Research and Rationale
Learning does not mean simply receiving and remembering a transmitted message;
instead, "educational research offers compelling evidence that students learn
mathematics well only when they construct their own mathematical understanding"
(Mathematical Sciences Education Board, 1989, p. 58). To help students learn
mathematics, teachers must become aware of how children have constructed
mathematics from their experiences both in and out of school and learn more
about what it means for students to construct mathematical knowledge. Three
basic tenets of constructivism are:
- Knowledge is not passively received but is actively created or invented
(constructed) by students. Students construct new mathematical knowledge by
reflecting on their physical and mental actions.
- Learning reflects a social process in which students interact, discuss, and
even argue their ideas, with themselves and with others, in the process of
understanding a particular concept.
- The National Council of Teachers of Mathematics, in the Assessment Standards
for School Mathematics (1995), emphasized the importance of having an alignment
(consistency) between the tools used for instruction in the classroom and for
assessment. Most recently, the NCTM Principles and Standards for School
Mathematics (2000) stated that "electronic technologies —
calculators and computers — are essential tools for teaching, learning,
and doing mathematics."
Such learning experiences are:
Hands-on, involving students in really doing mathematics — experimenting
firsthand with physical objects in the environment and having concrete
experience before learning abstract mathematical concepts
Minds-on, focusing on the core concepts and critical thinking processes needed
for students to create and re-create mathematical concepts and relationships in
their own minds.
Authentic, allowing students to explore, discover, discuss, and meaningfully
construct mathematical concepts and relationships in contexts that involve
real-world problems that are relevant and interesting to the learner.
The Use of Technology in the Learning and Teaching of Mathematics
The appropriate use of instructional technology tools is integral to the
learning and teaching of mathematics and to the assessment of mathematics
learning.
Technology has changed the ways in which mathematics is used and has led to the
creation of new and expanded fields of mathematical study. Thus, technology is
driving change in the content of mathematics programs, in methods for
mathematics instruction, and in the ways that mathematics is learned and
assessed. A vital aspect of such change is a teacher's ability to select and
use instructional technology to develop, enhance, and extend students'
understanding and application of mathematics. (See NCTM Position Statement at
http://www.nctm.org/about/position_statements/position_statement_13.htm.)
Calculators and the Education of Youth
The National Council of Teachers of Mathematics recommends the integration of
calculators into the school mathematics program at all grade levels.
Research and experience support the potential for calculator use to enhance the
learning and teaching of mathematics. Calculator use has been shown to enhance
cognitive gains in areas that include number sense, conceptual development, and
visualization. Such gains can empower and motivate all teachers and students to
engage in richer problem-solving activities. (See NCTM Position Statement at
http://www.nctm.org/about/position_statements/computation.htm.)