Number Talks

This week we explored several strategies outlined in our textbook Making Math Meaningful (Small, 2012), including strategies on prime factorization, mental math, estimation, and place value. I talked more about prime factorization last week, and this week I'm going to explore mental math strategies. 

I’ve never really thought about how to teach concepts such as mental math strategies, since by this time in my life they come quickly, but

Keenan, Casey (2014, August 23). Screen-grab from Number Talks
Strategies [Online Video]. Retrieved from: http://bit.ly/1MQnDFV

now that I’ve been introduced to the strategies it makes a lot more sense. It’s interesting to see all the different mental math approaches laid out since they help you realize that there are multiple ways to get to the same answer and may help students feel more confident if you change the focus from what your answer is to how you got to that answer. I think this concept of mental math would be well introduced as part of a number talk. Joe Boaler has done extensive research on making math accessible to all students, and one of her strategies, number talks, involves giving students a problem and having them work it out in their heads. Once they’re done then they raise a thumb in front of them (since we don’t want students to feel intimidated for not finishing quickly) and then everyone discusses how they got the answers that they did. For each student's answer the teacher ‘drew’ their reasoning using block representation (the whole activity makes more sense if you watch the video). This approach teaches students the importance of different problem solving methods, and would be an excellent strategy when talking about mental math since it requires just that and addresses the wide range of ‘algorithms’ a student can use (Small, 2012). 

A ‘number talk’ was attempted (although I don’t think it was a conscious decision on the teacher’s part) in my observation classroom earlier this week. It was a grade 7 math class and they were working on problem solving methods. They were given the locker problem and asked to work in groups to sort it out. Once all the students had reached the answer then students were asked to share their approach to the problem. I think that grade 7 is a crucial year to introduce number talks since that’s when students can become insecure about their math abilities, and they may feel that if they don’t answer the question the same as the teacher then they’re ‘wrong’. It's also interesting to see how other people approached the same answer. The same result may have been achieved if group discussion was the approach right from the start, but allowing students time to think about their answer first ensures that no student's ideas are silenced by louder, more confident students, and the group discussion becomes a reflection off each other's thinking rather than the problem solving approach itself. 

Tools such as the strategies outlined in Making Math Meaningful and Number Talks will become crucial once I begin my teaching practice. Every student learns in a different way, so it’s important to include multiple methods/activities for each concept so students don’t get frustrated and fall behind in math. As well, I like that Making Math Meaningful includes strategies on every aspect of the math curriculum - even the ones that could be easily overlooked for being so straightforward in my mind (like mental math).