This post is by Jason.
Well, I figure that I should take my turn at a post. First, a bit of background on me. I am a 5th grade teacher who is interested in teach mathematics in a meaningful, relevant way to students. The interesting thing about my experience with math, is that I was never one of those students who “got it”. Rather, I was the one that would cruise through the lesson and do what I needed to get by. It’s quite surprising that a passion of mine now is teaching math.
For the past few weeks in my class we’ve been working on order of operations and expressions. I was curious to see how students would respond to making expressions from situations rather than just the standard teaching of the order of operations. So I started them off with small situations where they had to make a number sentence to show the situation. The students outdid my expectations. So, I figured that I would provide them with a more challenging context that would require some recognition of the order of operations and yet still have multiple ways to access the problem. I’ve included the situation so that you can use it as a reference.
While running a lemonade stand you’ve earned $22.48. Just as you are about to leave a person buys $2 of lemonade. Since you’ve been working in a group of 4 you decide to share the earnings equally. When you get home you pay your mom $4.68 for the materials that you’ve used. Write an expression to represent the situation above, and then simplify to find out how much money you made in all.
After I posted this problem on the screen, and answered any questions about it, the students set to work creating the expression themselves and then discussing it in their groups. As the students worked I walked around to see what they were thinking, prompting those who needed a little push with questions to scaffold their thinking, and in general finding out what they were thinking to help structure the discussion.
As the work continued there were several expressions that emerged as general patterns across the class.
(22.48 + 2) + (24.48 ÷ 4) + (☐ – 4.68) — the box represents the parentheses that are in the middle.
((22.48 + 2) – 4.68 ) ÷ 4
((22.48 ÷ 4) + 2) – 4.68
(22.48 + 2) ÷ 4 – 4.68
As those expressions were put on the board there was a sudden buzz that filled the room as each group automatically started comparing the other expressions to theirs. Our discussion started with the first one and progressed through all of them. As the students shared their ideas and methods it became clear as a class how important it was to follow the correct order of operations, and basically provided those rules themselves!
Their discussion was quite instructive as they reasoned about the different representations and what they meant. There were students getting quite invested in their ideas, and others became very interested in seeking to prove their ideas to others. This lesson also surfaced basic conventions about parentheses and even the effect of doing the wrong operation at the wrong time. It was one of those experiences where you wished that it was being recorded so that you could see the thinking and reasoning going on.
Now, I do want to be down to earth in saying that not all were at the same level, or got the same out of the lesson. However, from some data I gathered afterwards it became quite clear that all had learned quite a bit about order of operations and expressions than they had known previously. In fact, for a lot of my struggling students, this activity excited them as they saw how math could be applied!
As a class we continued to look and deepen, as well as practice, the skills of evaluating expressions both with context and without. The students all seemed to enjoy the activities and even asked to go deeper and try more challenging things.
I haven’t told this story to toot my own horn and make myself more than I am (I know I have plenty to work on as a teacher), but I do hope that it shows how much kids can learn and do mathematically and how well they can reason! Sometimes I fear with math education we expect them to not be able to get it deeply and therefore just tell and explain instead of letting them do the learning in the way that they learn math best.
Please leave a comment about a great math lesson that you had that really deepened you understanding and where a teacher let you learn in a way that really helped you see how well math could be used.