I was just browsing through videos of teachers implementing the Common Core standards and found on one proportions that I thought was worth mentioning here. Some of the Calculus students I work with still struggle with proportions.
When I say struggle, I don't mean that they don't know how to cross multiply, but that they struggle to define what it means for two quantities to be proportional or identify a situation where two quantities are proportional.
In the video on proportions a teacher helps students review how to cross multiply by creating a game that they find engaging and fun. If you want, watch it and see what you think before reading on to see how I interpreted it.
…did you watch it?…..
What did you think? I believe this is a prime example of sending the message that math is not fun or interesting, so we need to spice it up by walking around the room. The problems the students were solving were boring, they liked the activity because they could walk around, race their friends and interact with peers.
I’m not saying that games are bad, and getting kids out of their seats is great, but sometimes I feel that teachers have to exploit kids desire to be social to get them to do really boring repetitive problems. Perhaps this teacher had a great conceptual lesson on proportions the day before and the kids are just practicing a procedure, but based on national test scores I'm going to guess that her students will probably end up like the majority of middle school students who can cross multiply but don't demonstrate proportional reasoning.
This video could have been useful to demonstrate games and activities, but it doesn’t seem to me to have a place on the common core website as this teacher is not promoting the standards of mathematical practice as I interpreted them.
In fact, the standard that the video is supposed to be about asks students to determine if two quantities are proportional and involves interpreting proportionality in a real-world or mathematical context. Nowhere do the standards tell the teacher to teach students the procedure for cross-multiplication without connections.
The students are following a procedure without thinking about its meaning, interpreting it, applying it, etc. I don’t see the math in the lesson. I see kids running around moving numbers around.
PS. For great, research based, free resources on fractions that exemplify what I’d rather see in schools go to the Rational Number Project. Mathinaz sent me an amazing email about how well they worked for her students and I know how brilliant the authors are.