I had a delightful opportunity to join a planning meeting with a group of teachers from one of the schools we work with in Chicago. The team was working on a lesson for their 8-year old students about interpreting remainders in problem contexts. Here is how the textbook presented the problem for their lesson:

23 children in boats

Students are expected to write the math sentence for this situation, 23 ÷ 4, solve it, and then have to interpret the remainder in the context of the situation. The focus of the lesson is to be on this interpretation step.

The group was discussing an alternative context for this problem, involving a field trip and parents driving cars that could hold up to 4 children. They thought this would be more relatable for their students.

What do you think of this alternative context? Maybe take a moment to consider it before you read on.

As the teachers and I discussed it, we saw that this new context might have disadvantages. First, they didn’t have a picture to illustrate it. This meant the students – some of them English language learners – would have to work a little harder to understand the problem from just the text. The cars in any picture the teachers might try to use or create would have roofs that would hide the actual seating space.

Second, there are complications with cars. In the U.S., 8-year-olds are not normally supposed to sit in the front seat, but there are only seatbelts for 3 persons in the back seat. Where would all 4 children sit? On the other hand, some of the students might have had experience with more than 4 children crammed into a car, or they might want to raise this as a possibility (perhaps one of their families owns a van). Either way, the problem launch becomes more complicated.

Finally, the boat context, especially the picture, suggests a process of doling out boats one at a time, as many as needed, which is different than deciding in advance how many cars will be needed. I am unsure whether this is good, bad, or neutral; what are your thoughts?

I have observed – and myself taught – too many lessons in which the attempt to create an engaging, relatable context ended up creating an obstacle to students learning the mathematics. As part of our kyouzai kenkyuu we need to carefully consider whether the problem context is well-suited to helping students focus on and make sense of the mathematics we want them to learn.


(P.S. The research lesson has not yet taken place, so I don’t know what the team will finally decide. When it does, I will report what happens.)