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The King's Chessboard by David Birch Review by: Diane Stephens The Arithmetic Teacher, Vol. 36, No. 6, FOCUS ISSUE: NUMBER SENSE (February 1989), pp. 65-66 Published by: National Council of Teachers of Mathematics Stable URL: http://www.jstor.org/stable/41194475 . Accessed: 15/06/2014 06:23 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. . National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extend access to The Arithmetic Teacher. http://www.jstor.org This content downloaded from 62.122.73.246 on Sun, 15 Jun 2014 06:23:49 AM All use subject to JSTOR Terms and Conditions

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Page 1: FOCUS ISSUE: NUMBER SENSE || The King's Chessboardby David Birch

The King's Chessboard by David BirchReview by: Diane StephensThe Arithmetic Teacher, Vol. 36, No. 6, FOCUS ISSUE: NUMBER SENSE (February 1989), pp.65-66Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194475 .

Accessed: 15/06/2014 06:23

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

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Page 2: FOCUS ISSUE: NUMBER SENSE || The King's Chessboardby David Birch

emphasis on process more than content. Stu- dents who have reading difficulties should expe- rience success when using these materials.

The lesson plan format is excellent in that teachers will have little preparatory work. The fact that the materials are designed to use with groups of any size will be helpful during the implementation phase. I am impressed with the section on curriculum applications contained in each lesson plan. Teachers will be able to incorporate critical thinking skills across the curriculum - something that rarely occurs when teachers rely solely on traditional teaching ma- terials.

Other noteworthy attributes of this book in- clude the following:

1. The material allows for student self-pacing. 2. The minimal emphasis on reading makes

the materials more culture free, thus enhancing its use with non-English-speaking and slow learners as well as with gifted learners.

3. The instructional matrix (pp. 8-13) is a ready reference that gives teachers a picture of the whole as well as the parts of the curriculum.

4. It includes answers for each of the student exercises.

In my opinion, the material could be im- proved by the following:

1 . Deleting some of the detail from teacher lesson plans (the plans are not as concise as those contained in the Building Thinking Skills - Primary plans). For example, the lesson plan (pp. 35-40) is much too cluttered to be practical; the demonstration portion is too long for the short attention span of young students.

2. Including more descriptive verbs in the lesson plan objectives. For example, in the lesson plan on page 26, learn is very vague and difficult to measure.

3. Requiring students to indicate answers by making stripes or other marks in the Venn diagram section (pp. 115-20). Such a procedure might lead to less confusion. For example, in C-133, making a striped drawing using a color other than black or white might make the lesson clearer.

In conclusion, the authors have adhered closely to Piaget's basic theory of learning, that is, that the most powerful learning occurs when students move from the concrete (manipulative) stage to the semiconcrete (paper-and-pencil) stage to the abstract (verbal) stage.

In my opinion, Building Thinking Skills - Book 1 is an easy, inexpensive, and effective tool for teaching critical thinking skills within the lower elementary curriculum. - Carole Spencer.

Building Thinking Skills- Book 2, Howard Black and Sandra Black. 1984, teach- er's manual and lesson plans, 260 pp., $15.95, ISBN 0-89455-321-6; reproducible pages, 296 pp., $19.95, ISBN0-89455-252-X. Midwest Pub- lications, P. O. Box 448, Pacific Grove, CA 93950-0448. In Building Thinking Skills - Book 2, the authors have capitalized on Piaget's learning theories by arranging the materials in a progressive

order from cognition to evaluation to conver- gent production. The heavy emphasis on pro- cess rather than content offers the teacher a powerful diagnostic tool. Understanding be- comes more important than memorization.

Although the material should aid in the de- velopment of language skills, the fact that the exercises are somewhat independent of the student's reading level makes the material ide- al. Most of the exercises contained in the stu- dent manual are relevant and should reinforce the concepts to be mastered.

When this book is used in conjunction with the earlier books in the series (Building Think- ing Skills - Primary and Book 1), one can readily recognize the spiral effect in action. This feature allows the teacher to accelerate stu- dents according to their level of development, that is, if a particular student is having difficulty understanding verbal sequence in book 2, he or she could review the section in book 1. Using the entire program makes the problem of trans- fer students more manageable.

The lesson plans adequately meet teachers' needs. Although they contain the important ingredients of most lesson plans, I believe that the inclusion of a formative (or summative, if appropriate) section would enhance the effec- tiveness of the material. The lack of an evalua- tion section throughout the series is a distract- ing feature from an otherwise superior set of curriculum materials.

As previously noted in my reviews of the primary and book-1 sets, I am most impressed by the sections on curriculum application con- tained in each lesson plan. Teachers will be- come more cognizant of thinking skills across the curriculum, and students will better recog- nize the significance of the material to be mas- tered.

The instructional matrix contained on pages 8-15 is a definite asset. It permits teachers to see the "trees" as well as the "forest." In coordinating new lessons with experiences gained from previous ones, the authors have provided continuity throughout the series. An added bonus is that teachers can progress from figurai to verbal strands at their discretion.

I object to the authors' statement that "ac- tively working on the thinking skills presented in these books will improve students' test- taking abilities and increase scores on most nationally normed tests." I do not disagree with this assertion; however, I am bothered by this type of conjecture.

I offer the following recommendations and suggestions relative to the entire Critical Think- ing Skills Program:

1 . That the series incorporate computer tech- nology, especially exercises to offer slower learners additional practice

2. That a set of references (i.e., those in- cluded under the extended-activities portion of lesson plans) be available for teachers' use

3. That extensive teacher training, including on-site visitation by curriculum specialists, be offered by school districts that adopt the Criti- cal Thinking Skills Program

In conclusion, my opinion is that Critical Thinking Skills - Book 2 will be most useful in

the development of thinking skills, especially in higher-ability students. The thinking skills of lower-ability students will also be significantly improved.

By adopting the program and incorporating the entire series into their curriculum, school districts will better prepare students to function in society as decision-making individuals. - Carole Spencer.

Fascinating Fibonaccis: Mystery and Magic in Numbers, Tmdi Hammel Garland. 1987, 103 pp., $9.95 paper. ISBN 0-86651-343-4. Dale Seymour Publications, P.O. Box 10888, Palo Alto, CA 94303. Fascinating Fibonaccis is a comprehensive study of Fibonacci numbers. The book dis- cusses the relationships of the numbers in the Fibonacci sequence to each other and their occurrence in nature, art, architecture, music, poetry, psychology, technology, science, and even the stock market. Throughout the text the historical perspective of the discovery of the pattern in an event is discussed. Diagrams and pictures are used extensively for illustration. This resource book could be used by the teacher as an information source for instruction or as a reference source for students' projects or reports. It is a good addition to the students' collection in middle school and high school libraries as well as a professional reference book for teachers.

This book is truly fascinating reading! It is filled with quality historical information as well as very interesting mathematical relationships dealing with the Fibonacci sequence. The beauty of mathematics and the order that math- ematics gives to our world are exemplified in this book. - Jeanette Gann.

The King's Chessboard, David Birch. 1988, 32 pp., $10.95 cloth. ISBN 0-8037-0365-1. Dial Books for Young Readers, 2 Park Ave., New York, NY 10016. Now is an interesting time to be involved in education. Nearly every day someone some- where writes about "bridging the gap," about schooling's relevance to everyday life. Cries are heard that real-world learning is collabora- tive and social, that it is functional and purpose- ful, that it is intrinsically rewarding. Out of school, people of all ages learn because they wish to learn and they seem to enjoy doing so.

For a while, educators seemed to attempt to bridge the gap via gimmicks; various "bags of tricks" were used to make school learning seem to be social, functional, and rewarding. Books like The King's Chessboard by David Birch with wonderful illustrations by Devis Grebu suggest that we have outgrown this adolescent gap-bridging stage and have reached a more mature stage where we have eliminated the gap; thus we have brought real-world learning into schooling.

The King's Chessboard is a good book from anyone's perspective. It is an interesting, well- written story about a king who wishes to reward a wise man for his services. The wise man does not want a reward but is pressured by the king

February 1989 65

This content downloaded from 62.122.73.246 on Sun, 15 Jun 2014 06:23:49 AMAll use subject to JSTOR Terms and Conditions

Page 3: FOCUS ISSUE: NUMBER SENSE || The King's Chessboardby David Birch

to accept something. The wise man asks for rice - one grain on the first day, the amount to be doubled every day for as many days as there are squares on the king's chessboard.

The King's Chessboard teaches lessons, as does all good literature. The reader learns about wise and foolish, about grace and humility, and about mathematical relationships. It becomes easy to understand the wisdom of the wise man's request and to be impressed with the awesomeness of doubling. The King's Chess- board also arouses one's curiosity. I found myself trying to figure out a formula that would allow me to compute just how much rice the king might have to give the wise man. I wanted to know the amount he would have to give altogether and how much the last delivery would be. I wanted to know if the king's math- ematicians used the same formula I had in- vented.

I think other learners would be similarly intrigued. I have visions of children computing how many days it would take, starting with a penny a day, to earn enough money for a new bicycle or "boom box." I can imagine children surprising parents and friends with their new understanding and even showing others how to do the computation.

This book presents mathematics that is so- cial, functional, and intrinsically rewarding. Wouldn't it be nice if other authors followed Birch's lead, and literature could be used in classrooms every day to show learners how mathematics is a part of our world? If more "mathematics" books like The King's Chess- board became the kind of books one would want to give, and receive, as gifts? If mathe- matics could be shared through the real-life events that fostered its invention?

The King's Chessboard is clearly a good beginning, a book to replace some of the nau- seatingly boring word problems that dominate most textbooks. It is, perhaps, the first book of many to eliminate the division between school and life, but definitely the first book I'd put in my mathematical literature collection. - Diane Stephens, University of North Carolina at Wilmington, Wilmington, NC 28403.

Math Instruction Using Media and Modality Strengths: How ... It Fig- ures, Joan C. Carson and Ruby N. Bos tick. 1988, 219 pp., $29.95 cloth. ISBN 0-398-05461- 4. Charles C. Thomas, 2600 South First St., Springfield, IL 62717. Carson and Bostick have sought to go beyond the traditional materials-and-media book to present a text that stresses matching media to a student's modality strengths. They have chosen mathematics as the subject to demonstrate the various ways that media can be used in instruc- tion. The book, a modality-based approach to learning, is divided into three sections. In the first section, the authors discuss visual, audi- tory, and kinesthetic modalities and the class- room practices that accommodate these dif- ferent modalities. In the second, various instructional media are described. The third section suggests media that can be used to meet specific objectives in mathematics, especially at the elementary school level. The book con-

cludes with an index of key terms and a bibli- ography.

This text would have profited from more careful proofreading, with particular attention being paid to coordinating the in-text citations with the bibliographies that conclude each chapter and the book as a whole. Dates did not match in several instances. In addition, typo- graphical errors, such as placements for placemats, are also distracting. An especially troubling error occurs on page 156 in a section labeled "Attribute Materials," where the au- thors state that "these are sometimes referred to as geopieces or pattern blocks "

Math Instruction Using Media and Modality Strengths is intended for college students, per- haps in a media course. Each chapter begins with a set of objectives that organizes the material and ends with a restatement of those objectives in the form of study questions.

Whereas the authors appear to know media, some curious omissions occur in the other areas encompassed by their work. For example, in their discussion of modalities, they do cite Barbe, but they make no mention of others, such as Bandler, Grinder, Satir, Watzlawick, Lankton, or even the grandfather of them all, Milton Erickson, who have broken ground in that field. With respect to the mathematical literature, the authors often cite the earliest edition of a book that is widely available in a second or third edition, and only 23 percent of their seventy-seven references have copyright dates later than 1984. Curiously, all references in their discussion of problem solving were published before 1978. It was also surprising,

given their thesis that instruction should be matched to preferred modality, that the authors did not present any informal methods, except comparison to a characteristics list, by which teachers could ascertain a given student's mo- dality. Such information might be useful when a student does not profit from instruction in the multimodality classroom that they suggest.

This book might be a useful reference for a professional with a strong mathematics meth- ods background who wishes more closely to match available media with identified student modalities. - Grace M. Burton.

Mental Math in Junior High, Jack a. Hope, Barbara J. Reys, and Robert E. Reys. 1988, 170 pp., $9.95. ISBN 0-86651-433-3. Dale Seymour Publications, P.O. Box 10888, Palo Alto, CA 94303. This book is the last in a series of three books designed to help teach students the techniques of computing "in your head." It may be used independently of the other two books and is designed for use with grades 7-9. Fifty lessons introduce calculating mentally with fractions, decimals, and percents, as well as with whole numbers. Various strategies emphasize pat- terns and shortcuts that help students perform difficult mental calculations. Techniques and strategies for computing mentally are presented on lesson pages set in large-sized type for display on the overhead projector or for use as blackline masters to produce handouts. Prob- lems for guided practice are included on the lesson page. Accompanying each lesson are

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