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
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
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,
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 Core-Plus Mathematics
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
As you talk to your student 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 Questions
to Ask When 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
encourage your student to reflect on what was recently learned,
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,
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.