Reports on a study comparing the use of Multi-base arithmetic blocks (MAB) and an alternative, LAB (linear arithmetic blocks) on the basis of epistemic fidelity and accessibility for students. Use of LAB was associated with more active engagement by students and deeper discussion. (Author/MM)

For many years I have been advocating the use of hands-on materials to assist students in the understanding and application of mathematical concepts. Some of the methods have been introduced as small parts of earlier Discovery articles, (de Mestre, 1994, 1996, 1998, 1999a, 1999b, 1999c, 2000a, 2000b, 2001), but here I propose to devote the whole…

Responding to the concern from our faculty that undergraduate students do not have robust laboratory skills, we designed and implemented a strategy to individually teach and assess the manipulative skills of students in first-year laboratories. Five core laboratory skills were selected for the course entitled Human Biology, a large, first-year…

Judge Harry T. Roman, an electrical engineer and inventor, has selected the best of the crop in the 2006/2007 Tech Directions Inventors Award Competition. The challenge this year called on students to slow the filling of landfills by devising uses for discarded plastic water, juice, soda, and sports-drink bottles. Judge Roman noted "many common…

All learners, including those who qualify for special education services, should have access to learning mathematical concepts. This study examined the efficacy of using hands-on sets of materials to teach two high school students with mental retardation the four situations for subtraction. This is a mixed methods study using a simple…

The authors describe a hands-on program that they developed after their attendance at the NCTM Algebra Academy. The article explains how to use literature to capture youngsters' attention and engage them in interactive mathematical activities.

In K-12 classrooms, as well as on the college and university level, the incorporation of digital games has played a vital role in the educational system. While introducing teachers to new fields, these digital games have been designed and implemented for the classroom and have shown positive results at a variety of educational levels. Cases on…

The Japanese, Chinese, and Russian abaci are described. Policies of the Japanese Education Ministry with regard to calculation are briefly discussed. (SD)

This booklet was designed to aid parents in making things at home to develop their newborn to 2-year-old children's skills. Suggested are easy-to-make visual stimuli for infants up to 6 weeks of age and 6 weeks to 3 months of age. For the latter, tactile stimuli also are considered. For infants 3 to 6 months of age, objects providing visual,…

Piaget's conception of cognitive development as the development of a set of skills resulting from interaction with the environment has had a great effect on contemporary educational theory and spurred the Educational Testing Service (ETS) to develop a set of written exercises based on this concept. Piaget's emphasis, however, was on concrete…

Free teaching materials which will be available at least until 1973, which have been evaluated by accredited teachers, and which have direct bearing on curriculum are listed in this catalog. Individual items are grouped under appropriate subject headings by title or source, and a description of the item is included. In addition, the approximate…

Detailed instructions are given for the construction of a line segment of length cube root of two. A proof is also given. (MP)

Some questions about the relevance of the philosophy of mathematics to mathematics teaching and to early mathematics learning are discussed. Books by Lakatos, Davis and Hersh, and Kitcher are referred to extensively, with comments on a variety of instructional practices. (MNS)

Learning theories and evidence from research and classroom practice support use of manipulative materials to help children learn and understand mathematics. Well-chosen and properly used manipulatives enhance children's learning, generate interest, relieve boredom, and promote problem-solving and computational skills. (JN)

There are numerous teaching suggestions to offer for guiding pupils to achieve more optimally in mathematics. There is, however, a problem involved in writing about the implementation of selected teaching suggestions: there needs to be a readiness of learning prior to implementing any teaching suggestion. If pupils cannot benefit from the teaching…