This study addresses the embodied approach of convergence of numerical sequences using the GeoGebra software. We discuss activities that were applied in regular calculus classes, as a part of a research which used a qualitative methodology and aimed to identify contributions of the development of activities based on the embodiment of concepts,…

In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

This report describes reflections from two cycles of developmental research that involved creating and refining a series of computer-based applets for reasoning about the relative magnitude of fractional quantities. The applet sequence stemmed from a cognitively demanding task used in face-to-face teacher education settings that involved placing…

This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…

In undergraduate mathematics courses, pre-service elementary school teachers are often faced with the task of re-learning some of the concepts they themselves struggled with in their own schooling. This often involves different cognitive processes and psychological issues than initial learning: pre-service teachers have had many more opportunities…

There are numerous teaching suggestions to offer in guiding pupils to greater achievement in mathematics. This paper suggests that the instructor should begin where the pupil is presently and observe what interests the pupil in learning. Different methods for teaching mathematics such as using blocks, beads, films, filmstrips or slides, a…

Two computer games, Guess and Rule, can be used to improve students' thinking strategies. BASIC and Logo programs are given for each game, and facts and additional references are included. (MNS)

Suggestions for using a computer disc containing unprotected programs are given. The Fibonacci sequence, prime factorization, sum puzzlers, and other examples are described. (MNS)

A variety of activities and information about computers and programing are included. (MNS)

An example is given of how to help students who have obtained a correct answer by a wrong method. They are asked to suppose that a child has found an easy method for division, and eventually write a computer program to show the correct method. (MNS)

Ways to combine the strengths of teacher and computer are suggested. Multiplication concepts and an algorithm for multiplication are taught in the same lessons. The computer is used as an electronic chalkboard to teach at a semiconcrete level. The computer program is included. (MNS)

This study focuses on the nature of preservice elementary school teachers' understandings of several concepts in elementary number theory that are evoked by a computer-based microworld called "Number Worlds". In particular, the focus is on the concepts of factor, multiple and prime number. The notion of "thickness" is examined with respect to…

Use of a microcomputer spreadsheet program to help students understand long division is described. An example of a problem with powers of 10 used with seventh graders is presented, with note of another lesson on decimals for grade 6. (MNS)

This manual is used with MATHBOXES, a computer program written for Apple II microcomputers to help children relate formal mathematical symbols for representing simple word problems to the informal strategies using physical objects that they naturally use to solve them. There is a substantial body of research that documents that young children are…

Programs (using Logo) developed by children to produce multiples, the Fibonacci series, and square numbers are presented, with graphical representations of functions introduced. Another investigation involves drawing a circle using turtle graphics. (MNS)