Distributivity, Partitioning, and the Multiplication Algorithm
Multiplicative thinking underpins much of the mathematics learned beyond the middle primary years. As such, it needs to be understood conceptually to highlight the connections between its many aspects. This paper focuses on one such connection; that is how the array, place value partitioning and the...
| Main Authors: | , |
|---|---|
| Format: | Journal Article |
| Published: |
Department of Mathematics Education, Universitas Muhammadiyah Surakarta
2020
|
| Online Access: | http://journals.ums.ac.id/index.php/jramathedu/index http://hdl.handle.net/20.500.11937/80385 |
| _version_ | 1848764206814330880 |
|---|---|
| author | Hurst, Chris Huntley, Ray |
| author_facet | Hurst, Chris Huntley, Ray |
| author_sort | Hurst, Chris |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Multiplicative thinking underpins much of the mathematics learned beyond the middle primary years. As such, it needs to be understood conceptually to highlight the connections between its many aspects. This paper focuses on one such connection; that is how the array, place value partitioning and the distributive property of multiplication are related. It is important that students understand how the property informs the written multiplication algorithm. Another component of successful use of the standard multiplication algorithm is extended number facts and the paper also explores students’ ability to understand and generate them. One purpose of the study was to investigate the extent to which students used the standard multiplication algorithm and if their use of it is supported by an understanding of the underpinning components of the array, partitioning, the distributive property, and extended number facts. That is, we seek to learn if students have a conceptual understanding of the multiplication algorithm and its underpinning mathematics that would enable them to transfer their knowledge to a range of contexts, or if they have procedurally learned mathematics. In this qualitative study, data were generated from the administration of a Multiplicative Thinking Quiz with a sample of 36 primary aged students. Data were analyzed manually and reported using descriptive statistics. The main implications of the study are that the connections among the multiplicative array, place value partitioning, base ten property of place value, distributive property of multiplication, and extended number facts need to be made explicit for children in terms of how they inform the use of the written algorithm for multiplication. |
| first_indexed | 2025-11-14T11:15:41Z |
| format | Journal Article |
| id | curtin-20.500.11937-80385 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:15:41Z |
| publishDate | 2020 |
| publisher | Department of Mathematics Education, Universitas Muhammadiyah Surakarta |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-803852021-01-13T03:09:37Z Distributivity, Partitioning, and the Multiplication Algorithm Hurst, Chris Huntley, Ray Multiplicative thinking underpins much of the mathematics learned beyond the middle primary years. As such, it needs to be understood conceptually to highlight the connections between its many aspects. This paper focuses on one such connection; that is how the array, place value partitioning and the distributive property of multiplication are related. It is important that students understand how the property informs the written multiplication algorithm. Another component of successful use of the standard multiplication algorithm is extended number facts and the paper also explores students’ ability to understand and generate them. One purpose of the study was to investigate the extent to which students used the standard multiplication algorithm and if their use of it is supported by an understanding of the underpinning components of the array, partitioning, the distributive property, and extended number facts. That is, we seek to learn if students have a conceptual understanding of the multiplication algorithm and its underpinning mathematics that would enable them to transfer their knowledge to a range of contexts, or if they have procedurally learned mathematics. In this qualitative study, data were generated from the administration of a Multiplicative Thinking Quiz with a sample of 36 primary aged students. Data were analyzed manually and reported using descriptive statistics. The main implications of the study are that the connections among the multiplicative array, place value partitioning, base ten property of place value, distributive property of multiplication, and extended number facts need to be made explicit for children in terms of how they inform the use of the written algorithm for multiplication. 2020 Journal Article http://hdl.handle.net/20.500.11937/80385 10.23917/jramathedu.v5i3.10962 http://journals.ums.ac.id/index.php/jramathedu/index http://creativecommons.org/licenses/by/4.0/ Department of Mathematics Education, Universitas Muhammadiyah Surakarta fulltext |
| spellingShingle | Hurst, Chris Huntley, Ray Distributivity, Partitioning, and the Multiplication Algorithm |
| title | Distributivity, Partitioning, and the Multiplication Algorithm |
| title_full | Distributivity, Partitioning, and the Multiplication Algorithm |
| title_fullStr | Distributivity, Partitioning, and the Multiplication Algorithm |
| title_full_unstemmed | Distributivity, Partitioning, and the Multiplication Algorithm |
| title_short | Distributivity, Partitioning, and the Multiplication Algorithm |
| title_sort | distributivity, partitioning, and the multiplication algorithm |
| url | http://journals.ums.ac.id/index.php/jramathedu/index http://hdl.handle.net/20.500.11937/80385 |