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:

1. 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.
2. 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.
3. 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.)