Children’s Fractional Knowledge pp 13-25 | Cite as

# Perspectives on Children’s Fraction Knowledge

## Abstract

The separation of the study of whole numbers and fractions is historical and contributes to the legendary difficulty children experience in the learning of fractions that inspired Davis et al. (1993) to comment that “the learning of fractions is not only very hard, it is, in the broader scheme of things, a dismal failure” (p. 63). I cite Davis et al. not because I believe that the teaching and learning of fractions is by necessity a dismal failure, but rather to accentuate the historical difficulties children experience in learning fractions in mathematics education. These difficulties are quite unsettling because they have been known for a long time. For example, in his famous study on the grade placement of arithmetical topics, Washburne (1930, p. 669) reported that a mental age level of 9 years should be attained by children if at least three out of four of them are to make the very modest mastery represented by a retention test score of 80% on the meaning of “nongrouping” fractions. But, in the case of “grouping” fractions, the analogous mental age was 11 years 7 months.^{1}

## Keywords

Mathematical Knowledge School Mathematics Constructivist Learning Stick Figure Composite Unit## References

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