What Can We Expect from Research?Author(s): James HiebertSource: The Mathematics Teacher, Vol. 93, No. 3 (March 2000), pp. 168-169Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/27971330 .

Accessed: 13/05/2014 13:05

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 support@jstor.org.

.

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

http://www.jstor.org

This content downloaded from 89.92.166.84 on Tue, 13 May 2014 13:05:22 PMAll use subject to JSTOR Terms and Conditions

UNDOFF!

James Hiebert

What Can We Expect from Research?

A

James Hiebert

s reform recommendations collide with traditional

practices, the questions on the minds of many interested teachers and parents are these: Should

we really adopt this new textbook series? Should we change the way we teach? What mathematics should students really be learning? It would be nice if research could give clear and simple answers to these kinds of "should" questions, but it does not and it cannot.

Research can be a powerful tool for making informed decisions in mathematics education, but it can never answer questions that have more to do with values and priorities than with the likelihood of effects. Failure to recognize the appropriate role of research leads to false optimism or disillusion ment. To harness the real power of research and use it wisely, it is essential to understand both its limitations and its promise. Many questions that are raising the temperature

of current debates, questions similar to those men

tioned here, are about goals and values. At the heart of many local disputes about curricula and

teaching methods are unsettled issues about the kind of mathematics that the school district wants its students to learn. Questions about learning goals must be answered by public debate and con sensus. Research can inform the debaters, but the final decisions must be made based on what society values most.

For example, many mathematics teachers and educators say that students should have opportuni ties to invent their own methods for solving mathe matical problems. Research augments this discus sion by identifying the kinds of problems for which

many students can invent solution methods,

The views expressed in "Soundoff!" reflect the views of the author and not necessarily those of the Editorial Panel of the Mathematics Teacher or the National Council of Teachers of Mathematics. Readers are en

couraged to respond to this editorial by sending double spaced letters to the Mathematics Teacher for possible publication in "Reader Reflections." Editorials from readers are welcomed.

describing instructional practices that support stu dents' efforts, revealing the kinds of methods likely to be invented, and even showing that students learn something different by inventing than they do

by watching a demonstration. But research does not say whether students should invent their own

methods. The answers to "should" questions depend, ultimately, on what kind of mathematics is most valued.

Once the learning goals for students are set, a

meaningful debate can begin about the most effec tive ways to reach the goals. Now research can play a more significant role in deciding which curricula and teaching methods support students' efforts to meet these goals. It would be misleading, however, to say that research can provide simple, straight forward answers. Classrooms are very complicated places, so complicated that the best ways to reach the goals will not be determined quickly or easily. This situation is not surprising, nor should it be

discouraging. The same dilemma is true in other fields; we live

with these kinds of uncertainties every day. Health

professionals have promoted the goal of a healthy life for years and have conducted a great deal of research but are still unable to specify the best way of meeting that goal. Exactly how much exercise do we need? Are seven servings of fruits and vegeta bles each day required, or would five be enough? What is your optimal weight? Our bodies are too

complicated to specify the best path to a healthy life. The same is true in mathematics education. Teachers cannot expect to get clear and specific answers from research for exactly which textbooks or activities to use.

Does this uncertainty mean that research is use

less? Not at all. Research can provide some very useful general guidelines for staying healthy and

for designing classrooms, and as more research is

James Hiebert, hiebert@udel.edu, teaches at the Universi

ty of Delaware, Newark, DE 19716. He is interested in

improving the quality of teaching and learning mathe matics in school classrooms.

168 THE MATHEMATICS TEACHER

This content downloaded from 89.92.166.84 on Tue, 13 May 2014 13:05:22 PMAll use subject to JSTOR Terms and Conditions

conducted, more details are filled in. Many impor tant decisions on the part of health professionals and of educators can be made using these guide lines. Although research can rarely prove that a

particular course of action is the best one for all

people and for all time, it can help boost the level of confidence with which decisions are made.

Here is a guideline for designing mathematics classrooms about which we can be quite confident: Students learn best what they have an opportunity to learn. Sometimes this idea is stated as, Students learn what they are taught. These two statements are not the same, however. Imagine first graders, for example, being taught calculus by listening to a

lecture. They probably will not learn much calcu lus. What they might learn instead is how to sit still and listen to things that they do not under

stand, because sitting still is what they have the best opportunity to learn. Although sitting still

might not have been what they were intended to

learn, it is what the conditions afforded. Providing opportunity to learn means establishing the condi

tions, based on students' entry knowledge and

capabilities, that are likely to engage them in the relevant tasks.

Evidence for this general guideline comes from

many sources, including national surveys of teach

ing and learning. It turns out that mathematics is

taught throughout the United States with similar

learning goals in mind and in much the same way. For the most part, the learning goals are proficient execution of mathematical skills, and most teachers work toward these goals in their classrooms by demonstrating procedures on sample problems, then giving students practice on similar problems. National assessments show that students perform best in areas in which they have had the most expe rience. They are much better at executing standard

procedures than they are at using these procedures in new situations or at developing new procedures.

Suppose that the current debate over learning goals for students moves toward acceptance of the broader and deeper goals described in the NCTM's Standards. (See the volumes published in 1989, 1991, and 1995 and the volume to be released in

April 2000.) What learning opportunities must stu

dents have to reach these goals? A second and third

guideline, supported by decades of research, can be

offered. The second guideline, a direct application of the

first one, is this: Students need opportunities to

engage directly in the kind of mathematics that they are to learn. The goals in the Standards include doing mathematics-reasoning, communi

cating, and solving problems-as well as knowing mathematics-remembering facts and procedures. To reach these goals, students must be given oppor tunities to do these things-to reason, communi

cate, and solve problems-as well as to recite facts and procedures.

A third guideline, one that might not be so obvi

ous, is that instruction can emphasize conceptual understanding without sacrificing skill proficiency. Not surprisingly, instruction can successfully pro mote deep conceptual understanding. If students have more opportunities to construct mathematical

understanding, they will construct such under

standing more deeply and more often. But at what cost? Will they fail to master facts and skills? The research evidence suggests that it is not necessary to choose between these two types of learning. The research programs generating this evidence include a balance of invention, demonstration, and practice. Students have opportunities to develop and present new procedures; listen to the shared procedures of

others, including their teachers and peers; discuss

why different procedures work; and practice proce dures that they understand.

Those who study learning, including many teach

ers, are not surprised that understanding does not detract from skill proficiency and may even

enhance it. If you understand how and why a proce dure works, you will probably remember it better and be able to adjust it to solve a new problem. If

you memorize a procedure and do not have a clue about how it works, you have little chance of using it flexibly.

Research can play a useful role in current discus sions of improving mathematics education but only if its promise and limitations are understood. Once clear learning goals for students have been agreed on, research can supply guidelines for designing classroom environments to reach those goals. Research cannot specify exactly which materials or

methods are the best, but the guidelines can help educators judge whether particular materials and methods fall within the range of practices that are

likely to help students reach the goals.

This column was prepared at the invitation of the Editorial Panel. It is intended as an abbreviated version of an article, "Relationships between Research and the NCTM Standards," that appeared in the first issue of the 1999 volume of the Journal

for Research in Mathematics Education (JRME) and of a chapter, "What Can We Say from Research about the NCTM Standards?" to appear in A Research Companion Volume to the NCTM Stan

dards, edited by Jeremy Kilpatrick, Gary W Martin, and Deborah Schifter. Readers who are interested in these and related ideas and who would like to

follow up on references that support these claims

might want to consult the JRME article or the Research Companion Volume. I would like to thank

Gwennyth Trice and Diana Wearne for their com

ments on a previous draft of this column. @

Understand

ing does not detract

from skill proficiency

Vol. 93, No. 3 March 2000 169

This content downloaded from 89.92.166.84 on Tue, 13 May 2014 13:05:22 PMAll use subject to JSTOR Terms and Conditions