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close this bookImproving Student Achievement in Mathematics (IAE - IBE - UNESCO, 2000, 48 p.)
View the document(introduction...)
View the documentThe International Academy of Education
View the documentPreface
View the documentIntroduction
View the document1. Opportunity to learn
View the document2. Focus on meaning
View the document3. Learning new concepts and skills while solving problems
View the document4. Opportunities for both invention and practice
View the document5. Openness to student solution methods and student interaction
View the document6. Small-group learning
View the document7. Whole-class discussion
View the document8. Number sense
View the document9. Concrete materials
View the document10. Students’ use of calculators
View the documentConclusions
View the documentAdditional resources
View the documentReferences
View the documentThe International Bureau of Education-IBE

8. Number sense

Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view mathematics as a discipline in which thinking is important.

Research findings

‘Number sense’ relates to having an intuitive feel for number size and combinations, as well as the ability to work flexibly with numbers in problem situations in order to make sound decisions and reasonable judgements. It involves being able to use flexibly the processes of mentally computing, estimating, sensing number magnitudes, moving between representation systems for numbers, and judging the reasonableness of numerical results.

Markovits and Sowder studied seventh-grade classrooms where special units on number magnitude, mental computation and computational estimation were taught. From individual interviews, they determined that after this special instruction students were more likely to use strategies that reflected sound number sense, and that this was a long-lasting change.

Other important research in this area involves the integration of the development of number sense with the teaching of other mathematical topics, as opposed to teaching separate lessons on aspects of number sense. In a study of second graders, Cobb and his colleagues found that students’ number sense was improved as a result of a problem-centred curriculum that emphasized student interaction and self-generated solution methods. Almost every student developed a variety of strategies to solve a wide range of problems. Students also demonstrated other desirable affective outcomes, such as increased persistence in solving problems.

Kamii worked with primary-grade teachers as they attempted to implement an instructional approach rooted in a constructivist theory of learning that is based on the work of Piaget. Central to the instructional approach was providing situations for students to develop their own meanings, methods and number sense. Data obtained from interviews with students showed that the treatment group demonstrated a greater autonomy, conceptual understanding of place value, and ability to do estimation and mental computation than did students in comparison classrooms.

In the classroom

Attention to number sense when teaching a wide variety of mathematical topics tends to enhance the depth of student ability in this area. Competence in the many aspects of number sense is an important mathematical outcome for students. Over 90% of the computation done outside the classroom is done without pencil and paper, using mental computation, estimation or a calculator. However, in many classrooms, efforts to instil number sense are given insufficient attention.

As teachers develop strategies to teach number sense, they should strongly consider moving beyond a unit-skills approach (i.e. a focus on single skills in isolation) to a more integrated approach that encourages the development of number sense in all classroom activities, from the development of computational procedures to mathematical problem solving. Although more research is needed, an integrated approach to number sense will be likely to result not only in greater number sense but also in other equally important outcomes.

References:

Cobb et al., 1991; Greeno, 1991; Kamii, 1985, 1989, 1994; Markovits & Sowder, 1994; Keys & Barger, 1994; Keys et al., 1991; Sowder, 1992a, 1992b.