1. Please find a seat and complete the brief questionnaire
Welcome!
2 min.
Please find a seat and complete the brief questionnaire
as honestly as you can. .

2. Teaching for a Mathematical Mindset
2 min.--S
Sue Myette ISD Instructional Coach
August 24, 2016

3. Preparation for Facilitator
Handout Packet (1/participant):
Math mindset questionnaire (see next slide)
Mindset messages practice page
Sample growth mindset norms
Number talk handout
How Close to 100
Other materials
Square paper for tables
Large chart paper and markers for number talk

4. Note for facilitator: Entry task will be for participants to complete a brief questionnaire.
Questionnaire will have 5 statements with a 5-point answer scale (strongly agree=0, agree=5, neutral=10, disagree=15, strongly disagree=20)
When math gets hard it makes me feel that I’m not very smart.
The parts of math I like best are the ones where I make the fewest mistakes.
My level of math ability is a trait I inherited from my parents.
When I struggle with a hard math problem I feel like giving up.
Math is much easier to learn if you are male or come from a certain culture.
Participants will find their total score. The scoring will range from 0 (all responses are strongly agree) to 100 (all statements are strongly disagree).
Participants will use their score for the slide that follows. N

5. What color are you on the Math Mindset Meter?40 60 20 80
2 min N

6. Let’s do some math!
Work with a partner to complete these paper folding tasks. Explain to your partner how you know each shape you make has the specified area.
Construct a square with exactly ¼ the area of the original square.
Construct a triangle with exactly ¼ of the area of the original square.
Construct a square with exactly ½ the area of the original square.
Construct another square, also with ½ the area, but oriented differently from the one you just made.
6 min N

7. How did the task feel? For reds and oranges? For yellows?
For light greens?
For dark greens?
T&T, volunteers share out
2 min N
Developing a mathematical mindset—a growth mindset applied to approaching mathematics conceptually—can change how you feel about math, how your brain works, how you learn, and how you teach.

8. Objectives: By the end of this session you will…
Understand the impact of mindset on mathematics learning.
Begin to develop and encourage a growth mindset in math.
Understand, and be prepared to apply, 3 strategies to teach math for conceptual understanding.
1 min S

9. Part 1: Encouraging a Growth Mindset in Mathematics
The highest- achieving students in the world are those with a growth mindset, and they outrank other students by the equivalent of more than a year of mathematics. (Boaler, 2016)
Part 1: Encouraging a Growth Mindset in Mathematics
1 min S

10. What messages did you receive about math?
I’m slow so I must be stupid.
Math class is tough!
It’s bad to make mistakes in math.
Boys are better than girls at math.
Math is boring, not for creative people.
Asians are naturally better at math.
I have to find answers the same way my teacher does.
2 min S
Ask participants to share any messages they were given, either directly or indirectly, about math. We’re going to watch a video that shows why each one of these messages is false.

11. Yes, we can!!
More than 50% of Americans between ages 18 and 34 say they can’t do math.
1 min S

12. Listen for Growth Mindset Messages
Play 8 ½ minute video by clicking the rectangle. 9 min. N

13. Video Discussion Discuss with a partner:
What were the main messages for students?
Which parts aligned with your previous thinking?
Which parts surprised you or made you wonder?
4 min N

14. What do growth messages sound like?
I don’t get division.
I notice you began by drawing a picture. Good thinking! What are you thinking about doing next?
I need help.
This is too hard.
I see you’re using what we know about adding whole numbers to add the numerators and denominators. Now let’s look at…
1/2 + 1/4 = 2/6
Reinforce the positive steps the students has already taken… S

15. Mistakes grow your brain!

16. Teaching Actions to Consider
Establish growth mindset classroom norms
because
…the most successful students are those with a growth mindset.
Intentionally send growth mindset messages about math
…a growth mindset can be developed at any time in life.
Teach students to value mistakes as opportunities for learning
…struggles make our brains grow more than when the work comes easily.
Reconsider the emphasis given to timed math fact tests
…speed is not the most important skill in math.
Refer to sample norms in packet; some teachers have their students build a growth mindset rubric. 4 min N

17. Part 2: Teaching for Conceptual Understanding
Giving students growth mindset messages will not help them unless we also show them that math is a growth subject. (Boaler, 2016)
Part 2: Teaching for Conceptual Understanding
1 S

18. Why is Conceptual Understanding Important?
The brain can only compress concepts; it cannot compress rules and methods.
(Thurston, 1990 )
Experts see meaningful patterns of information and use them to organize their knowledge in ways that reflect a deep understanding of their subject matter.
(Bransford et al., 1999)
Successful math users search for patterns and relationships and think about connections.
(Boaler, 2016)
2 min S
Approaching math conceptually is the essence of a mathematical mindset.

19. Methods vs. Concepts Repeated addition Concept of Product Counting on
Concept of Sum
1 S
Counting
Concept of Number
(Boaler, 2016)

20. How can we help all students successfully learn mathematical concepts?
Facilitate number talks
Use visual representations
Present multidimensional, real world problems
3 min N
Multidimensional = more than one aspect of math may be used to solve the problem

21. Number talks promote number sense and mathematical mindset
Choose problems intentionally to encourage flexible thinking beyond standard algorithms.
Focus on having students share multiple pathways to the answer.
Use both visual and numerical problems.
10 min N
Resist the temptation to teach a strategy; math string to help kids discover a pattern
Visual: value different ways of seeing as different pathways to a solution
Number sense and mathematical mindsets develop together. Moreover, number sense is the foundation for all higher level mathematics.
(Boaler, 2016; Feikers & Schwingendorf, 2008)

22. Let’s try it!
15 x 12 = __
10 min S

23. Visual representations promote number sense and conceptual understanding
How Close to 100? Game to practice multiplication facts with visual representations to reinforce conceptual understanding, not just memorization.
Have one ready to do (6 min)--handout with website/if time is short, just show website N

24. Visual Representations, cont.
How do you see this pattern growing? Draw case 4. Use shading to show the “new” squares.
Show from 4:29- 7:50
Some of Jo Boaler’s Stanford students have started to name the different ways they see this pattern grow.
Raindrops
Bowling Alley – row of pins across the bottom
Volcano Method - central column grows up first and lava flows down on top
Square Method – flip the left side across the central column and it forms a square.

25. The Turkey Problem: How would you solve it?
A man is on a diet and goes into a shop to buy some turkey slices.
He is given 3 slices which together weigh 1/3 of a pound but his diet says that he is allowed to eat only 1/4 of a pound.
How much of the 3 slices he bought can he eat while staying true to his diet?
3 N
Sometimes a visual solution path makes more sense than an algorithm.

26. Multidimensional, real world problems encourage reasoning and application
This is stupid. Normal people would just order more pizza.
A pizza is divided into fifths for 5 friends at a party. Three friends eat their slices, but then 4 more friends arrive. What fraction should the remaining 2 slices be divided into?
Warning!! Beware of pseudo-contexts: they can make math seem irrelevant.
1 min. S
Mean and median in drafting football players

27. What do mathematicians do?
Pose a question about a real world situation.
Make a mathematical model to find a way to answer the question.
Perform some calculations.
Analyze the results to see if the original, real-world question was answered.
2 min S
Think about the gap between school math and real world math. We emphasize calculation, yet that is the component of mathematics that is automated.
Focusing on #3 alone is like, in reading, practicing an isolated skill versus making meaning of an authentic text.
It used to be that employers needed people to calculate; they no longer need this. What they need is people to think and reason. (Wolfram, 2010)

28. How many of each kind of chip should go into the box?
What kind of “model” or approach should we take to answer this question?
What information would we want to have?
How could we get that information?
What calculations would we do?
What would that tell us?
3 N

29. Objectives: By the end of this session you will…
Understand the impact of mindset on mathematics learning.
Begin to develop and encourage a growth mindset in math.
Understand, and be prepared to apply, 3 strategies to teach math for conceptual understanding.
Our math mindset comes from messages we receive.
Mindset can become a self-fulfilling prophecy: whether you believe you can or believe you can’t: you’re right.
Everyone can learn math at high levels.
Struggles and mistakes help our brains grow.
Understanding is more important than speed.
Number talks to promote number sense.
Visual representations.
Multidimensional real-world problems.
1 min S

30. Useful Resources https://www.youcubed.org/
Teaching resources, research, and courses from Jo Boaler
Many links to mindset resources for the classroom
-of-the-month/download-problems-of-the- month
Differentiated low floor, high ceiling tasks for conceptual understanding N