Teaching Propotional Reasoning – How NOT to do it!

Posted: January 12, 2012 in Teaching and Learning Philosophy, Uncategorized

My 8th grade son was doing his homework last night. I was washing dishes and he said, “Dad…this homework is easy!” I said, “Great! What are you doing?” My son, replies “We have to find out if a proportion is true or not.” I looked at the worksheet…it had things like this:

7/21 = 1/3

and he had to say “True” or “False”

I then had a struggle in my mind…do I ask him if he understands what it means for two quantities to be in proportion or do I just relax that he knows how to DO his homework? I chose to ask…I said, “Zach…what does it mean to say that the two fractions are proportional?”

Zach: It means that they are the same.
Me: Ok…would you say that 2 and 6 – 4 is proportional?
Zach: Yes…they are the same…

Zach then asked me the following question as he continued to work on his homework that is “easy” and he knows how to “do it.”

Zach: Do I cross multiply to see if the numbers are the same or do I multiply straight across the tops and the bottoms?
Zach: What’s wrong with you?
Me: I can’t answer that question…I need to leave now…

Maybe because I have been teaching for so long now…but I am becoming more and more impatient with this kind of thing with my students at school, my colleagues, and my own kids! Think about it…Zach is really saying, “I can’t remember what to do…I have learned so many meaningless procedures in my math classes that I am having trouble remembering what meaningless procedure to do and when to do it.”

Where are the big ideas behind proportional reasoning that should help to inform Zach as to what to do? I wish he as taught in such a way so that his FIRST thought is not, “what should I do…” but his first thought should be “what does this mean?” Then, based on what this means, he determines what to do because it makes sense to do it!

Thanks for letting me vent…parenting is hard…


  1. Andrew says:

    Maybe you could walk through what it means for two ratios (fractions) to be equal and why cross-multiplying works.

    Kids are in a hurry. Adults help them to slow down, especially when they’re working on something that they don’t care about – that they’re just doing for school. Just because a teacher thinks that something is important or interesting, doesn’t mean that it is relevant for a student. Showing them real-world examples doesn’t change this fact. If it is relevant to them, they’ll be asking you about it, instead of you showing them. My daughter asks me about philosophy 🙂

    • getrealmath says:

      I agree that it is important for student to find things relevant. I try to create a learning environment where students can at least see the real-world potential of a topic/lesson. Also, I work to give students the opportunity to make sense of what they do…as you say, work to make sense of why cross multiplication works. This involves focusing on the multiplicative (as opposed to additive) relationship between quantities…etc…I will stop here and suffice it to say that you are right and I appreciate your comment!


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