Our Director of Education, John Malloy, speaks frequently about academic optimism, which to me really equates to “success for all.” I love how this is a focus for our Board, and I think of John’s words frequently when lessons go well and when they don’t. Yesterday, I was really thinking about “academic optimism,” when one of my math lessons did not go as expected.

We’re learning fractions right now, and the students are working on comparing and ordering fractions. After students “played” with these concepts (as they tried to order fractional amounts in an open-ended word problem), we worked together to create an anchor chart highlighting strategies that students could use to compare and order fractions. While the class seemed to quickly understand the number line and picture strategies, they struggled with finding common denominators. Most students did not understand how to figure out a common denominator, and then they did not understand how and why to switch back to the initial fractions in their final answers. As I left the class at the end of Period 6 for Kindergarten prep coverage, I saw a class of frustrated and confused students, and I knew that this was my fault.

As the signature on all of my school emails, I have the title of Jacquie McTaggart’s book, If They Don’t Learn The Way You Teach, Teach The Way They Learn. I believe strongly in these words, and if the class did not understand the lesson, I was to blame. I knew that my goal for today had to be to try again … and I had to try something different than I did before. That’s when I thought back to a conversation that I had with Tyler Amidon, an amazing teacher in the States. He spoke about how he uses colour-coding to help teach fractions. This was it!

When I got to school today, I created five different problems involving ordering fractions. Then I wrote a problem on a piece of chart paper, and hung it on the whiteboard. When we started math class, I handed out hundreds charts, and had everyone take out their math book. I explained that I know students were confused after yesterday’s math lesson on fractions and common denominators, so today, I was going to try again. I had students each get a pencil and a different coloured pencil, crayon, or marker. Then we started our problem together. I asked the students what the first step was in figuring out a common denominator. They said that we needed to find the multiples for each denominator, and figure out the least common one. Excellent! Together, we used the hundreds chart (a tool that I explained that students might want to use for skip counting), and figured out the multiples for our first denominator. Then I had students work on their own to figure out the other two. I circulated at that point, and helped out students that needed it. We then got back together as a full class, and wrote down the multiples for the two denominators. Students quickly found the common one.

Our Math Problem And Solution

I knew that I lost students yesterday after this point, so I decided to slow things down. This is when I had the students take out their coloured writing instrument. In pencil, I got them to write down the first fraction, and then in the colour of their choice, I got them to make the fraction line and write down the common denominator. We figured out what number we had to multiply the initial denominator by to get the common denominator. Then I asked, “If you multiply the denominator by _____, what do you need to multiply the numerator by?” Everyone knew. Some students even equated it back to balanced equations that we did earlier in the year. Yes!

Once we followed the same steps for the remainder of the fractions, I then got to the important part: why do we do this? I explained to the students, now that all of the denominators are the same, we can compare the numerators. We know now that all of the fraction pieces are equal. That’s when I drew the pie cut into six at the bottom of the chart, and we spoke about the fact that all of the fractions are divided into sixths, so we don’t have to worry about equality any more. Now we can just focus on the numerators. I was seeing nodding heads. I knew that this was making sense.

At this point, students easily ordered the fractions. But now I had to make sure that they wrote the fractions as they were in the question. This is when the colour-coding helped. We looked back at the conversions, and students knew, “Oh right! 27/6 is really 9/2.” Now they could make the connections back to the original question.

Then I tried something that I haven’t done before. I said to the class, “I know that many of you understand this now, but it’s okay if you’re still confused. We can work on this more together. Now I need you to do a very grown-up thing. I need you to think about what you know (and not about what your friends know), and if you’re still confused or want to review this together again, take your chair and go to the guided reading table.” It worked! One student stood up right away, and then others followed. Soon I had about six students at the guided reading table with me. The other students divided into groups, and I gave out the different problems.

In the guided group, we went through a problem together, and I wrote their ideas on chart paper, but the students wrote them in their workbooks. They asked good questions, and started to clarify their own thinking. As we finished the problem together, one student turned to me and said, “Thank you, Miss Dunsiger. That small group really helped.” Wow! That’s never happened before. 

Equally as exciting though, the students then got questions of their own to answer, and they were able to use what they learned in the guided group, and answer the questions correctly. They showed all of their thinking as well. It was worth going back and trying again. 

Today reminded me that we need to believe that all students can learn, and then we need to figure out a way to ensure that they do. How do you support a climate of academic optimism at school? I’d love to know your thoughts on this!

Aviva