helping preservice teachers develop an awareness of curricular issues

Helping Preservice Teachers Develop an Awareness of Curricular IssuesAuthor(s): Phares G. O'DafferSource: The Arithmetic Teacher, Vol. 31, No. 9 (May 1984), pp. 6-8Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192401 .

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Teacher Education Helping Preservice Teachers Develop an Awareness of

Curricular Issues By Phares G. O'Daffer

Illinois State University, Normal, IL 61761

A teacher refuses to allow calculators in the classroom because "the children won't learn their facts and computational skills." Another teacher elects not to read anything about computers, since "we don't have one in our classroom anyway." A third teacher skips the text's chapters on geometry, since "I don't see any real use for it." A fourth teacher "doesn't see why people think problem solving is so important" and calls it a passing fad. Another teacher wants a book that doesn't teach fractions because "we are in a metric age, and decimals are all that are needed." At the same time, another teacher wants a book that teaches only the customary units of measurement, since "the metric system didn't catch on."

It would be easy to discount these ideas by viewing these particular teachers as slightly out of focus on some of the current curricular issues. However, the main impact of their comments might be to cause us to ask the following:

As teacher educators, do we really help preservice teachers develop an awareness of the mathematics curriculum and a personal philosophy that will enable them to establish reasonable priorities when they are teachers?

During the past several years, one trend in methods courses for preservice teachers (PSTs) has been toward developing more practical ideas and techniques. Experiences such as planning bulletin boards, preparing activity cards, collecting games and puz- zles, making manipulative teaching

6

aids, watching videotapes about teaching, planning lessons, and in- creasing school participation are all extremely valuable. However, if we are to help PSTs develop an awareness of the curriculum and a working philosophy of mathematics instruction, we must offer them experiences that go beyond "what do I do on Monday?"

To increase their awareness of content and process goals, appropriate sequences, and major curricular issues, PSTs require a carefully devel- oped set of experiences. Because of the limited time available in the methods class and because, at this level, PSTs tend to reject "theory," these experiences must be brief, vivid, and interesting.

The remainder of this article gives some specific learning experiences you may wish to provide for your PSTs.

Motivating textbook analyses Since many beginning teachers rely on a textbook for curricular content and sequence, it seems reasonable to focus initially on this interpretation of the curriculum.

One technique that can motivate PSTs to examine textbooks and teacher's manuals carefully is to have them complete a ' 'textbook scavenger hunt." Examples of some questions for the scavenger hunt are shown in figure 1.

Questions that are appropriate for the hunt should have the potential to heighten the PSTs' awareness of the major types of content taught at each grade level, developmental se-

quences, and the depth at which topics might be presented. Also, students can be encouraged to focus on the role of the textbook in handling important curricular issues related to basic computational skills, calculators, computers, problem solving, geometry, and the metric system.

After such an examination of a textbook series, one PST remarked, "I had no idea that so much is taught in third grade!" Other questions can focus on important things to be learned, such as concepts, facts, generaliza- tions, skills, and the higher level pro- cesses of estimation, problem solving, and logical reasoning. The proportion of the program devoted to each type of learning can be assessed and noted for further discussion as the methods course progresses.

Note that the scavenger-hunt technique can also be used to analyze and compare curriculum guides in differ- ent districts.

Although this general look at the curriculum "through the eyes of a textbook series" is important, natural limitations in textbooks make it im- perative that enlightened teachers use other sources to provide PSTs with a way to understand curricular issues and make intelligent decisions.

Making creative reading assignments In methods courses, many mathematics educators have students read "how to" articles and prepare card files that contain practical ideas to be used when they begin teaching. How- ever, a methods course can have so many things to do that students may

Arithmetic Teacher



have very little time for, or interest in, reading other articles that are more philosophical or theoretical.

Here are some ideas for brief "curriculum awareness" reading experiences that you may wish to adapt to your own setting:

1. Replace part of a regular exam with a take-home exam that includes an item like one of the following:

a. Read pages 1-35 of John Holt's How Children Fail. Summarize the major pedagogical problems in the teaching and learning of mathematics that were presented. What are some of the things you could do as a teacher to minimize these problems?

b. Read the introduction to Mind- storms by Seymour Papert. Give your reaction to the author's philosophy and major points. What is your philosophy regarding the use of computers in the elementary school classroom?

с Read Zalman Usiskin's "One Point of View" in the May 1983 issue of the Arithmetic Teacher. Do you agree with the author's position on the role of computational skills? Give reasons to support or rebut the arguments in the article.

d. Read the chapter by Osborne and Kasten in NCTM's 1980 Year- book, Problem Solving in School Mathematics. Rank the problem- solving goals and respond to the items on pages 54 and 55. Justify your rankings and compare them with the rankings of the groups in the study. 2. Create a letter that a parent

might write on a current issue in mathematics education (inclusion of the metric system, hand-held calculators in the classroom, classroom use of microcomputers, etc.). Have your students prepare a thoughtful re- sponse to the letter, based on some study of the topic.

3. Select students to make ten-minute "Why Should We Teach It?" presentations on key topics suggested for inclusion in the curriculum by NCTM's Agenda for Action, the NCSM's Basic Skills Report, or other similar recommendations. Students

May 1984

Fig. 1

Mathematics Textbook Scavenger Hunt

Name Date

Select a textbook series (grades K-8) with a copyright date or later. Name of series chosen

Publisher Copyright date

Authors

Study the texts and their teacher's editions to answer the following questions.

I. Some numeration concepts A. At what grade level are these concepts first explained?

• three-digit place value • expanded notation • decimal place value • comparison using > and < • scientific notation

B. What types of models are used to show place value?

II. Computational skills A. At what grade level are these skills first introduced?

• adding, with regrouping • subtracting, with regrouping • multiplying, three digits x one digit • dividing with one-digit divisor, two-digit

quotient

B. About what percentage of the grade book deals with computation?

III. Problem solving A. Are techniques or strategies for solving

problems presented? Where? B. Where does a problem not solved directly by

+, -, x, or 4- appear? C. Where do two-step problems first appear?

IV. Calculators and computers A. Describe how calculators are used in the

series

B. Does material on computer literacy appear? Where? :

7



can find additional information for their presentations in the Arithmetic Teacher (e.g., in the February 1979 issue on the comprehensive curriculum), from other journals, or from such publications as Selected Issues in Mathematics Education (McCut- chan Publishing Corp. 1980). Follow this activity with a class discussion of these issues.

Providing time for presentation and discussion of issues

Much has been said recently about on-task time and the importance of making every minute count in the elementary school. As teacher educators, we can practice what we preach about good use of class time. Why not use some of those minutes at the beginning or end of a class to discuss some current issues in mathematics education? For example, key points in a newspaper article about computers in schools can be highlighted. PSTs can be asked to give three or four words that come to mind as the points are presented. This brief word-associ- ation exercise might provide a spring- board for a minidiscussion. Another newspaper article about a new program for gifted students in the local schools might be discussed. Interest- ing items from the "What's Going On ..." section of the Arithmetic Teacher can provide an awareness of curricular developments. Even a re- mark about an important issue you've read about or a meeting you've at- tended is fair game for focusing on issues. An announcement about the theme and program emphases in up- coming local, regional, or national mathematics conventions would also be in order. This approach might go a long way toward instilling a desire to keep informed in PSTs. This desire, in turn, will contribute to the continued growth of teachers and an ever broad- ening awareness of the curriculum.

Another way to stimulate interest in major issues is to encourage PSTs to communicate with teaching col- leagues. A mathematics convention is a great place for such communication! One methods instructor gives students credit for attending conference sessions and reporting on their experi-

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enees. Some instructors plan field trips to nearby conventions. A lot can be learned by PSTs about curricular issues by studying the topics presented at a mathematics education convention.

I would be remiss if I did not men- tion how history can provide a per- spective on the ongoing process of curricular development. Many PSTs are surprised to learn that for decades a variety of groups (SMSG, UICSM, etc.) have wrestled with the what, where, when, why, and how of helping children learn mathematics. It is important for PSTs to understand, for example, that the current emphasis on problem solving is not new but a part of the cyclical pattern of concerns as the mathematics curriculum evolves.

Why not risk chuckles from acade- mia and make an active-involvement bulletin board in your classroom to provide a brief encounter with the history of mathematics education for your PSTs?

Concluding remarks

It is a tall order to deal adequately with the needs of PSTs. Yet the effort and creativity we bring to this task may have a far-reaching impact. Such efforts may well mean the difference

between a PST who continually im- proves as a teacher and who is excited about teaching mathematics and another PST who never has a significant commitment to the task.

Let's do our best to give PSTs the information and practical techniques they need for teaching mathematics, but let's also help them develop an awareness of the curriculum that is necessary in helping children learn mathematics.

References

Holt, John. How Children Fail. New York: Pitman Publishing Corp., 1964.

Lindquist, Mary Montgomery, ed. Selected Is- sues in Mathematics Education. Berkeley, Calif.: McCutchan Publishing Corp., 1980.

National Council of Supervisors of Mathemat- ics. "Position Paper on Basic Skills." Arith- metic Teacher 25 (October 1977): 19-22.

National Council of Teachers of Mathematics. An Agenda for Action: Recommendations for School Mathematics of the 1980s. Reston, Va.: The Council, 1980.

Osborne, Alan, and Margaret B. Kasten. "Opinions about Problem Solving in the Cur- riculum for the 1980s: A Report." In Problem Solving in School Mathematics, 1980 Year- book of the National Council of Teachers of Mathematics, edited by Stephen Krulik and Robert E. Reys, pp. 51-60. Reston, Va.: The Council, 1980.

Papert, Seymour. Mindstorms. New York: Ba- sic Books, 1980.

Usiskin, Zalman. "One Point of View: Arith- metic in a Calculator Age." Arithmetic Teacher 30 (May 1983):2. W

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