#BuildMathMinds18: How Slow Thinking, Playing and Challenge Create Mathematicians

In the Build Math Minds Summit, Dan Finkel elaborated on this notion that “what books are to reading, is what play is to math.” And as he said this, my ears perked up, I leaned in and listened intently because this is all I’ve been thinking about for the last week as I begin to plan for next year’s inquiry maths with play as a pedagogical stance. He articulately beautifully how math thinking comes from asking questions, solving problems, playing and exploring.

So as I marinated in his words and ideas, I began binge learning all over again. Glutton for punishment?–I guess I am. But they say that when you teach others, you learn twice. So I want to share my takeaways from some of the presenters, Dan Finkel included, for the Math Minds Summit (which you should go watch right now if you read this post before August 6th, 2018). And because I know that the brain is more switched on when you present ideas as questions, my gleanings are represented in that way for this blog.

I hope it inspires you…..

During unstructured play, what kinds of questions can provoke analytical and divergent thinking?

How many? (number)

What kind? (classification)

How big? (measurement)

What if? (creativity and logic)

What makes games good to develop mathematical thinking?

1. Anything with Dice
2. 5 in a row
3. Number sense cards (that show alternate variations of number patterns)
4. Checkers
5. Nim
6. Anything with cards
7. Anything that you can advance pieces on a board
8. Games that involve making choices so that children develop strategy and thinking.

Provocations= Puzzles and Challenges

These can be concrete opportunities to explore estimation and making conjectures, but the heart of a mathematical provocation is that it must be intriguing to get the students curious and motivated to solve the problem. Consider if the provocation is going to…

1. Allow all students to show their thinking and understanding in interesting ways.
2. Invite conversation and collaboration among peers.
3. Provide opportunities to assess what students know and can do mathematically.
4. Have an ROI (return of investment) of time and resources–all the set up is worth it because of the cognitive demand and depth of learning that is going to come from this provocation.

(These 4 criteria were inspired from Jon Orr  and his work with starting a Math Fight)

These are some examples that I think were great examples:

“About” how many ketchup packets do you think can fit inside these containers?

Prompts that incite a variety of answers:

What language encourage mathematical dispositions?

• Demonstrate that wrong conjectures can be the jumping off point for refining our ideas with counterexamples which enrich our thinking and deepen our conceptual understandings.
• Using descriptive and numerical language to highlight the math concepts  (He gave the simple example of saying “Get your 2 gloves” vs. “Get your gloves”.
• Use language that shows that we, as adults, aren’t afraid of making mistakes, so they feel safe also.
• Do NOT use words that suggest that you have to be “smart” or “fast” to do the math.
• Likewise, do NOT give praise for being “fast” or “smart”.
• Ask questions that provide challenge and make students take a position (conjectures):
  • Do you agree or disagree with this idea?
  • Why?
  • How do you know?
  • Say more about that?
  • In your own words, could you explain….?
  • Would you rather….. or would you rather……?
  • How might you represent your thinking?

What routines or thinking systems encourage mathematical conversations and develop conceptual understandings?

(Click to learn more on the links)

• EVERYTHING WE KNOW ABOUT THIS routine: Present a problem or puzzle, asking them to….Write down, tell a neighbor, tell me EVERYTHING you know about this.
• Number Talks: a simple problem shown that students try to solve mentally in a variety of ways.
• Number String: a specifically structured string of number problems in which the numbers get progressively harder.
• Counting Collections: The routine speaks for itself- students count set collections of objects. This develops a variety of counting strategies.
• Claim, Support, Question: providing a claim (conjecture) that students have to provide evidence to support their claim. In order to deepen the conjecture, students can use counterexamples or ask questions that help develop a better math argument.
• Two Truths and a Lie: students are presented with a math problem or graphic.  Students are instructed to create two truths and one lie about the math.  Then, students share their “truths” and “lie” and have other students decide which are the truths and which is the lie.
• Which One Doesn’t Belong?: These are visual puzzles that have multiple answers. Click on the link to see a plethora of them. There’s also a book written by the same title.

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Next week, when our 1st graders start piling into the classroom, I have an arsenal of ideas that I’ve gotten from this summit. (And it’s not even over!!) I really would invite you to check it out. I know, beyond a doubt, that our students are going to fall in love with math at an early age because they will engage in play, feel challenged at their level and construct meaning on their own timeline. I wish the joy of math for all children (and adults) out there. Don’t you?