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NZAMT13 Wellington Oct 2013

NZAMT13 Wellington Oct 2013. Accelerating Multiplicative Thinking a nd Visual Models “Keep a robust and unrelenting focus on making every student a multiplicative thinker” Jim Hogan

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NZAMT13 Wellington Oct 2013

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  1. NZAMT13 Wellington Oct 2013 Accelerating Multiplicative Thinking and Visual Models “Keep a robust and unrelenting focus on making every student a multiplicative thinker” Jim Hogan Facilitator, math advisor, 2002 to 2014 with a 5 Term sojourn in a low Decile Area School 2011, SNP Coord. Mathematics, Calculus, Statistics and Physics. A very special period in teaching and learning for me.

  2. Profile of this Group • A formative assessment 1. What shape is multiplication? 2. Draw a model of 3 x 4 = 12 3. What % of your students are mult? And how do you know?

  3. Do we have a problem? • From 2002 Year 9 NZNP Report • If students have not developed multiplicative thinking by year 9, it could be the most important focus of a remedial programme.

  4. Do we have a problem? • From a small 2013 Indepth School • A larger school, SEPT 2013 Y9 and 10

  5. Do we have a problem? • From a large 2008 SNP School I commonly see 15% to 20% and this varies between 1% and 80%.

  6. “Houston, we have a problem” • Students gain 2/3 of a CL if they are at school, in class and engaged in learning. • Projected success = Does this look like 85% NCEA L2 in 2017?

  7. Getting Data • Asttle • Hughes/Lomas • PAT? • Teacher tests • Noticing how students solve problems • Asking how • So what do we do about it………………

  8. So Acceleration… The good news is …we do. The bad news is…not enough. So • Multiplication is an array. This is a good model to develop student thinking at CL4 and beyond. • Learning to make comparisons based on multiplication rather than just addition.

  9. Noticing Multiplication A wee activity (2 or 3 mins). 6 groups or just buddy up somehow. Take a strand and write 10 multiplication based ideas or notions. EgProbability – Pr(three heads in a row) EgGeometry – Volume of a cone EgNumber – Factors, Multiples EgAlgebra – nth Term

  10. What is Multiplication • It is thinking of two things at once. • Students who operate multiplicatively know that there is a certain quantity in each of the numbers multiplied, but do not need to refer to the individual items or numbers in a group. • Multiplication is two dimensional.

  11. So here are some ideas… • Use the array model • ASK “How did you get your answer?” • Give multiplicative problems • Tables knowledge is essential • Expect an answer and a reason • Expect a diagram or model • Set harder problems! • Think in groups or “lots of”.

  12. Good Problems • Garbo the Gardener • King Arthur • Series-ous Escape • A Triangular Journey • Math Investigations • Snakes and Ladders • More Powers of Investigations • Any nth Term pattern

  13. So Let’s Do One

  14. Summary • Everything is on my website • Array model.

  15. And Lastly Your answer to • a counted solution is “Do it another way, anyway!” • A solution that smells of addition is “Do again using multiplication” [even if it is right”. AN UNRELENTING FOCUS!

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