Friday, October 17, 2014

Name That Fraction

I came across a fraction misconception last week that I've never seen before (or to be more precise, I've always missed before). We asked students what fraction was shaded:
Most said 'one-sixth' apart from one student who was adamant it was a fourth. Initially, I thought she had miscounted the parts but upon further questioning it was apparent that this student also thought that the following were also fourths: can you see why?

Basically she is describing the fractions using ordinal or positional language. What was neat about this is that before I had a chance to challenge her thinking, her partner did it for me (referring to the first diagram above):

"Well if that's the case, you could count from the right side and it would be called a third and it can't be a fourth and a third!"

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The original student was pretty adamant that she was correct though which got me wondering what experiences she might need to understand how we name fractions. Perhaps she never had an opportunity (or not enough opportunities) to split a shape into equal parts like this as shown in this previous post . After the lesson I realised that I could also have challenged her fractional thinking by bringing in spatial reasoning and asked her if each of the following are fourths:
Or by asking her to name each of these fractions (will she name them 'firsts', 'seconds', 'thirds' and 'fourths'?)
It got me thinking how important spatial reasoning is in helping students understand fractions.
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There are some other great ideas for thinking about how we can teach fractions in the Ontario Ministry of Education's latest document Paying Attention to Fractions. One of the ideas coming out of this is to avoid solely teaching fraction as a unit but rather to incorporate it as much as possible throughout other strands and subjects all year long.

Or to put it another way, Fraction Immersion.

1. Not math but ... Reminds me of the student, who, when asked to show me the beginning of a paragraph, counted three sentences in (as she saw it: the intro sentence, the body sentence and the closing sentence. This paragraph was 6 sentences long). Perception is everything.. as teachers its so important to check student thinking and pick up misconceptions.

1. Absolutely agree with your last sentence. I'll admit that when I started teaching I didn't give students opportunities for them to explain their thinking to me, or for me to just listen to what they were saying. I just told them what I thought they needed to know. I've changed now so that I intentionally create situations where I can listen to students' thinking so that it allows me to hear (and then address) any misconceptions.
Thanks so much for your comment.