Number sense#

Boaler (2015)

Number sense reflects a deep understanding of mathematics, but it comes about through a mathematical mindset that is focused on making sense of numbers and quantities. It is useful to think about the ways number sense is developed in students, not only because number sense is the foundation for all higher level mathematics (Feikes & Schwingendorf, 2008) but also because number sense and mathematical mindsets develop together, and learning about ways to develop one helps the development of the other. (p. 36)

Number sense as the difference between low and high achievement#

Boaler (2015) describes work by Gray & Tall (1994) with students 7-13 examining differences between low and high achieving students. High achieving students were found to have better number sense.

Low achieving students with out the flexibly (mathematical-mindset) were relying on formal rules, beyond when it made sense to not use those rules. Consequently low achievers are given more drill and practice which is more likely to prevent the development of a mathematical-mindset

The high-achieving students solved the questions by using what is known as number sense—they interacted with the numbers flexibly and conceptually. The low-achieving students used no number sense and seemed to believe that their role was to recall and use a standard method even when this was difficult to do. For example, when students were given a problem such as 21 – 6, the high-achieving students made the problem easier by changing it to 20 –5, but the low-achieving students counted backward, starting at 21 and counting down,which is difficult to do and prone to error.After extensive study of the different strategies that the students used, the researchers concluded that the difference between high- and low-achieving students was not that the low-achieving students knew less mathematics, but that they were interacting with mathematics differently. Instead of approaching numbers with flexibility and number sense, they seemed to cling to formal procedures they had learned, using them very precisely, not abandoning them even when it made sense to do so. The low achievers did not know less, they just did not use numbers flexibly—probably because they had been set on the wrong pathway, from an early age, of trying to memorize methods and number facts instead of interacting with numbers flexibly (Boaler, 2015, pp. 35)

References#

Boaler, J. (2015). Creating Mathematical Mindsets: The Importance of Flexibility with Numbers. In Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching (pp. 33--56). John Wiley & Sons, Incorporated.