Students often explain the
commutative property of multiplication in terms of 'switching the numbers around' rather than through the language of factors.
While the
Commutative Property provides the context for this activity, the activity is about far more than having students understand the property, since students probably already understand it intuitively.
The children had already learned the
commutative property of multiplication (e.g., 6 x 7 = 7 x 6).
Surprisingly, although none of the students had experience with multiplication in class, three students understood the
commutative property of multiplication and used it as an explanation.
Lucas appears to know something about the
commutative property but does not understand it as shown by his comment that turning around 20 x 30 would make a difference.
These two equations suggested that Sandy had already learned the
commutative property of multiplication, a x b = b x a.
Specific focus areas were students' ability to reason and explain their knowledge and their understanding and use of arrays, the
commutative property, the distributive property, and the inverse relationship between multiplication and division.
Soon another teacher announced that the same generalization applied to even-numbered rows; the pattern emerged when the
commutative property of multiplication was applied.
Throughout their work with subitising, students are also able to process and utilise the critical mathematical properties of the
commutative property and the associative property at the multiplicative level as well (See C8, C9, C10, Table 1).
Learners apply the
commutative property when they compute 3 + 14 by counting on from 14 rather than 3, and 23 x 2 by doubling 23 rather than adding 2 twenty-three times.
Precisely and consistently defining equality also has a clear impact on our discussions of mathematical principles such as the
commutative property. Take for example a classroom talking point of 4 + 3 = 3 + 4.
For example, the "Cruncher Candy" tutorial will accept a formula entered as 0.75 * 38 but rejects 38 * 0.75; the potential insight of a student who is thinking about the
commutative property will be frustrated by this approach to error correction.