the Common Core Math…

A whimsical mathematics event for children and adults, derived from Lewis Carroll's Alice's Adventures in Wonderland, was held at the Providence Children's Museum in Rhode Island. NCTM's Standards were the basis of all the activities. (Contains 10 figures and 1 table.)

Rule learning in mathematics among elementary school children is described. Samples of dialogue between experimenters and children are presented, and the concept of rule learning is described in relation to two subgroups, gifted children and "regular" ones. (MP)

Presents an investigation, applicable for grades 3-6, that focuses on the concept of randomness and encourages children to conjecture and to conduct experiments which verify or contradict their intuitions. Involves using hands-on explorations, collecting data, and drawing conclusions on the basis of the information. (JRH)

Using arrays of dots and grids many numerical concepts can be illustrated for students. (SD)

This teaching experiment investigated variables which affect how well children learn from manipulative aids and how to use such aids in teaching mathematics. Five small groups from one second-grade classroom were stratified by achievement and taught using (1) counting sticks; (2) Dienes blocks; (3) abacus; (4) all three materials; or (5) counting…

The author describes the areas in the kindergarten classroom--blocks, toys, cooking, games, job charts--which can be used in furthering a child's developing mathematical skills. (KC)

This manual was designed for use in conducting staff development sessions for elementary teachers of mathematics in Mississippi in grades K-6. The four topical areas treated in the document are: (1) measurement and geometry; (2) fractions; (3) procedural errors in arithmetic; and (4) problem solving. The number of instructional hours necessary for…