Douglas H. Clements
Julie Sarama Meredith
What might be the role of using Logo in mathematics education, given the information in the Curriculum and Evaluation Standards (NCTM 1989) and the appearance of numerous new software packages? A recent rare interview with the Logo turtle may dispel some rumors and offer new insights into this question.
Interviewer: Start us off with the big picture. Can computers be used effectively in school?
Turtle: Research shows that students make significant learning gains using computers, especially in mathematics (Clements and Nastasi 1992; Roblyer, Castine, and King 1988). These gains are consistent across schools and grades.
I: So, computers are effective.
T: Yes, but this research doesn't imply that using any software in any way guarantees automatic learning.
I: The Logo language has been around for decades. Shouldn't we be looking at what's new?
T: This issue really gets under my shell. Logo is not "old" software; it is evolving. I've heard people say that newer software is easier to use. One consultant said, "I don't suggest Logo anymore, now that we have Dazzle Draw." The point is not the drawing, it's thinking about doing the drawing (Clements and Battista 1992). A lot more thought has to go into deciding what should be "easy" and what should remain a struggle, in the positive sense of the word. Sometimes you have to stick your neck out.
I: But shouldn't students use a lot of different types of programs?
T: Yes, except that the programs they use should become tools for thinking. We need to be wary of serving a potpourri of applications with no internal coherence. Research comparing Logo with a set of utility and problem-solving programs demonstrated that stronger feelings of control and mastery emerged with Logo (Clements and Nastasi 1992).
I: Well, how about good drill and practice? Did you say that it doesn't matter whether you use drill-and-practice software or Logo, as long as it's a good quality product?
T: No! I agree that research indicates that both approaches, done right, can raise achievement scores. But that's just the beginning. You have to consider your goals. Recent recommendations for school reform, such as those in the Curriculum and Evaluation Standards (NCTM 1989) demand that certain approaches be emphasized.
The turtle went on to further discuss the connection between Logo and the curriculum standards. The standards document discusses Logo specifically.
Computer microworlds such as Logo turtle graphics and the topics of constructions and loci provide opportunities for a great deal of student involvement. In particular, the first two contexts serve as excellent vehicles for students to develop, compare, and apply algorithms. (p. 159)
However, other excerpts from the curriculum standards that do not mention Logo better exemplify its full power.
In learning geometry, children need to investigate, experiment, and explore... (p. 48).
When mathematics evolves naturally from problem situations that have meaning to children and are regularly related their environment, it becomes relevant and helps children link their knowledge to many kinds of situations (p. 23).
A major goal of mathematics instruction is to help children develop the belief that they have the power to do mathematics and that they have control over their own success of failure (p. 29).
The Logo philosophy and the constructivist philosophy of the curriculum standards have the same two major goals (Clements and Battista 1990). First, students should actively experience building ideas and solving personally meaningful problems. Second, students should become autonomous and self-motivated.
I: So, Logo fits the philosophy of the curriculum standards.
T: I don't mean to be too hard-shelled, but I remember when some mathematics educators called the Logo philosophy "romantic" and "unrealistic." Now that the standards document expresses a similar point of view, Logo should be increasingly discussed at professional conferences. But it's not nearly enough.
I: But I've heard that students don't always do mathematics when they use Logo.
T: I never intended to work alone. I talk mathematics. But students don't always listen (Leron 1985). I need teachers' help. To produce successful Logo projects, teachers don't load Logo and then withdraw into their shells. They think about the Logo tasks. They help students enrich their intuitive, visual strategies ("It looks like about FD 30") by presenting problems that also require analytic solutions, such as drawing following figures with the turtle (see fig. 1).
Figure 1: Figures drawn using the Logo turtle
Successful teachers talk to students about their work and encourage them to talk to each other. They are responsible for guiding and supporting students' viable ideas rather than transmitting "correct" adult knowledge. As a result, their students reflect on their individual work and link what they know in and out of the Logo environment (Clements and Battista 1992) (A Bibliography of teaching resources is listed at the end of this article).
Surprising research results from using Logo appear in its social and emotional benefits to students. Students cooperate more while working in Logo environments, and they cooperate on learning. They also disagree more about ideas, but they are more likely to resolve these disagreements successfully by synthesizing their ideas (Clements and Nastasi 1992; Nastasi, Clements, and Battista 1990).
I: I know you must leave to make a screen appearance. Can you summarize your thoughts for us?
T: I don't mean to "repeat" myself, but research suggests that If you want a safe and relatively easy path, choose drill-and-practice software. You'll probably increase achievement. If instead you want to effect substantive change in the quality of your students' educational experiences, use Logo software, but be ready to work hard at it. But, as my grandfather told me, slow but steady wins the race.
Clements, Douglas H., and Michael T. Battista. "Research into Practice: Constructivist Learning and Teaching." Arithmetic Teacher 38 (September 1990):34-35.
-----. "Geometry and Spatial Reasoning." In Handbook of Research on Mathematics Teaching and Learning, edited by D. A. Grouws, 420-64. New York: Macmillan Publishing, 1992.
Clements, Douglas H., and Bonnie K. Nastasi. "Computers and Early Childhood Education." In Advances in School Psychology: Preschool and Early Childhood Treatment Directions, edited by M. Gettinger, S. N. Elliott, and T. R. Kratochwill, 187-246. Hillsdale, N.J.: Lawrence Erlbaum Associates, 1992.
Leron, Uri. "Logo Today: Vision and Reality." Computing Teacher 12 (February 1985):26-32.
Nastasi, Bonnie K., Douglas H. Clements, and Michael T. Battista. "Social-Cognitive Interactions, Motivation, and Cognitive Growth in Logo Programming and CAI Problem-solving Environments." Journal of Educational Psychology 82 (March 1990):150-58.
National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. Reston, Va.: The Council, 1989.
Roblyer, M. D., W. H. Castine, and F. J. King. Assessing the Impact of Computer-based Instruction: A Review of Recent Research. New York: Haworth Press, 1988.
Battista, Michael T., and Douglas H. Clements. "Research into Practice: Constructing Geometric Concepts in Logo." Arithmetic Teacher 38 (November 1990):15-17.
-----. Logo geometry. Morristown, N.J.: Silver Burdett & Ginn, 1991.
Clarke, Valerie A., and Susan M. Chambers. Thinking with Logo. New York: McGraw-Hill, 1985.
Goldenberg, E. Paul. "Learning to Think Algebraically." Logo Exchange 5 (October 1986):16-20.
Harper, Dennis. Logo: Theory and Practice. Pacific Grove, Calif.: Brooks/Cole Publishing Co., 1989.
Hoyles, Celia, and Richard Noss. Learning Mathematics and Logo. Cambridge, Mass.: MIT Press, 1992.
Logo Exchange. Eugene, Oreg.: SIGLogo/ISTE.
Nevile, Liddy, and Carolyn Dowling. Let's Talk Apple Turtle. Reston, Va.: Prentice-Hall, 1983.
Ryoti, Don E. "Computer Corner: Using the Computer and Logo to Investigate Symmetry." Arithmetic Teacher 34 (November 1986):36-37.
Shimabukuro, Bini. Thinking in Logo: A Sourcebook for Teachers of Primary Students. Menlo Park, Calif.: Addison-Wesley Publishing Co., 1988.
Shumway, Richard J. "Why Logo?" Arithmetic Teacher 32 (May 1985):18-19.
Thomas, Eleanor M., and Rex A. Thomas. "Exploring Geometry with Logo." Arithmetic Teacher 32 (September 1984):16-18.
Watt, Molly, and Daniel Watt. Teaching with Logo. Menlo Park, Calif.: Addison-Wesley Publishing Co., 1986.
Portions of this article were originally published by ISTE in Clements, D. H. (1991). Logo: Search and research. Turtle Talk. Logo Exchange 10(1), 43-47. Time to prepare this material was partially provided by the National Science Foundation under Grants No. MDR-8651668, MDR-9050210, and MDR-8954664. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.
The views expressed in "One Point of View" do not necessarily reflect the views of the Editorial Panel of the Arithmetic Teacher or the National Council of Teachers of Mathematics. Readers are encouraged to respond to this editorial by sending double-spaced letters to the Arithmetic Teacher for possible publication in "Readers' Dialogue." Manuscripts of approximately six hunderd words are welcomed for review for "One Point of View."
Douglas Clements teaches at the State University of New York at Buffalo, Buffalo, NY 14260. He is interested in students' learning of geometry, especially in computer environments. Julie Meredith is a research assistant currently workin gon a new version of Logo with Clements.
Other Articles by Douglas H. Clements:
Other Articles by Julie Sarama: