Which is more difficult to teach/learn: Algebra or Fractions?
Last week, I was a guest at Discovery Education’s “Beyond the Textbook” forum. During one of the breakout sessions, my group (Christopher Danielson, Angelia Maiers, and Chris Harbeck) got to discussing about how hard it is to write math curriculum and that no digital textbook would be worth its weight in bytes if it didn’t acknowledge that. Christopher Danielson wrote a great blog post which both summarizes and expands upon that discussion.
To illustrate that most non-math teachers don’t quite get the nuances involved in science and math instruction, I asked Angela which concept she thought was more difficult: algebra or fractions. She answered algebra without hesitation. And I said I felt fractions were more difficult. I said that my 8-year old son has no problem with algebra: 5 + [_] = 7. What goes in the box?
But what does 3/4 mean? Is it 3 objects out of 4 objects? Is it one object split into 4 pieces, but we only care about 3 of those pieces? Is a ratio of 3 things to 4 different things? Or is it division and we are taking 3 objects and splitting them evenly to 4 groups? Is is 75%? Or is it 0.75?
Angela was blown away by this discussion and wondered how other people (math folks vs. non-math folks) would respond. We decided to conduct a little experiment. We would both ask our PLNs the same question and compare responses. My prediction was that since my PLN tends to have a math and science focus, the majority of my followers would say fractions are more difficult. And I predicted that Angela’s PLN, which is more broad than mine, would say algebra is more difficult.
Here are the results:
I was correct in my predictions, but I was surprised at how my PLN was much closer to a 50/50 split rather than a 2:1 split like Angela’s. Here’s the raw data — it’s interesting to comb through the responses to read why they chose algebra or fractions:
Many people said fractions were easier because they are concrete — you just slice up some pie or look at a Hershey bar.
I’ve singled out two thoughtful replies on Angela’s Facebook page below. Jodi’s is great because she polled her second grade class:
And Susan’s is great because she sees the many possible meanings of a fraction:
What do you think? And do I think fractions are more difficult because I am misunderstanding something about the nature of algebra?