Tag: strategic fluency

Strategic Fluency: The Missing Middle

Written by Chris Hogbin on . Posted in Learn & Develop.

I once asked a student whether 3 was a factor of 48. He paused, thought for a while, then said: “Well, I know 8 × 6 is 48, so 6 is a factor of 48. And 3 is a factor of 6, so 3 must be a factor of 48.” He didn’t retrieve an answer. He built one — moving through known relationships, using factors, multiplication, division and structure to reason his way to a conclusion. That is strategic fluency: not flashy, not always fast, but powerful. If that number looks familiar, it should — it’s the same 48 from a piece a little while back, the one about all the ways a...

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Stat card titled 'The Research.' Headline stat: 7 years, the achievement gap within a single year level, almost entirely explained by whether a student has developed multiplicative thinking. Below: 25 to 55% of Year 8 students don't have it, hitting lower-income students hardest. And 8.3% of students could solve a real-world problem requiring this thinking, even ones who breezed through times tables checks. Source: Siemon, Callingham, Day and Seah; AAMT Growing Mathematically project. Number Hive.

The Research: Why a Right Answer Isn’t Always Understanding

Written by Chris Hogbin on . Posted in Learn & Develop.

A student can get 12 × 7 correct by adding 12 seven times. Another student gets the same answer by reasoning that 12 × 7 is 12 × 10 minus 12 × 3. On paper, both answers look identical. Only one shows what researchers call multiplicative thinking, the ability to reason about the relationship between quantities, not just retrieve or construct a number. That distinction turns out to matter more than almost anything else in a student’s mathematical development. A study of nearly 7,000 Victorian students in Years 5 to 9 found a seven-year range in mathematics achievement within the same...

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