1. Seeing the Whole Elephant!
Andrew Chen
Seeing the Whole Elephant! Leadership for Excellence in Mathematics
NISL Course 2, UNIT 6
EduTron

3. Graphing x + ay = b
Given ab > 0, a and b are real numbers, which graph(s) can be described by x + ay = b? Why?

4. Designer Numbers II
A, B, C, D, E, and F are numbers as indicated on the following number line:
How can one construct the largest number using one operation (+ - x ) of two of these numbers ? 

5. A, B, C, D, E, and F are numbers as indicated on the following number line:
How can one construct the largest number using one operation (+ - x ) of two of these numbers ? 
Given ab > 0, a and b are real numbers, which graph(s) can be described by x + ay = b? Why?

6. Computational Fluency
Balance (“Rigor”)
K-12 Mathematics
Conceptual Understanding
Problem Solving
Computational Fluency

7. Andrew Chen February 19, 2016 Boston MA, U.S.A. Standards Institute
"The Music Is Not in the Guitar" and Other Lessons from Yoda and Morpheus
Andrew Chen
February 19, Boston MA, U.S.A.
Standards Institute

8. Taiwan Central Police University Entrance Exam in Math (1996)
Massachusetts Mathematics Framework Revision August 21, EduTron Andrew Chen

9. Double Standard How Good Are You at…? 6% 44% 26% 56% 0% 3% 0% 21% 0%
EduTron

10. OUTLINE Poke Data Speaks--Expectations Nature of the Beast
Attractive Nuisances
Attractive Nuances
The Music is NOT in the Guitar
The “Physics” of Math Education
Peek Into Modules
Lessons

11. Variance in State Performance Standards 8th Grade Math
% proficient 2011 State Test
% proficient 2011 TIMSS

13. Released December 2013 PISA 2012 PISA 2012 Released December 2013
Taiwan MA CT
Released December 2013 PISA 2012
PISA Released December 2013

14. Higher Expectations
“We are systematically underestimating what our kids can do— sometimes out of the goodness in our hearts.”

16. 2011 TIMSS 8th Grade Mathematics Item ID M052228
Which Leg Is Missing?
EduTron

17. Which Leg Is Missing? 8 x 24 =? 24  8 =? 8  24 =?
One inch is 2.54 cm (centimeters). How many inches are in 8 cm?
One pound of apple is $2.54. How many pounds can $8 buy?
One pound of apple is $2. How many pounds can $8 buy?

19. Computational Fluency
Balance (“Rigor”)
K-12 Mathematics
Conceptual Understanding
Problem Solving
Computational Fluency

20. Nature of the Beast

21. What does it take to add two fractions?

22. Mathematics is ruthlessly cumulative.

23. CCSSM Graph (Popup)
Google “edutron popup”

26. Participant Question #1: Gaps
Q: “What is the best way to fill in the gaps for Grade 7?”
A: Train yourself to be self-contained, grade- wise.

27. Theorems A Math Teacher at Grade N is actually Teaching Grades K to N
A Math Teacher at Grade N should know the math in Grades K to N+2 and beyond
A happy teacher = a teacher who knows the coherent progression from grade to grade—how concepts connect and build up.

28. 4.NF.3 and 4.NF.4
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Understand … 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/ /8 ; 2 1/8 = /8 = 8/8 + 8/8 + 1/8, etc.
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
b. …express 3 × (2/5) as 6 × (1/5), …

29. Quizzes:
What is Coherence in CCSSM?
How do I take advantage of it?

30. Quizzes: What is SMP and Rigor in CCSSM?
How do I pull them of in my classroom?

31. Concrete Pictorial  Abstract
GK-M5-L7
Concrete Pictorial  Abstract
© 2015 Great Minds

32. GK-M5-L8
Grade K
© 2015 Great Minds

33. Grade K
GK-M5-L9
© 2015 Great Minds

34. G1-M2-L25
Grade 1
© 2015 Great Minds

35. Grade 2 Elsa needs 65 craft sticks to make a gift box.
G2-M5-L4
Elsa needs 65 craft sticks to make a gift box.
She only has 48.
How many more craft sticks does she need?
© 2015 Great Minds

36. G2-M5-L4
Grade 2
© 2015 Great Minds

38. G4-M3-L13
Grade 4
In one month, Charlie read 814 pages. In the same month, his mom read 4 times as many pages as Charlie, and that was 143 pages more than Charlie’s dad read. What was the total number of pages read by Charlie and his parents?
© 2015 Great Minds

39. Grade 4 Solution C: x = 814, x + 4x + (4x – 143) = ? G4-M3-L13
© 2015 Great Minds
Solution C: x = 814, x + 4x + (4x – 143) = ?

40. G7-M3-L24
Grade 7
A fuel tank is the shape of a right rectangular prism and has 27 L of fuel in it. It is determined that the tank is ¾ full. The inside dimensions of the base of the tank are 90 cm by 50 cm. What is the height of the fuel in the tank? How deep is the tank? (1 L = 1000 cm3)
© 2015 Great Minds

41. Participant Question #2: Practices
Q. “How can I strengthen student involvement and assess students with the math practices? There is not enough time.”
A. Make time to “torture” every student.

42. the pattern will continue!
G9-M3-L1 Problem Set
Geometry
Just because there appears to be a seemingly predicable pattern
does not guarantee that
the pattern will continue!
© 2015 Great Minds

43. AI-M1-L4
Algebra I

44. AI-M1-L26
Algebra I
Exercise 2
Given a starting number, double it and add 𝟓 to get the result of Round 1. Double the result of Round 1 and add 𝟓, and so on. The goal of the game is to find the smallest starting whole number that produces a result of 𝟏𝟎𝟎 or greater in three rounds or fewer.
Number
Double and add 5 𝟖
𝟖∙𝟐+𝟓=𝟐𝟏 𝟐𝟏
𝟐𝟏∙𝟐+𝟓=𝟒𝟕 𝟒𝟕
𝟒𝟕∙𝟐+𝟓=𝟗𝟗, no!
Number
Double and add 5 𝟐
2∙𝟐+𝟓=9 𝟗
9∙𝟐+𝟓=23 𝟐𝟑
23∙𝟐+𝟓=51, no!

45. Algebra I 𝑎 0 𝑎 𝑖+1 =2 𝑎 𝑖 +5, 𝑖≥0 Exercise 3
AI-M1-L26
Algebra I
𝑎 𝑎 𝑖+1 =2 𝑎 𝑖 +5, 𝑖≥0
Exercise 3
Find a formula for 𝒂 𝟏 , 𝒂 𝟐 , 𝒂 𝟑 , 𝒂 𝟒 in terms of 𝒂 𝟎 .
𝒂 𝟏 =𝟐 𝒂 𝟎 +𝟓, 𝒂 𝟐 =𝟐 𝒂 𝟏 +𝟓=𝟐 𝟐 𝒂 𝟎 +𝟓 +𝟓=𝟒 𝒂 𝟎 +𝟏𝟓, 𝒂 𝟑 =𝟐 𝒂 𝟐 +𝟓=𝟐 𝟐∙𝟐 𝒂 𝟎 +𝟏𝟓 +𝟓=𝟖 𝒂 𝟎 +𝟑𝟓, 𝒂 𝟒 =𝟐 𝒂 𝟑 +𝟓=𝟐 𝟐 𝟑 ∙ 𝒂 𝟎 +𝟑𝟓 +𝟓=𝟏𝟔 𝒂 𝟎 + 𝟕𝟓.

46. Attractive Nuisances

47. Attractive Nuisances in K-12 Mathematics Education
SMP
Commonalities Among the practices in Math/Science/ELA
NGSS Appendix L

48. Standards for Mathematical Practice in Common Core Standards
Make sense of problems & persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.

49. Grin Without the Cat?
But developing ‘habits of mind’ outside of the context of the material being learned is like the Cheshire Cat of Alice in Wonderland. Such approach forces students to consider a grin well before they are presented with the cat associated with it.

50. Attractive Nuisances Nuances

51. Attractive Nuances in K-12 Mathematics Education
Solving “real-world and mathematical” problems
Interaction of OA and NBT
Fractions
Logical progressions
Start “+” with Common Denominator, Not LCD
Fractions before Decimals
Backbone of K-8 math
Improper fractions?
Number lines for #s & linear model of “+” & “-”
Area model for multiplication (and division)

52. Attractive Nuisances Nuances in K-12 Math Education
Separation of Algebra and Functions in HS
Geometry based on transformations
HS Pathways and Courses (Appendix A)
(simple repeating) Patterns? To Teach or not to teach in lower grades? Why and how?
Pedagogy neutral (with necessary exceptions, e.g., 3 and 7)
Stresses fluency (even with ONE algorithm)

53. Lessons

54. “Stop trying to hit me and hit me."
Morpheus Yelled…
“Stop trying to hit me and hit me."

55. Adywans Empire Strikes Back - Raising the X-Wing Video 0:40 to 1:27

56. Alright, I’ll give it a try.
No. Try not. Do, or do not!! There is no try.

57. I can't promise I'll try, but I'll try to try.

58. Adywans Empire Strikes Back - Raising the X-Wing Video 3:40 to 5:13

59. I can’t… I don’t believe it.
That is why you fail.

60. Yoda: Train yourself to be self-contained you must.
You: Alright, I’ll give it a try.
Yoda: No. Try not. Do, or do not!! There is no try.
[Translation: One must genuinely believe that the more you know, the more flexible and effective you will be in helping every student. So, you must actively grow yourself across grades.]

61. How Do I Train Myself to be Self-Contained?
Use the Force (CCSSM-Graph, CSSM Progressions, etc.)
Familiarize myself with the coherent progression of materials so that I can use them for patching up gaps and enrichment
Learn with and through others
Duh! COHERENCE!

62. Yoda: Make time to “torture” every student you must.
You: But my students… I can’t believe you’re asking me to … no time…
Yoda: That is why you fail.
[Translation: High expectation works. Make every student taste the productive struggle and success you are inducing.]
actively grow yourself across grades.]

63. How Do I Make Time and use material to “Torture” Every Student?
Build 3-Legged Stools (Common Core Rigor)
Dare to Demand (Practices)
Use the Force, e.g., Illustrative Mathematics, EngageNY, etc.
“Listen” CAREFULLY to Students
Take Zen Master Approach
Do NOT Rob Students of Their Productive Struggle
Duh! RIGOR!

64. The Music is NOT in the Guitar

67. The Music Is Not in the Guitar
“It's like saying 'Give a man a Les Paul guitar and he becomes Eric Clapton,' ….”
“It's not true.”
Roger Waters, 1972

68. The “Physics” of K-12 Math Education
Instruction
Perfect
Standards
Perfect
Perfect
Instructional Materials
Perfect
Tests
PARCC
SBAC
Educator Evaluation
Teacher Content Knowledge
Teaching Practices
PD on Content Knowledge Coaching on Teaching Practices

69. Learn from Santana
"The key... is discipline. Teens don't want to hear that. They think they can just snap their fingers, and Voila! But with discipline comes knowledge, coordination, balance, muscle memory, confidence-- things that make it possible to hit the bull's-eye three times in a row. But you must practice."
-Carlos Santana
2003, Parade Interview

70. Learn From …
"It is a mistake to think that the practice of my art has become easy to me. I assure you no one has given so much care to the study of composition as I. There is scarcely a famous master in music whose works I have not frequently and diligently studied."
- Wolfgang Amadeus Mozart

71. Takeaways Be Humble Be Analytical
Have World-Class High Expectations for all
Enjoy the Modules
Stay Sane (w/ Focus, Coherence and Rigor)
Stay connected:

72. Can I Teach Good Math with ONLY Stick and Sand?
Stay connected:

73. This Space For Rent