Correction: By Way of IntroductionSource: The Arithmetic Teacher, Vol. 34, No. 9 (May 1987), p. 55Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/80000195 .Accessed: 12/06/2014 16:18

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In closing, I present a problem from a sec- ond-grade girl who was asked to "use some- thing from the classroom to write a subtrac- tion problem." Her response was, "There are two alphabets in our classroom. E.T. went home. How many letters are left?"

Werner Lie dike University of Victoria Victoria, BC V8W 2Y2

Hosmer responds: We at Hawken School are especially fortunate to have Linda Gojak as our mathematics head. In 1984-1985, work- ing under a Jennings grant, she put together grade-level notebooks of techniques and sam- ple problems for many varieties of problem- solving activities. We add to these notebooks materials we find, and spend time each week with special sessions on problem-solving tech- niques. Because our pupils tend to need little remediation and much enrichment, we are free to go above our levels and to do many unusual enrichment activities.

Among the materials I have used for years in third grade are Mind Benders, comics, fig- urai and word analogies (much discussion, children create their own), having bright stu- dents work with kindergarten teachers to cre- ate original games for their students, peer tu- toring or having fifth or sixth graders tutoring, and cut-and-paste geometry with the children stating the theorem they are proving.

Most of all, I, as an older teacher, learn from my peers, especially younger teachers who've learned newer ways in college. Re- cently I heard a young teacher explaining what she was doing and thought instantly, "I can do that this way (a different way)." I try to apply this rule in my classroom - much lis- tening to how children work, and especially praising the child who solved a problem differ- ently than the way demonstrated. That, I be- lieve, is why the next generation of American students will be stronger and more confident in problem-solving situations.

Let's count

Although I have no disagreement with Ro- berta Flexer's (November 1986, 5-9) method of using 5- and 10-frames for addition and sub- traction, or her conclusion that children con- struct basic facts on the 5- and 10-frame with- out counting, her view of counting appears to be very narrow. The use of a 5- and 10-frame is valuable, she speculates, because counting leads to ignoring of the base-ten system.

However, her premise and the sources that she quotes that "one-to-one counting is dis- tracting and limits children" ignore the many uses to which counting can be applied in teaching concepts. Physical manipulations and images and patterns created by counting are aids to understanding mathematical concepts. Further, counting can give the child successful experience, and it does not preclude place val-

ue or any other mathematical skill. Indeed, counting can be woven into the strand of many mathematical concepts. For example, counting for addition should not, as she claims it would, inhibit the understanding of multipli- cation, since children readily use repeated ad- dition when they have not fully grasped multi- plication.

Although Flexer's 5- and 10-frames are use- ful, they do not justify discontinuing the use of counting for many mathematical concepts.

Margaret Godfrey 29 Bay view Avenue New Rochelle, NY 10805

In NCTM journals

Readers of the Arithmetic Teacher might en- joy the following articles in this month's Mathematics Teacher:

"Tape Constructions," Lisa Evered "Activities: Crystals: Through the Looking

Glass with Planes, Points, and Rotational Symmetries," Carole J. Reesink

And in the Journal for Research in Mathemat- ics Education:

"Calculators and Instruction in Problem Solving in Grade 7," Walter Szetela and Doug Super

Focus corrections

On p. 34 in IDEAS (February 1986), under "Estimating a Product in Two Tries," the top example should have read as follows:

Second try: 7 x 723 = 5061

Also on p. 2, at the end of the second para- graph, "text" should be "test."

Thanks from the Editorial Panel (Continued from page 33)

B. Ross Taylor Kathy Wiber Deborah Tempest Donald E. Diane Thomas Wieder/anders Alba G. Thompson Jack D. Wilkinson Denisse Thompson Bruce Williamson Frances M. Thompson George H. Willson Kay Tobin Kathy Willson Kenneth J. Travers Alice- Ann Winner John H. Trent Sandra Wittenbrink Cecil R. Trueblood Rachel K. Witter Sandra V. Turner Donna M. Wolfinger A. Edward Uprichard Sharon Young James H. Vance Karl G. Zahn Henry Van Engen Marilyn K. Zak Sharon Vogt Judi Zawojewski Lee N. VonKuster Dorothy Zjawin Ingrid B. Weise Alan Zollman David W. Wells Marilyn Zweng David J. Whitin

May 1987

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Article Contentsp. 55

Issue Table of ContentsThe Arithmetic Teacher, Vol. 34, No. 9 (May 1987), pp. 1-60Front MatterReaders' Dialogue [pp. 2, 4, 54-55]Correction: Ideas [pp. 55-55]Correction: By Way of Introduction [pp. 55-55]Let's Do ItFun with Primary Math Centers [pp. 5-7]

Popsicle Sticks, Computers, and Calculators: ImportantConsiderations [pp. 8-12]Do You Think You Might Be Wrong? Confirmation Bias in ProblemSolving [pp. 13-16]Helping Children Understand Ratios [pp. 17-21]Research ReportMetacognition and School Mathematics [pp. 22-23]

Estimation and Mantal Computation [pp. 24-25]Ideas [pp. 26-32]Problem Solving: Tips For Teachers [pp. 34-35]Division of Fractions: Developing Conceptual Sense withDollars and Cents [pp. 36-42]Triangular Tiles for Your Patio? [pp. 43-45]Computer Corner [pp. 46-48]Reviewing and ViewingComputer MaterialsReview: untitled [pp. 49-49]Review: untitled [pp. 49-50]Review: untitled [pp. 50-50]Review: untitled [pp. 50-50]Review: untitled [pp. 50-51]Review: untitled [pp. 51-51]Review: untitled [pp. 51-52]

New BooksFor TeachersFrom NCTMReview: untitled [pp. 52-52]

From Other PublishersReview: untitled [pp. 52-52]Review: untitled [pp. 53-53]Review: untitled [pp. 53-53]

EtceteraReview: untitled [pp. 53-54]

From tha FileBack Matter