Help Your Students Read MathematicsAuthor(s): David E. GullattSource: The Arithmetic Teacher, Vol. 33, No. 9 (May 1986), pp. 20-21Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192914 .

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Help Your Students Read Mathematics

By David E. Gullatt

Many students have difficulty rec- ognizing the words in their assigned texts (Hollander 1977). Yet well over half the learning that takes place in school is based to some extent on reading. Some students who can read aloud do not understand the message the author is attempting to convey.

This article outlines ways to help the student who is unable to read a mathematics textbook. Success in the reading of mathematical material ap- pears to be related to specific rather than general reading skills. Bond and Bond (1941, 186-94) and Treacy (1944) suggest that mathematical read- ing must take into account the follow- ing: noting details, weighing the importance of details, following direc- tions, organizing facts, making infer- ences, discriminating between the rel- evant and irrelevant, and noting relationships. Here are four steps to help the student achieve these kinds of analytical reading skills.

Four-Step Approach Read slowly The first step toward helping students comprehend technical material is to slow down their reading speed. Most technical writing contains little or no extraneous information. Each word has been carefully selected for its pre- cise meaning. It is difficult to make

David Gullatt serves the Lincoln Parish School Board as principal of Simsboro High School, Simsboro, LA 71275. He was formerly supervi- sor of mathematics with the Louisiana State Department of Education and is immediate past president of the Louisiana Association of Teachers of Mathematics, an NCTM affiliate.

use of contextual clues because of the sparseness of language, and the lan- guage is usually technically sophisti- cated.

The student has been taught to read narrative material by skimming, searching for key words, and looking for main ideas (Hollander 1977). The reading of technical material requires more deliberation. Axelrod (1947, 1 1 1-14) states that because of the den- sity of information to be presented, each word is usually vital to the total comprehension of the material.

Reread The second step involves teaching the student to reread. Thomas and Robinson (1972) developed a struc- tured reading-study method called PQ4R for working with technical problems and reading structured tech- nical material. Their method was re- vised by Maffei (1973) but is still known as the PQ4R method: Preview, Question, Read, Reflect, Rewrite, and Review. This process works well with word problems. These guidelines tell the students to slow down their narra- tive reading speed and look for inter- relationships of concepts. Often stu- dents become discouraged when the solution of problems is not obvious. A good deal of thinking must take place as a student tries to plan a method of attack and then carry it out. This process requires time. In mathemat- ics, an effort must be made to writs down ideas and techniques as well as think about them.

Learn technical vocabulary The third step is to familiarize stu-

dents with the technical vocabulary and symbols necessary to their under- standing of the new material. Mathe- matics uses some ordinary words in a specialized sense so that the meaning differs from the traditional use (Morgenstern 1969, 132-36). For ex- ample, words like root, table, posi- tive, mean, and net have specific mathematical meanings as well as more familiar meanings. Other words, such as polygon, diameter, half -line, and angle are more readily under- stood as mathematical words. Addi- tional difficulties arise from symbols used in text (e.g., ", +, + , -, 0, %, @, $); numerous abbreviations (e.g., min., Ib., LCD, ft., and sq.); and such symbols as cm and m.

Oral instruction in the specialized language of mathematics is a prereq- uisite to understanding it in written form. This progression should begin when formal mathematics is intro- duced in kindergarten or first grade. When the manipulation of concrete objects is accompanied by verbaliza- tion in the special language of mathe- matics at this very early stage, the youngster develops a firm base for learning this new technical language.

Adjust patterns of eye movement A fourth step toward solving the mathematics reading problem is to help students adjust to patterns of eye movement that vary from the tradi- tional left-to-right movement. In mathematics, students must read ex- pressions with exponents, parenthe- ses, and brackets, and they must look at tables and diagrams in several dif-

20 Arithmetic Teacher

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ferent ways. When algebraic equa- tions involve fractions, students often make the mistake of reading across the numerators rather than reading the entire fractional coefficient. Teachers need to emphasize that a variety of eye-movement patterns are necessary to interpret mathematics.

Summary Strategies for reading and interpreting technical writing differ somewhat from those used in reading materials in the humanities. Because of the complexity of the material in most mathematics or science textbooks, students cannot simply scan the ma- terial and search for main ideas in the same way that they might read a novel or short story. Four suggestions have been offered here to help increase students' comprehension of written technical material: • Try to slow down the reading rate of students working with mathematical or scientific material. This material is

written concisely and should be read 4 'word for word" as well as for overall meaning. • Encourage students to reread mate- rial they do not understand the first time. • Familiarize students with the spe- cial vocabulary and symbols neces- sary to communicate technical mate- rial. • Encourage the students to adjust their eye movements to patterns other than the normal left-to-right pattern used in reading literature.

Bibliography Axelrod, Joseph. "Steps in Understanding and

Interpreting Different Kinds of Writing." In Improving Reading in Content Fields, Sup- plementary Educational Monographs, No. 62. Chicago: University of Chicago Press, 1947.

Bond, Guy, and Eva Bond. Developmental Reading in High School. New York: Macmil- lan, 1941.

Earle, Richard A. Teaching Reading and Math- ematics. Newark, Del.: International Read- ing Association, 1976. Also available from the NCTM. (ERIC Document Reproduction

Service No. ED 120-670) Hollander, Sheila K. "Reading the Special Lan-

guage of Mathematics." Paper presented at the Annual Meeting of the International Reading Association, 1977, Miami Beach, Fla. (ERIC Document Reproduction Service No. ED 137-726)

Maffei, Anthony C. "Reading Analysis in Mathematics. "Journal of Reading 16 (April 1973):546-49.

Morgenstern, Anne. "Reading Mathematical Material." In Reading and Realism, Pro- ceedings of the Thirteenth Annual Conven- tion of the International Reading Association. Newark, Del.: The Association, 1969.

Simmons, Virginia. "Reading Patterns in Math- ematics." Paper presented at the Annual Meeting of the International Reading Associ- ation, 1977, Miami Beach, Fla. (ERIC Docu- ment Reproduction Service No. ED 138-928)

Strange, Ruth, et al. The Improvement of Read- ing, chap. 7. New York: McGraw-Hill Book Co., 1961.

Taschow, Horst G. Reading in Mathematics. Regina: Saskatchewan University, 1970. (ERIC Document Reproduction Service No. ED 046-670)

Thomas, Ellen L., and H. Alan Robinson. Improving Reading in Every Class. Boston: Allyn & Bacon, 1972.

Treacy, John F. "The Relationship of Reading Skills to the Ability to Solve Arithmetic Prob- lems." Journal of Educational Research 38 (October 1944):86-96. W

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