Two ideas of mathematics that the students discuss here, demonstrate how sometimes a teacher can learn something new from the students. The examples given use geoboard and show relationships of the two ideas with the Pick's theorem.

Methods to automatically convert graphics into tactile representations have been recently investigated, creating either raised-line or relief images. In particular, we briefly review one raised-line method where important features are emphasized. This paper focuses primarily on the effects of such emphasis and on comparing both raised-line and…

In this article, the author discusses the Soroban (Japanese abacus) in the age of computers and its structure. Since the advent of computers, the Soroban has started to shift from being used purely as a calculating device to being a useful tool in general mathematics education. The beauty of the Soroban is that it represents numbers exactly as you…

Whether teaching mathematics in a contained elementary classroom, as a specialized math teacher, or as an ELL teacher, this new resource will help meet the needs of English Language Learners. Offering strategies, guidelines, and classroom vignettes, this book demonstrates how to adjust mathematics instruction to make the learning less…

The use of manipulatives in the classroom has been advocated for decades. However, the theoretical and empirical support for this practice is mixed. Some researchers suggest that manipulatives facilitate learning by (a) providing an additional channel for conveying information, (b) activating real-world knowledge, and/or (c) improving memory…

This paper discusses the use of Numicon number teaching materials with children with Down syndrome. The theory underlying the design of the materials is discussed, the teaching approach and methodology are described and evidence supporting effectiveness is outlined. (Contains 4 figures.)

Both virtual and physical manipulatives are reported as effective learning tools when used with different groups of students in a variety of contexts to learn mathematical content. The use of multiple representations and the flexibility to translate among those representational forms facilitates students' learning and has the potential to deepen…

We investigated the effects of transparent fraction names on children's reasoning about fractions. U.S. and Korean first and second graders were tested using verbal and nonverbal measures. On a verbal task, Korean students were worse at interpreting their own conventional fraction names than interpreting modified terms with a more familiar word…

The ultimate goal of high school mathematics teachers is to create a meaningful learning environment that is conducive to teaching students the necessary concepts for academic achievement. Unfortunately, evidence suggests that many secondary educators still teach in a rote lecture style that focuses on the teacher providing information to passive,…

This report describes a program for increasing adolescent visualization and understanding of geometry problems. The targeted population consisted of high school students in two geometry classes in a growing middle-class community. The inability of students to adequately visualize and understand geometry problems was documented through teacher-made…

A study compared the effectiveness of three different story-telling strategies on a preschool disabilities population. Participants were exposed to stories through oral story telling using auditory cues only, story telling with illustrations such as Big Books, or story telling using illustrations and puppets. Participants were asked to retell the…

A series of activities involving comparing weights of objects directly, using non-standard units, using standard units, using simple scales, and using complex scales are described. (SD)

Directions are given for activities designed to help children realize that linear measurement is continuous, that it involves the repeated use of a unit in the same way each time, and that measurement is approximate. Non-standard units as well as standard units are included. (DT)

Seventy-one college students were taught probability and statistics for one month by one of three methods: MP, manipulative-pictorial; P, pictorial; and S, symbolic. Analysis of variance yielded significant differences (p.05) between treatment groups for selected subtests of an achievement test and generally favored MP and P over S.