Beginning Third-grade Students’ Manipulative-based Understanding of the Place-value Position Principle for Two-digit and Three-digit Numbers

Abstract

One important of primary school mathematics education is understanding of the base-ten number system, encompassing the regrouping and the place-value position principle. When extending the number space, students need to extend their understanding of these principles. Converting between manipulatives and symbolic number representations is one indicator of such emerging understanding. We investigate whether beginning third-grade students can transfer their understanding of the place-value position principle from two-digit to three-digit numbers. Students show substantial, but not perfect manipulative-based understanding for two-digit numbers, and that they can transfer it to three-digit numbers to some extent. We find no evidence, that this transfer is supported by the salience of the principle in the manipulative.

Keywords

place-value understandingplace-value position principleprimary schoolbase-ten systemmanipulatives

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