Number Sense, or number fluency, plays a major role in how flexibly students use numbers when performing maths operations and how successful they are in Maths. What exactly is fluency and how can it be improved?
This is a re-blog post originally posted by Roopesh Shenoy and published with kind permission.
The original post can be found here.
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Have a look at this video of Teacher Cathy Young, engaging in a technique called “Number Talks” with her fourth grade students.
As students listen to different ways of breaking the problem up, solving different parts and then arriving at the final solution, they start to make sense of Maths – and instead of looking at Maths as something “rigid”, they look at it as something flexible; with freedom to arrive at the exact same solutions in more than one ways.
Number Talks is one of the things Professor Joe Boaler recommends in a Maths classroom.
Jo Boaler is an Education Professor at Stanford and a researcher. She makes some very interesting points in this interview about what is wrong with how we teach Maths today –
The key point she is driving home is that drilling without understanding number sense can make Maths seem much more difficult than it is, and can lead to poor learning outcomes for students.
What is number sense? The ability to use numbers flexibly and understanding how they relate to each other. For example –
- 5 x 6 is same as 6 x 5
- 23 – 17 = (23-20) + (20-17) (the right hand side is easier to evaluate than the “counting on” method)
- 7 x 11 = 7 x 10 + 7 (especially since 7 x 10 is much easier to evaluate to 70)
Knowing some of these properties of Maths can help students derive strategies to simplify complex problems before attempting to arrive at a solution. Memorising Maths facts blindly does not scale – however attempting to gain number sense does.
Some of these methods are intuitive to students who do well in Maths, but they are not as evident to others unless they are specifically encouraged to consider them. This is what Jo is hinting at – unless students learn to use these numbers flexibly while calculating different expressions, they will not be able to succeed in maths by purely focussing on Drills. And this is where Number Talks can help.
Number Talks can be helpful at any age – have a look at this Number Talk session held with Elementary Teacher candidates in Stanford.
Other activities Professor Boaler recommends are Addition Block games and Multiplication games such as “How close to 100?” and “Pepporoni Pizza”. Do read her working research paper, “Fluency Without Fear” on the subject for more details.
Read other posts by Roopesh by clicking here.