Research on Communication

Mathematics as a Language
As with all language acquisition, we learn by talking, listening, reading, and writing. In mathematics class, we build the skills that allow us to communicate our thinking with many others. We make conjectures, try these out, report on our progress, and refine our thinking. An important aspect of communication of mathematical ideas is to have a variety of ways to think about and express those ideas. Students may use sketches, graphs, tables, symbols, or words to facilitate both thinking and communicating. The overarching goal is to make sense of and take ownership of mathematical concepts. This goal is more efficiently reached when students are given opportunities to discuss their thinking with peers and teachers. The metacognitive activity of formulating, representing, clarifying, and communicating ideas leads to an increase in learning. (Lampert and Cobb, 2003)

Communication in the CPMP Classroom
An observer would see students poring over their collaborative work, making suggestions for improvements, and in the process, making mathematical sense of the ideas being studied. Investigative questions deliberately call for collaboration. "Effective learning environments are community-centered. These communities can build a sense of comfort with questioning rather than knowing answers and can develop a model of creating new ideas that builds on the contributions of individual members." (Pellegrino, 2000) Homework questions consciously ask for explanation and reflection, all with the goal of being able to do new and somewhat different problems. See CPMP Classrooms.

Parent Role
Parents can also be part of this metacognitive process (Garafolo, 1985) when they allow students to explain what they have learned and identify where they still have difficulty. Having your child teach you a concept learned in class is a powerful way of reinforcing that learning. See Helping with Homework and Tips for Helping a Student.

Communication as an Assessment Tool
Communication is integral to a CPMP classroom, both to develop understanding of mathematics and as a means for the teacher to assess what each student knows. Thus, teachers can be seen monitoring group investigations, leading class discussions, making informal assessments of individual and whole-group knowledge, and adjusting their teaching plans as they gather information. Of course, tests and quizzes and homework also require students to communicate their thinking clearly, to convince themselves and their teachers that they really have mastered new ideas.

International Research
The emphasis on communication in mathematics is a fairly new development in this country. Most state mathematics standards now reflect this. In some other countries, this emphasis on communication is not so new. Watching TIMSS videos of Japanese classrooms or reading about Chinese classrooms in Liping Ma's book will reveal careful communication, far more elaborate than the short answers quickly given that you may recall from your own schooldays. (Ma, 1999)

Research to consider:

  • National Research Council. How People Learn: Brain, Mind, Experience, and School. Committee on Developments in the Science of Learning and the Committee on Learning Research and Educational Practice. J. Bransford, A. Brown, R. Cocking, S. Donovan, and J. Pellegrino (eds.). Washington, DC: National Academy Press 1999.
  • Kaput, James J. "Linking Representations in the Symbol Systems of Algebra." In Research Issues in the Learning and Teaching of Algebra, edited by Sigrid Wagner and Carolyn Kieran, pp. 167-194. Research Agenda for Mathematics Educators, vol. 4. Reston, VA: Lawrence Erlbaum Associates and NCTM 1989.
  • Garafolo, Joe and Frank K Lester, Jr. "Metacognition, Cognitive Monitoring, and Mathematical Performance." Journal for Research in Mathematics Education 16 (May 1985): 163-76.
  • Hiebert, James. "Relationships between Research and the NCTM Standards." Journal for Research in Mathematics Education 30 (January 1999): 3-19.
  • Lampert, Magdalene. "When the Problem is not the Question and the Solution is Not the Answer: Mathematical Knowing and Teaching." American Educational Research Journal 27, no. 1 (Spring 1990): 29-63.
  • Lampert, Magdalene, and Paul Cobb. "Communication and Language." In Research Companion to NCTM's Standards, edited by Jeremy Kilpatrick, W. Gary Martin, and Deborah Schifter. Reston, VA: National Council of Teachers of Mathematics, 2003.
  • Ma, Liping. Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, 1999.
  • Silver, Edward A., Jeremy Kilpatrick, and Beth G. Schlesinger. Thinking Through Mathematics: Fostering Enquiry and Communication in Mathematics Classrooms. New York, NY: College Entrance Examination Board, 1990.
  • Silver, Edward A., and Margaret S. Smith. "Implementing Reform in the Mathematics Classroom: Creating Mathematical Discourse Communities." In Reform in Math and Science Education: Issues for Teachers. Columbus, OH: Eisenhower National Clearing House for Mathematics and Science Education, 1997. CD-ROM.
  • Stigler, James W., and James Heibert. The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom. New York, NY: The Free Press, 1999.
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