Fraction Number Talks: Early and Often

By the middle school years students should be able to solve problems using all operations for multi-digit whole numbers and rational numbers (Common Core State Standard Initiatives). One way students can practice these operations is through number talks. “Number talks are short discussions among a teacher and students about how to solve a particular mental math problem” (The Coaching Center, para. 1). While looking at these open-ended problems the focus is less on the right answer but more about how students think about the problems. I wonder if the reason these are successful with whole number operations is it avoids the pressure to get the answer right and praises creative thinking. In math I often find that the students are so focused on getting the right answer they disregard the opportunities for a creative and playful approach to problem solving. Perhaps number talks are the way to shift that mindset and have more students feel success in math.

Faction number talk from Math For Love

The difficulty I have found with number talks is that students freeze up when fractions or decimals are thrown into the mix. With my middle school students I use the Year-long Number Talks from Rise Over Run. These number talks start by introducing strategies with whole numbers then apply the same strategies to fractions and decimals.  As I rely on my Knowledge of Content and Students (KCS) (Hill & Ball, 2009), I can identify that many of my students struggle with basic fraction operations. At the middle school level most of the fraction concepts are just expected to be known but in reality students have not yet mastered these skills. I find that my students who do well with fractions often are relying on an instrumental understanding and do not see the why behind their tricks instead of a  relational understanding in which students understand the why behind the meaning of fractions and decimals (Skemp, 1978). What I have noticed from my students is when they are given number talks with whole numbers they have a variety of strategies to try but come up short handed while applying this to fractions. I have also noticed that when fractions are involved students do not have the number sense to estimate or round their numbers to whole numbers.

I wonder if in the early grades students gained a deeper understanding of what a fraction is and what it looks like if they would be able to better apply these skills to operations in upper elementary and middle school. For example, if students could visualize different ways to write the benchmark fractions of zero, one half, or one whole they could apply these skills to estimating and determining the reasonableness of their answer. While I am relying on my KCS I have been working with two small groups helping students develop their relational understanding, I have seen great growth through using Developing Fractions Sense. Through observing students as I work through the lessons I have noticed that when students are able to visualize different representations of the same fraction and decompose fractions they can better manipulate fraction problems. I wonder if number talks were used in earlier grades and when fractions were introduced it would give students opportunities to develop relational understanding and increased knowledge and confidence to work with fractions throughout middle school.  

References

Common Core State Standards Initiative (CCSSI). (n.d.). Mathematics standards. Mathematics Standards | Common Core State Standards Initiative. https://corestandards.org/wp-content/uploads/2023/09/ADA-Compliant-Math-Standards.pdf

Hill, H., & Ball, D. L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71.

Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9-15.

The Coaching Corner. (n.d.). Number Talks. The Coaching Corner. https://sites.google.com/epcusd401.org/thecoachingcorner/instructional-playbook/number-talks