1. Teaching is not telling
Teaching is not telling. It is modeling, questioning, comparing, challenging, valuing and validating then posing challenges to prod, prompt and extend.

2. It is our professional responsibility to make every effort to understand students’ ways of thinking and coming to know. Working from what they “know” we must provide specific focused feedback and carefully constructed lessons to provide opportunities for students to link their ways of thinking and knowing to the symbol system we want them to learn.
We lose students when we start from the symbol system and try to work back to understanding.
Seeing and understanding comes before a2 + b2 = c2

3. they connect the pieces to recognize whole concepts quickly
Strong Visual spatial learners bring several natural advantages to the learning of mathematics:
they connect the pieces to recognize whole concepts quickly
they see links between pieces and tie them into webs of connections
they find patterns easily
they think graphically and understand dimensionality.
Thinking 101

5. Number is in Number and Shape is in Shape..
Two, three, five and ten are numbers we look for inside other numbers. This is how strategies for adding and subtracting emerge.
Fractions are inside fractions . That is how we come to know equivalent fractions.
Decimals are inside other decimals.
Shapes are inside other shapes...
A huge idea in mathematics is to see the embedded relationships.

6. Critical Thinkers are logical but flexible in their thinking.
Flexible thinkers accept multiple approaches and multiple perspectives.
Logical thinkers seek out the order, what common in all these ways... How do they connect.

7. Students describe what they saw and how they thought to draw it.
Teachers encourage and model appropriate vocabulary....
Encourage students to see 3D as well. How does that change the description?

8. Quickdraw works on flexible thinking.
We all can describe what we see different ways but we all see the same things once we discuss.
Moving things in space allows you to really describe and understand their properties.. What changed? What stayed the same when you moved it or changed your perspective?

9. Quickdraw works on developing vocabulary and practicing with it until you really understand it. The teacher does not give definitions to memorize. We discuss properties of shapes until we are sure we have the most concise way to explain the attributes that make it this and not that.

10. This kind of mental fluency affects all areas of learning
This kind of mental fluency affects all areas of learning. Look, think, then draw what you saw.

11. The draw time is to give your brain a chance to really think about what it saw... Use pens, markers, fingers in the air, fingers on a surface to draw if you find the drawing is stopping students from engaging. It is not a drawing contest.

12. Talk about what you saw and how you thought about it is critical
Talk about what you saw and how you thought about it is critical. Sometimes just have students tell a partner.

13. Compare what you saw, how you described it, how you tried to draw it with others. The comparing is where the learning happens.

14. Build vocabulary lists to make the descriptions more mathematical over time.

15. B. E. R. C. S.

16. Think 2 dimensional and 3 dimensional. If you trace the shape it is 2D
Think 2 dimensional and 3 dimensional. If you trace the shape it is 2D. If you describe an object moving off or out of the page, it is 3D.

17. I show the image for 3 seconds, give you time to do first draw.
I show again, 3 seconds. Give you time to draw again.
I show again, 3 seconds, really look.
Do you see something a new way?

18. The Here’s What I saw slides are for the teacher, not meant to show students.

20. Ready?

26. Class Discussion I leave the image up to discuss it
Class Discussion I leave the image up to discuss it... Otherwise students change their minds.

27. Some things I saw Are the triangles congruent?
I saw a square and broke it in parts.
I saw a triangle and then added to it.
I thought of an envelope.
Are the triangles congruent?
Are they iscoceles, equilateral, scalene?
Right angles, obtuse, acute, reflex? Do the outside triangles fold in to make the centre triangle? Reflect, rotate, translate?
A trapezoid. Four sides, one set parallel.
Quadrilaterals, rectangles, squares how are they related?
How would you prove a square? Not a square?
Some things I saw
Angles: 90 degree, 45 degree? 180 degree?
How would you prove? Acute obtuse

28. Ready?

35. Some things I saw Are the triangles isoceles? Scalene? Acute?
I saw 3 triangles. Two are congruent.
A see five sided shape. An irregular pentagon.
Are the triangles isoceles? Scalene? Acute?
What kinds of angles can you identify?
If I lift the overlapped triangle up, this is a huge triangle folded.
If I move the overlapped triangle over, it is laying over a trapezoid.
Some things I saw
I see a 7 sided shape. Seven sides is a heptagon or septagon.
It is irregular

36. Compare the two images. How the same, how different
Compare the two images. How the same, how different. Use paper to fold into these two different shapes.

37. Ready?

44. Some things I saw The outside shape is a rhombus.
That is the math word for diamond.
It has 2 acute and 2 obtuse angles.
It has adjacent sides equal length.
It has 4 sides so it is a quadrilateral.
It has parallel sides so it is a parallelogram
If you want to get technical it is also called a kite.
Are these equilateral triangles. If not what?
Are there 90 degree angles. Where are they.
What is an interior angle, what is an exterior angle?
What other angles can you estimate without a protractor? How?
What happens if you stretch or shrink the sides.
Do you see congruence? Symmetry?
I can trace at least 2 pentagons. They are irregular.
Some things I saw

45. Ready?

51. I see trapezoids. Four sides so quadrilaterals
I see trapezoids. Four sides so quadrilaterals. One set of sides is parallel, so trapezoid. (side length has nothing to do with it.)
I see 3D. A hallway? A room? A 3 sided box?
If it is 3D the “sides” are rectangles not trapezoids (I am looking down on them)
I can trace some irregular hexagons in here.
I see congruent trapezoids.
I see rectangles or is one a square?
How could I prove without measuring with a ruler?
What angles do you see? Can you explain?

52. Ready?

59. Ready?

60. Compare

61. Ready?

68. Ready?

75. Ready?

82. Ready?

89. Ready?

96. Ready?

103. Ready?

109. READY?
NRLC Thinking 101 Math Cohorts

110. Quickdraw is the property of Dr. Grayson Wheatley
Quickdraw is the property of Dr. Grayson Wheatley. If you wish to purchase the full set of images, Grayson will send you to Thinking101 as I sell it for him in Canada. The original book and set of images sell for $30 Canadian. Additional images are available on CD 2 and CD 3 for $16 each.
Grayon Wheatley:
Geri Lorway: