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Summary of Reference

Ball, Deborah Loewenberg

With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics

Bibliographic data:
Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93, (4), 373-97.


An essential hypothesis in curriculum development is that any subject can be taught in some intellectually honest form to any child at any stage of his or her intellectual development. This paper is a report on Ball’s work in teaching mathematics to a mixed group of third grade children in the United States. Ball sets out in her teaching with an intention of developing a practice that respects the integrity both of mathematics as a discipline and of children as mathematical thinkers.

Three components of mathematical discourse frame Ball’s work: the content; the discourse; and the community in which teaching and learning takes place. All are important and they are interdependent one with the other.

Ball explores several dilemmas.

The first, of content, relates to the way that negative numbers are taught. Ball discusses the rationale for teaching integers (because the children need to understand them in real life) and analyses the various models about learning that are available for teaching the subject.

The second dilemma discussed by Ball is of respecting children as mathematical thinkers in their own right. She notes how children can form their own patterns without overt teaching interventions and gives examples of children’s reasoning when discussing odd and even numbers.

Ball’s third dilemma is in creating and using community. Her aim is to ensure that the classroom is a forum for engaging in mathematical discourse. She shows how she engages the whole class in problem solving and in the discussion of concepts, but equally is aware of the dangers of spending more time than might be sensible on specific problems in the attempt to ensure thinking and discussion.

Teaching is a complex process and the insights in this article show how some of the complexity and inherent uncertainty arising from competing teaching aims can be worked through.