One Point of View: Step-by-Step: What Are You Doing This Year?Author(s): Mary Montgomery LindquistSource: The Arithmetic Teacher, Vol. 30, No. 1 (September 1982), p. 6Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192027 .

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One Point OF X7ÌGCD Step-by-Step:

What Are You Doing This Year?

By Mary Montgomery Lindquist National College of Education, Evans ton, Illinois

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Previous editorials on An Agenda for Action* have expressed many dif- ferent points of view, but two themes were common: change in schools is a process that occurs step-by-step over time, and the teacher is a crucial in- gredient in this change. We are now one-fourth of the way through the 1980s and beginning a new school year, so it is appropriate to ask your- self what you are going to do in this step-by-step process of change?

Before you decide on your answer, reread An Agenda for Action. There are some hidden gems that tend to get lost in the push for problem solving and technology. Choose a reasonable goal for the one step you will take this year.

Consider the powerful statement in Recommendation 4:

Instructional time is a precious commodity. It must be spent wisely. . . . [Teachers] must apportion instructional time according to the importance of the topic (p. 11).

This statement brings many goals to mind, but let me suggest one: make a plan for your mathematics class for the year. Many teachers are surprised when they realize they have only about 150 "good" days for teaching. Consider how you will apportion the year's work. What is an ideal amount of time to spend on concept develop- ment? on skills? on problem solving? What percentage of time should be spent on each strand - numbers, com- putation, measurement, geometry, and so on? on testing? on review? on maintenance of skills? Careful plan- ning for the year will help you use time wisely.

6

From Recommendation 5 we have this statement:

The informed judgment of teachers should be considered a vital part of the evaluation of any student (p. 15).

One way to make judgments more informed is to interview each child at least once on some topic. Ten minutes with individual children, letting them tell how they are solving particular problems or thinking about algorithms or basic facts, often reveals much that you do not gain from paper-and-pencil tests, exercise assignments, or even questioning in a class situation.

Recommendation 2 begins as fol- lows:

There must be an acceptance of the full spec- trum of basic skills and recognition that there is a wide variety of such skills beyond the mere computational if we are to design a basic skills component of the curriculum that enhances rather than undermines education (p. 5).

After you examine your program to see if it includes a wide spectrum of basic skills, choose one topic to con- centrate on this year. Can you include other basic skill areas as you teach this topic? Suppose you choose deci- mals. Are there measurement skills that can be sharpened as the students study decimals? How much problem solving or applications can you in- clude? What about graphing or read- ing tables? Can you use this topic to review many of the computation skills and to extend estimating and problem- solving skills? Only by integrating many of the basic skills will we find time to include a wider spectrum. This integration can also help students see how mathematics fits together and is used.

Recommendation 2 also includes the following statement: Teachers should incorporate estimation activi- ties into all areas of the program on a regular and sustaining basis, in particular encouraging the use of estimating skills to pose and select alternatives and to assess what a reasonable answer may be (pp. 7-8).

There are many questions you need to ask yourself before implementing this goal. How will you allot the time to include estimation? What strategies of estimation will you encourage? What skills do your students need to help them estimate? What materials are available to help you with estimation activities? Can you change your ques- tioning techniques to include more estimation?

Hidden in Recommendation 7 is the following statement: Even the best prepared, competent, and dedi- cated teachers must continue their development to keep abreast of changing needs, tools, and conditions (p. 24).

There are many options for imple- menting this action, but consider choosing one topic that has caused you difficulty in teaching (fractions?), or that you have never felt fully pre- pared for (geometry?). Become an "expert" on that topic by doing some research - reading, attending classes or conferences, talking with others about the topic, collecting or design- ing material to use, and trying out the material in your classroom. Keep a careful record of what does and does not work, so that you can revise your plans for the following year.

The quotes and comments that have been included here are just a few of the many that may be gleaned from the Agenda. Plan now for whatever step you decide to take. Otherwise you may soon realize that another school year has passed without your making any substantial changes in your mathematics teaching or pro- gram, v

* As long as the supply lasts, single copies of An Agenda for Action are available free from the NCTM Headquarters Office, 1906 Association Drive, Reston, VA 22091.

Arithmetic Teacher

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