THE DAY I TAUGHT A LESSON: HOW RELATIONSHIPS AFFECT MATH

(Click on the image above to access the slideshow mentioned in this post.)

Sometimes we have the best intentions and what we think are the best strategies, and then we end up having some doubts about them. As a math tutor a few years ago, I was given a tip that I thought I would try. Veteran tutors said that if I made word problems with my students' names and interests, they would be more invested in their learning. I did this for the 2 years I taught; I also allowed my students to write their own word problems, for as long as they related to the current lesson. They came up with interesting stories where their tutoring partner inevitably got hurt, for example, by tripping and falling down so many feet down the mountain.

For the lesson I taught in my mentor's classroom, I thought I would do the same. The students were very engaged, which I expected. They especially enjoyed it when the story had them doing something they would not do in real life, like share their pencils.

When we got to slide 9, where they all needed to get in canoes that held 3 persons each, they inevitably added their teacher to the count, even if the problem did not say she was part of it. They logically assumed that if the class was going on a trip, that she would be there as well. However, I reminded them to focus on the problem itself, and not to embellish the story. While it did not affect the final answer, it needed to be brought to their attention.

We again encountered the problem on slide 12, where half of the class assumed that Geo would share his money with Osvaldo. I had the students work on this problem independently and hold up their whiteboards to share their answers. As soon as everyone got a look at everyone else's answers, discussions ensued. I brought it to order and asked a representative from each side to explain their thinking. I started with the students who said that, yes, Osvaldo can afford to buy the tacos. Then I asked someone who answered no about how they came up with a different answer. All the students who answered yes assumed that Geo would share his money. I found it necessary to ask where in the problem it stated that Geo did that. I had to point out again that they cannot add to the story given to them.

It was hours after the lesson that I started thinking about how relationships within the classroom could have affected the outcomes. I started wondering if the outcomes would have been different if the names weren't familiar. If I hadn't used their teacher's name, would they have thought to include the teacher in the count? If I didn't pick the names of 2 students who were friends, would they have assumed that the second person would be so generous? Did I skew the results by getting them too engaged in the lesson? Is there such a thing as being too engaged in a lesson? Hmmm.