Research reveals that many mathematics teachers find it difficult to stimulate learners' interest in learning geometry. One major reason suggested is that geometric concepts are not well conceptualised and comprehended by both learners and teachers. The study explored learners' views on how polygon pieces and dictionary mediate learning of…

This paper provides historical insights and educational background of Froebel's Gifts, hands-on materials developed in the early 19th century. Based on an explorative study with 54 German children (aged 5 to 10) in 2016, we first took steps to explore how these materials meet the demands for early mathematics learning of primary children. Starting…

"Mathematical modeling of the physical world should be the central theme of physics instruction" (Hestenes 1987). Science teachers know this, but because of standardized state testing, many math teachers and some science teachers feel the need to focus on memorizing facts that will be on a multiple-choice test (Volante 2004). As a…

Teaching computer concepts to individuals with visual impairments (that is, those who are blind or visually impaired) presents some unique challenges. Students often have difficulty remembering to perform certain steps or have difficulty remembering specific keystrokes when using computers. Many cannot visualize the way in which complex computing…

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…

This hands-on project uses a paper helicopter to teach students how to distinguish between common and special causes of variability when developing and using statistical process control charts. It allows the student to experience a process that is out-of-control due to imprecise or incomplete product design specifications and to discover how the…

Invented by English mathematician and pedagogist, Caleb Gattegno (1911-1988), the geoboard was designed as a manipulative tool for teaching primary geometry in schools (Williams, 1999). Traditionally made out of plywood and nails, geoboards today are usually made out of plastic and come in a variety of different sizes and colours. Rubber bands are…

The mechanism of routine practice and problem solving that is used as a method of teaching and learning is not simply interpreted as a way in which students only mechanically imitate and memorize rules and skills. Manipulative practice is the genetic place of mathematical thinking and the foundation of concept formation. (ASK)

An outline of practical experiences from which the concept of length measurement may be learned. (MM)

This paper traces the growth of the concept of a mathematics laboratory and reviews recent research and developments in this field. The first section quotes several interpretations of the term and discusses some of the activities advocated by its proponents. The second section quotes extensively from E. H. Moore (1902) and McLennan and Dewey…

Presents a series of lessons that extend the concrete experiences many elementary students have had with attribute blocks to provide middle school students with informal opportunities to explore the concepts and properties of relations and functions. (DDR)

Presents a sequence of hands-on activities to help students understand the concept of arithmetic mean and gain experience in using mathematical models. Students create models in the process of solving problems and communicate to the class the meaning attached to the models. (MDH)

This curriculum guide presents a program of 20 open-ended math activities to be used to supplement the math programs in kindergarten, first, or second grade classrooms. The program consists of child-oriented counters and gameboards used to explore the concept of number from counting to making up and solving addition and subtraction equations. Each…

Presents an activity that uses M & M's candy to initiate discussion about the mathematical concepts of empty set, zero, more than, less than, most least, and equivalent sets. Suggests extensions that could follow this activity. (MDH)

Presents a study to examine the effects of a verbal teaching strategy versus a strategy providing instruction using activities and manipulatives in four seventh grade earth science classes with students of varying cognitive abilities (n=83). Results indicate that students with more cognitive structures perform better and that using manipulatives…