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> found no way to dissuade the student that 0.35 was bigger than 0.4, no matter what we tried. Out of curiosity, assuming you tried a number line, do you remem

• ColinWright 13y ago
  I think if I could ever have understood the difficulty, I would've had a chance of working around it. The problem seemed to be that they could place things on the number line, see that this was to the right of that, say that 0.4 was to the right of 0.35, say that hence 0.4 was bigger than 0.35, and then go right back to doing what they had always done. My model of what was happening in the student's head is illustrated by this. A survey was conducted asking people: A. Which is true: (a) The Sun goes round the Earth. or (b) The Earth goes round the Sun. ? B. How long does it take? Of those people who gave the answer to A as (b), over 80% answered B with "a day" or "24 hours" or something equivalent. In short, they got the "right" answer to A, and then a completely disconnected and obviously "wrong" answer to B. In this case I think people are answering A by reciting a fact they learned when young. We are told that the Earth goes round the Sun, so that's what people recount. By they don't connect that with their personal experience. Their personal experience is seeing the Sun going overhead. They "know" that the Sun goes round the Earth, and that it takes a day. They're told the Earth goes round the Sun, and that's what they parrot for question A, but when asked B, they answer from their own personal experience of seeing the Sun go overhead. And that takes a day. So I think the student could follow the things they had been told, and they could recite, parrot fashion, all the "right" things that would get them the marks on the test designed specifically to assess their knowledge of decimals places, and then when they had to put it into action, they fell back on what they felt things looked like, and were driven by their intuition and experience. Which was completely wrong. So that's my "theory" of where the disconnect lay. But maybe I'm wrong, because I certainly never fixed it.
  • ScottBurson 13y ago
    Unlearning is always much harder than learning. I know that when I'm debugging a piece of code, and I get an idea in my head about how it works or should work, and that idea is shown to be wrong by clear and incontrovertible evidence, it can still take between a few hours and a few days for me to stop thinking it.
• Trianglemancsd 13y ago
  A number line doesn't help some students decompose numbers. The key insight in this example is noticing that 0.35 is "3 tenths and 5 hundredths", in addition to being "35 hundredths". The former is a decomposition. Number line approaches more commonly rely on students being able to think of 0.4 as 0.40, which some interpret as an arbitrary rule, rather than as related to facts about equivalent fractions. The particular approach offered by the Rational Number Project in the article I linked to in the original post focuses kids on that decomposition from the very beginning using area models and colors to highlight multiple ways of seeing (e.g.) 0.35