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TRANSCRIPT
Where’s the Math?
Saturday, 8:30 AM - 10 AM Convention Center, Mesquite C
Zack Miller Summit Public Schools
@zmill415
Welcome!
While you wait for the session to start:
• What is math? What’s your definition? What is the definition you would share with students?
• Come up with an example and non-example for your definition.
Where’s the Math?Zack Miller
Summit Public Schools San Francisco, CA
Email: [email protected] Website: ZackMillerMathBlog.com Twitter: @zmill415
@zmill415
T S P
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Target Status Proposal
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1. What is math? 2. What’s happening in schools and why? 3. What can we do about it?
@zmill415
1. What is math? 2. What’s happening in schools and why? 3. What can we do about it?
@zmill415
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A
B
C
D E
Z
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What about this is math?
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– Paul Lockhart, A Mathematician’s Lament
“Asking simple and elegant questions about our imaginary creations, and crafting
satisfying and beautiful explanations.”
@zmill415
What about this is math?
• Math is social.
• Feels like play.
• Notation, symbols, figures —> they serve us.
@zmill415
Source: Kuta Software
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Pick 3 numbers that add up to 10. Place the 3 numbers in the blanks below, in
any order.
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Pick 3 numbers that add up to 10. Place the 3 numbers in the blanks below, in
any order.
27
1
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Pick 3 numbers that add up to 10. Place the 3 numbers in the blanks below, in
any order.
31
6
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Pick 3 numbers that add up to 10. Place the 3 numbers in the blanks below, in
any order.
What is the largest value possible?
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Pick 3 numbers that add up to 10. Place the 3 numbers in the blanks below, in
any order.
What is the value closest to 0 without hitting it?
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Pick 3 numbers that add up to 10.
18
1 72
1
What is the value closest to 0 without hitting it?
Left Right
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Pick 3 numbers that add up to 10.
18
1 81
1
What is the value closest to 0 without hitting it?
Left Right
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Pick 3 numbers that add up to 10.
What is the value closest to 0 without hitting it?
Left Right
18
1 82
0
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Pick 3 numbers that add up to 10.
What is the value closest to 0 without hitting it?
Left Right
18
1 90
1
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Pick 3 numbers that add up to 10.
What is the value closest to 0 without hitting it?
Left Right
18
1 10-1
1
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100
0? or 1?
@zmill415
– Eugenia Cheng, How to Bake Pi
“The key in math is that things exist as soon as you imagine them, as long as they don’t cause
a contradiction.”
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a · a · a · a a · a · aa 4 a 3
a 4 · a 3
a 7
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a b · a c
a b + c
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10 3 · 10 0 = 10 3
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@zmill415Source: Kuta Software
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“Math is the study of anything that obeys the rules of logic, using the rules of logic.”
– Eugenia Cheng, How to Bake Pi
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Runs Created
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Runs Created
Source: Wikipedia
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Total Runs Scored 1950-2015
Model: Actual:
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Total Runs Scored 1950-2015
Model: Actual: 1,129,286 runs
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Total Runs Scored 1950-2015
Model: 1,126,591 runs
Actual: 1,129,286 runs
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Runs Created
Source: Wikipedia
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Runs Created
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Runs Created
Source: Wikipedia
Source: Common Core
Source: Dan Meyer
Source: Thanks Textbooks (tumblr)
@zmill415
“Math is the study of anything that obeys the rules of logic, using the rules of logic.”
– Eugenia Cheng, How to Bake Pi
@zmill415
1. What is math? 2. What’s happening in schools and why? 3. What can we do about it?
@zmill415
1. What is math? 2. What’s happening in schools and why? 3. What can we do about it?
@zmill415
@zmill415
image p/41
Warm-up
Source: Stigler & Hiebert, The Teaching Gap
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Teacher: Here we have vertical angles and supplementary angles. Angle a is vertical to which angle?
Students: Seventy (in chorus)
Teacher: Therefore angle a must be?
Students: Seventy degrees (in chorus)
Warm-up
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Teacher: “Get out the worksheet I gave earlier in the week and make sure we understand complementary, supplementary, and angle measurements”
Checking Homework
The class checks thirty-six problems on the worksheet during six minutes of question-and-answer interaction.
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Teacher distributes a worksheet that contains problems that, he notes, are “just like the warm-up.”
The top of the worksheet is a sample problem with the solution and a suggested method shown.
Teacher goes over a sample, asks for questions, there are none, students begin working independently.
Demonstrating Procedures
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The “problems,” like the homework and warm-up, emphasize terms and procedures.
Practicing Procedures
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Teacher gives a quick oral review with the class on the meaning of terms, assigns homework.
Reviewing Procedures & Definitions
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I do, We do, You do
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You, Y’all, We
Teaching by Thirds
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You Y’all We
Math TaskFor instruction
@zmill415Source: Stigler & Hiebert, The Teaching Gap
@zmill415Source: Stigler & Hiebert, The Teaching Gap
@zmill415Source: Stigler & Hiebert, The Teaching Gap
@zmill415Source: Stigler & Hiebert, The Teaching Gap
@zmill415Source: Stigler & Hiebert, The Teaching Gap
@zmill415Source: Stigler & Hiebert, The Teaching Gap
@zmill415
“In Japanese lessons... the students engage with the mathematics, and the teacher mediates the relationship
between the two. In Germany... the teacher owns the mathematics and parcels it out to students as he sees fit,
giving facts and explanations at just the right time... In U.S. lessons, there are the students and there is the
teacher. I have trouble finding the mathematics; I just see interactions between students and teachers.”
- Stigler & Hiebert, The Teaching Gap
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“The main problem with school mathematics is that
there are no problems.”
- Paul Lockhart, A Mathematician’s Lament
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Math is largely absent from “math” classrooms
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Why?
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Why?• Teaching
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“The teaching gap is the set of real differences in teaching methods used in every day in
typical classrooms. These differences that accumulate over time and across the country are bound to affect what and how
students learn.”
- Stigler & Hiebert, The Teaching Gap
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Why do these exist?
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Perils of Tricks
• Too much stuff to remember!
• Over-generalizing
• Under-generalizing
• Missed opportunities
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– Jim Doherty
“If it is so limited in its usefulness, why grant it the privilege of a name and some memory
space. Cluttering heads with specialized techniques that mask the important general
principle at hand does the students no good, in fact may harm them.”
Tricks to Nix
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Why?• Teaching
• Curriculum
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Why?• Teaching
• Curriculum
• Policy-makers
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Why?• Teaching
• Curriculum
• Policy-makers
• The educational infrastructure
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Why?• Teaching
• Curriculum
• Policy-makers
• The educational infrastructure
• Culture
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“If your art teacher were to tell you that painting is all about filling in numbered
regions, you would know that something was wrong. The culture informs you—But if your math teacher gives you the impression… that
mathematics is about formulas and definitions and memorizing algorithms, who will set you
straight? The cultural problem is a self-perpetuating monster.”
- Paul Lockhart, A Mathematician’s Lament
@zmill415
1. What is math? 2. What’s happening in schools and why? 3. What can we do about it?
@zmill415
The Opportunity• Math is in.
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The Opportunity• Math is in.
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The Opportunity• Math is in.
• Policy is changing for the better.
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The Opportunity• Math is in.
• Policy is changing for the better.
• The internet is really catching on (and curriculum authors have noticed).
@zmill415
Pick 3 numbers that add up to 10. Place the 3 numbers in the blanks below, in
any order.
@zmill415
OpenMiddle.com
@zmill415
The Opportunity• Math is in.
• Policy is changing for the better.
• The internet is really catching on (and curriculum authors have noticed).
• MTBoS
@zmill415
The Opportunity• Math is in.
• Policy is changing for the better.
• The internet is really catching on (and curriculum authors have noticed).
• MTBoS
• New tools are changing the game.
@zmill415
Doing math in class is tough without tech
• progressively disclose information and questions • facilitate a discussion using student ideas (where work is often on paper) • offer teachers a window into student thinking and feedback cycle to
students • help students catalog and organize a record of their thinking and work • help students who are absent stay up to speed • much more!
@zmill415
The Opportunity• Math is in.
• Policy is changing for the better.
• The internet is really catching on (and curriculum authors have noticed).
• MTBoS
• New tools are changing the game.
@zmill415
Move points A, B, and C such that they each form a right angle
If we overlaid all responses in the room, what would we see?
@zmill415Source: Dan Meyer
@zmill415
@zmill415
– Paul Lockhart, A Mathematician’s Lament
“Asking simple and elegant questions about our imaginary creations, and crafting
satisfying and beautiful explanations.”
@zmill415
What about this is math?
• Math is social.
• Feels like play.
• Notation, symbols, figures —> they serve us.
@zmill415
Call to Action
@zmill415Source: Jim Collins, Good to Great
@zmill415
Call to Action: Empower students to do math
@zmill415
Call to Action Empower students to do math by…
1. Committing to try a new approach to instruction.
2. Committing to look for and use some low-floor, high-ceiling tasks.
3. Committing to try a new tech tool.
4. Committing to change how you prepare for lessons.
5. Commit to joining or supporting a community of teachers (such as your dept, or MTBoS).
Places to find good tasks
@zmill415
Bookshelf
• Paul Lockhart, A Mathematician’s Lament
• James Stigler & James Hiebert, The Teaching Gap
• Eugenia Cheng, How to Bake Pi
• NCTM, Principles to Action
• Jim Collins, Good to Great
Send your text message to this Phone Number: 37607
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