Research on Learning

How People Learn
The kinds of learning required for the twenty-first century go beyond those required for the last century. The National Research Council, among other groups, has drawn attention to the growing body of research that suggests that "learning is a complex cognitive process that builds on prior knowledge and requires active engagement with new situations." (How People Learn, 2000) Programs that encourage students to develop their own strategies, that pay attention to both cognitive and social variables, and that foster opportunities to reason about correct and incorrect answers prove to be effective. (Siegler, 2003)

What Educators Can Do to Maximize Learning
Educators make decisions about what to teach, how to teach it, and how to assess what students have learned. When educators take recent research into consideration, they will want to provide an environment that

  • emphasizes understanding and sense-making,
  • starts with current student understandings,
  • uses a variety of problem contexts,
  • builds concepts carefully,
  • includes opportunities to revisit mathematical topics with increased complexity, and
  • encourages students to reflect and refine their understandings.

Characteristics of Effective Instruction
"The process of inquiry, not merely giving instruction, is the very heart of what teachers do." (See Before It's Too Late.) There is a striking difference between what U.S. teachers have typically done and what Japanese teachers do, as recorded in the TIMSS videos and related research. Some findings from recent research indicate that instruction should:

  • be organized around meaningful problems,
  • give students time, encouragement, and support to struggle with these problems,
  • recognize that a student's struggle with a problem is an indication that the student's brain is actively involved in comparing new ideas to preconceived notions, and organizing and synthesizing new information, and
  • provide cognitive scaffolding, recognizing that individuals learn through interactions with more knowledgeable others. ("Knowledgeable experts model good thinking, provide hints, and prompt students who can not get it on their own." How People Learn.)

Relevance to CPMP
The developers of CPMP were cognizant of recent research in learning and developed a program intended to foster inquiry and reflection, provide meaningful problems in a variety of contexts, and focus students on understanding mathematical ideas.

Parent's Role
As you talk to your child about what he/she has learned in class, you are an active part of the learning process. You are one of the "knowledgeable experts," in your student's universe. By helping your student think about mathematics, you are part of the process that researchers tell us enhances achievement and develops the ability to learn independently. (See Tips for Helping a Student.) You can

  • provide hints or ask questions when helping with homework, without taking away all the gains to be made from the student's individual struggle,
  • encourage your student to reflect on what was recently learned, and
  • ask questions that encourage your student to explain concepts.

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 2000.
  • National Research Council. How People Learn: Bridging Research and Practice. J. Bransford, A. Brown, R. Cocking (eds.). Washington, DC: National Academy Press 2000.
  • U.S. Department of Education. Before It's Too Late: A Report to the Nation from the National Commission on Mathematics and Science Teaching for the 21st Century. Washington, DC. (September 2000).
  • Forman, Ellice Ann. "A Sociocultural Approach to Mathematics Reform: Speaking, Inscribing and Doing Mathematics Within Communities of Practice." In A Research Companion to Principles and Standards for School Mathematics, edited by Jeremy Kilpatrick, et al. Reston, VA: NCTM, 2003.
  • 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.
  • Mason, J., and M. Spence. "Beyond Mere Knowledge of Mathematics. The Importance of Knowing to Act." In Educational Studies in Mathematics. 38, 1/3 (1999): 135-161.
  • Siegler, Robert S. "Implications of Cognitive Science Research for Mathematics Education." In A Research Companion to Principles and Standards for School Mathematics, edited by Jeremy Kilpatrick, et al. Reston, VA: NCTM, 2003.
  • 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 Hiebert.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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