VISUAL MATHEMATICS Trident COL Jim Hogan 29 th

VISUAL MATHEMATICS Trident COL Jim Hogan 29 th March 2018

A statement I made from 2003. . . ■ “if you cannot model it, do not teach it’. JH ■ I claimed this in a workshop with Waikato teachers not long after I started as an advisor.

A picture is a thousand words. . .

Task =Draw or model. . . ■The number we know as 1

A picture is a thousand words. . .

Task = Draw or Model. . . ■ An odd number

A picture is a thousand words. . .

Task = Draw or model. . . ■A square number

A picture is a thousand words. . .

The Information in a Picture. . ■ Can show meaning ■ Can expose understanding. ■ This is what I want to explore, because this is the world of the teacher and the student.

Returning to this Task. . . ■The number we know as 1

Showing meaning. . . Make a model of 1.

Showing meaning. . . ■ Where is the 1? ■ Can you make another different 1? ■ Can you make a generalisation about 1?

A Generalisation. . . ■ One can be anything I choose one to be! ■ Would you be happy if your students used that idea?

A complex model of 1.

Returning to this task. . . ■An odd number

Showing meaning. . . ■ Make a model of an odd number.

Showing meaning. . . ■ Where is the essence of being odd? ■ Can you make another odd number? ■ Can you make a generalisation joining two odd numbers? ■ Can you make a conjecture?

A Generalisation. . . ■ Odd numbers have a 1 left over after you half them. ■ Odd numbers join to make an even number.

A lt e r n a ti v e V i e w s

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Returning to this task. . . ■A square number

Showing meaning. . . ■ Make a square number.

Showing meaning. . . ■ Where is the essence of being square? ■ Can you make another square number? ■ Can you link odd and square? ■ What is a triangle number? ?

A Generalisation. . . ■ 1+3+5=3 x 3=9 ■ T 3 +T 4 = 4 x 4 ■ The difference between the square numbers is very odd!

Problem for you. . . ■ Some squares also form cubes! ■ Can you find two such numbers? ■ Can you generalise this for all squares that are also cubes? ?

Website links ■ https: //www. gozerog. com ■ https: //www. desmos. com /calculator ■ J. hogan@auckland. ac. nz

Learning. . . ■ What are you going to take away and try? ■ Any questions?