A few weeks back during one of our previous classes, we had a brief discussion on what contexts we would choose to use in teaching fractions. Many of us mentioned food, baking, measuring time and distances, money. These we believed were things students knew about and had back ground knowledge on, and potentially things our students would find interesting or care about - who doesn't like food?
This past week during an observation, I realized more so just how important the context is that we choose to use. I was in a seventh grade classroom. The students were reviewing for their upcoming test the next day over percentages (comparing percents, fractions, and decimals, finding percentage change, what's the percentage of a whole?). I was walking around the classroom, helping students who had questions. Most of the students in the class seemed unafraid to ask questions if they were uncertain about something - which seemed to be a result of the sort of classroom the teacher had cultivated. Anyway, as I was walking around I had a girl ask me over to see if she was solving a problem correctly. The problem gave her the price of a good, the percent of a mark up on the good, and asked for the new price of the good after the mark up. When I asked her what she was thinking, she explained to me how she had solved the previous problem (given the price of a good, and the percentage of discount, find the new price). She asked if she would then solve this one in the same way - after all she was given a price and a percentage and asked to find the new price. So to her the two problems seemed very similar, if not the same. I asked her if she knew what "mark up" meant and she shook her head no. I helped to explain to her the concept and then she was able to solve the problem on her own.
Originally, viewing the problem, it sounded like the previous one. While she may not have known or simply had forgotten, not knowing what a mark up was, she made an assumption that felt logical to her so she could keep going and solve the problem. Luckily she had asked a question, but not all students will. On a test, she might have gotten points off, even though once she understood the situation she knew how to correctly solve it.
Context is important. We want to see what students have learned and understand, instead of whether they know what the term "mark up" means. We may think students know what a mark up is (it uses the word up, so wouldn't students think increasing?), but they may not. Lots of students haven't had jobs yet and are more familiar with ideas of sales and discounts, than the marking up of prices by suppliers. When using contexts, we need to be careful and ensure they are relate-able to students and that students understand them and any vocabulary or ideas that accompany it.