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• Author or Editor: Werner Liedtke
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## One Point of View: Let's Talk about Talking Mathematics

A elementary chool teachers we continually strive to make our mathematics teaching as effective as we possibly can. One way of reaching this goal involves changing the proportion of time allotted for development mental activities and individual seatwork for a lesson. Some evidence suggests that increasing the time spent on developmental tasks and student participation and thus decreasing the time students spend on practice can have a positive effect on mathematics achievement. This evidence implies that we, as teachers, should search for and collect strategies that are conducive to the implementation of developmental activities.

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## Diagnosis in Mathematics: The Advantages of an Interview

Before a teacher can offer meaningful mathematics remediation, data about a student's strength and weaknesses need to be collected. Although written responses on an activity sheet or on a test may indicate areas of concern, many times more information is required before accurate guesses about appropriate remediating task can be made. We have found that a guess based solely on examining written responses may in fact be incorrect.

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## What can you do with a geoboard?

A “mathematical problem” that upper elementary pupils might find challenging and enjoy solvi ng could be the construction of their own pegboard (with a friend's, father's, or big brother's help, if necessary).

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## The young child as a problem solver

In mathematics, there are problems—like trisecting an angle with a straightedge and a compass—and theorems—Fermat's last theorem—that do not have a solution or for whrch a proof has not been found. Some riddles or problems do not have an answer.

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## Games for the Primary Grades

The statements “Let's play a game” or “We will play a game” are sure to generate some excitement in any classroom. There is something intrinsically motivating about a game. The majority of young children enjoy playing games, which alone could justify their occasional use. However, many other worthwhile reasons for the use of games as part of the instructional setting or learning process in the mathematics classroom can be given.

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## From the File

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## Learning Difficulties: Helping Young Children with Mathematics—Subtraction

Most teachers in the primary grades, when they are asked to do so, have no problem identifying several chiidren in their classroom who are having some difficulties in learning mathematics. How can these children be helped? Before this question can be answered, and before any specific suggestions for remediation can be made, information about each child's strengths and weaknesses must be gathered.

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## Young Children—Small Numbers: Making Numbers Come Alive

When parents discuss the abilities of preschool children, they will frequently volunteer such statements as, “My child can count to______.” “My child knows the numbers to_____.” “My child can add numbers.” It is likely that these skills were taught at home, and it is more than likely that these parents frequently overestimate the level of understanding their young children possess. Elkind (1975) noted that “because young children are often so capable linguistically, adults often overestimate their capacity to think” (p. 1). This statement is especially applicable to comments that relate to rote counting, a procedure likely to consist of nothing more than the ability to match a name or sound to an object or a series of objects like those below.

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## Letter to the Editor

I wish to offer one practitioner's reaction to some of the content of the very informative July 1995 issue of JRME.

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## Developing Spatial Abilities the Early Grades

Most, if not all, geometry learned in the early years should be conceptual in nature, state Hiebert and Lindquist in Mathematics for the Young Child (1990). The authors point out that students need the opportunity to develop spatial sense, and they share the observation that “[t]oday, children are often able only to name selected examples of geometric figures.