![]() Now as a past educator I can identify with teaching the two without context since that was a simple go to as a teacher to get kids moving through the standards. True, I am over 30 and the way I remember being taught perimeter, area and volume was to visualize a drawer: If we trace around the drawer you have perimeter, if you rub the bottom section inside the drawer you have area while if you fill your drawer with clothing you were measuring volume hence the inclusion of height (I guess more two dimensional for perimeter and area and three dimensional for volume). What do you think about this? Do you see this happening in other contexts? What am I right about and where am I mistaken? Please let me know in the comments. My concern is that we penalize students for not knowing their vocabulary words in situations devoid of context when in reality, this never happens. What’s important to realize is that in both cases, students are being asked to demonstrate the same skill: finding the perimeter of a rectangle. That would simultaneously provide the kind of context they would expect to find in real life and would better support conceptual understanding. ![]() What if the problem’s context was less fake and more useful? For example, if it was about a backyard, students could then be asked to find out how much fencing they would need. The only hope students have is to have memorized the terms area and perimeter and know which one to apply. While the problem involves a basketball court, there is no context for what part of the court we are talking about. To me, this is an example of a fake context. To better illustrate what I mean, consider the problem below that comes from the outgoing California standardized test prior to the Common Core State Standards. As a result, the terms “area” and “perimeter” remain abstract labels rather than something attached to a relatable meaning. This makes me wonder about whether it’s possible that the reason students confuse area and perimeter is because we often present problems without context or with fake/trivial contexts. I realize that we’ve come to accept this as normal, but have you ever thought about why it happens? Does this also happen in real life? Could this possibly be a problem of our own creation? After all, when a person is buying grass turf and fencing for their home, does that person ever get confused as to which measurement is which? I can’t imagine that happening often. Based on my experiences, this seems to be a pretty typical outcome for all math educators. For example, if you ask a student to find the perimeter of a rectangle, they will often give you the rectangle’s area. If you’ve ever taught students how to find the area or perimeter of a shape, you won’t be surprised to read that students commonly confuse the two measurements.
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