Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

In this study, we examine how prospective teachers perceive the efficacy of manipulatives and if these perceptions relate to their future use of manipulatives and their mathematics self-efficacy. Survey responses from 97 preservice educators who had completed a mathematics method course indicate three essential findings. One, preservice teachers…

The primary purpose of this classroom experiment was to examine the effectiveness of concrete (hands-on) manipulatives as compared with virtual (computer-based) manipulatives on student review of fraction concepts in third grade and introduction of symmetry concepts in fourth grade. A pretest-posttest design was employed with a sample of 91…

Using data from 503 inservice elementary teachers, this study investigated the relationship between teachers' background characteristics, teachers' beliefs about manipulatives, and the frequency with which teachers use manipulatives as part of their mathematics instruction. Findings from the study show that teachers' grade level and beliefs about…

This collective case study analyzes the use of manipulatives in math lessons developed and taught by 4 groups of elementary teachers (K-8) involved in lesson study as part of a professional development program. The study found that in three of four lessons studied manipulative use was turned into an end in and of itself, rather than a tool, and…

Plans are given for the construction of a "counting frame." This device consists of beads strung on a wire and used as a counting aid. (JP)

Angle measurement activities utilizing tinker-toys, geoboards, and paper-and-pencil constructions are given which could be used with children prior to the development of the degree concept. (MN)

Following background information on Rubik's Cube, a bibliography of print materials and computer software useful in using the cube in mathematics and science instruction is presented. (MNS)

A presentation of learning experiences involving materials is recommended which reflects the sequence of the developmental stages. This sequence is concrete, concrete-abstract, pictorial-abstract, and abstract. Instructional examples at each level are presented. (JP)

The effectiveness of using a set of models in two protein synthesis laboratory exercises accompanied by a series of two lectures on the topic was assessed. The purpose, procedure, example test items, the findings, and a discussion are included. (KR)

This research study examines the instructional practices of 10 middle grades teachers related to their use of manipulatives in teaching mathematics and their control of mathematics tools during instruction. Through 40 observations of teaching, 30 interviews, and an examination of 67 written documents (including teachers' plans and records),…

Construction of a series of 13 nested, regular tetrahedrons from 12 square sheets of paper without using geometric instruments, scissors, or glue is described. (MN)