Transcript Keynote: Music is Not in the Guitar

Seeing the Whole Elephant!
Andrew Chen
Seeing the Whole Elephant! Leadership for Excellence in Mathematics
NISL Course 2, UNIT 6
Graphing x + ay = b
• Given ab > 0, a and b are real numbers, which
graph(s) can be described by x + ay = b? Why?
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 ?
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?
Balance (“Rigor”)
K-12 Mathematics
Conceptual
Understanding
Computational
Fluency
Problem
Solving
"The Music Is Not in the Guitar"
and Other Lessons from
Yoda and Morpheus
Andrew Chen
February 19, 2016 Boston MA, U.S.A.
Standards Institute
Taiwan Central Police University
Entrance Exam in Math (1996)
1  3i
2
24

1      ...  _____
then
2
Massachusetts Mathematics Framework Revision August 21, 2008 EduTron Andrew Chen
How Good Are You at…?
6%
26%
44%
56%
3%
0%
21%
0%
0%
44%
OUTLINE
1.
2.
3.
4.
5.
6.
7.
8.
9.
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
Variance in State Performance Standards
8th Grade Math
% proficient 2011 State Test
% proficient 2011 TIMSS
NAEP 2013 8th Grade Mathematics
300
Average Scaled Score
290
280
270
260
250
240
1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435363738394041424344454647484950515253
Taiwan
MA
CT
Released
PISA 2012
PISA 2012December
Released2013
December
2013
Higher Expectations
“We are
systematically
underestimating what
our kids can do—
sometimes out of the
goodness in our
hearts.”
2011 TIMSS 8th Grade Mathematics
Item ID M052228
90
% of correct response
80
Which Leg Is Missing?
70
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Which Leg Is Missing?
A. 8 x 24 =?
24  8 =? 8  24 =?
B. 8 x 2.54 =?
2.54  8 =? 8  2.54 =?
C. One inch is 2.54 cm (centimeters). How
many inches are in 8 cm?
D. One pound of apple is $2.54. How many
pounds can $8 buy?
E. One pound of apple is $2. How many
pounds can $8 buy?
Balance (“Rigor”)
K-12 Mathematics
Conceptual
Understanding
Computational
Fluency
Problem
Solving
Nature of
the Beast
What does it take to add
two fractions?
Mathematics is
ruthlessly cumulative.
CCSSM Graph (Popup)
Google “edutron popup”
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, gradewise.
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.
4.NF.3 and 4.NF.4
Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers.
3. Understand … 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 +
2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8, etc.
4. Apply and extend previous understandings of
multiplication to multiply a fraction by a whole
number.
a) a. Understand 5/4 as the product 5 × (1/4), recording
the conclusion by the equation 5/4 = 5 × (1/4).
b) b. …express 3 × (2/5) as 6 × (1/5), …
Quizzes:
What is Coherence in CCSSM?
How do I take advantage of
it?
Quizzes:
What is SMP and Rigor in
CCSSM?
How do I pull them of in my
classroom?
Concrete Pictorial  Abstract
GK-M5-L7
© 2015 Great Minds
Grade K
GK-M5-L8
© 2015 Great Minds
Grade K
GK-M5-L9
© 2015 Great Minds
Grade 1
G1-M2-L25
© 2015 Great Minds
Grade 2
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
Grade 2
G2-M5-L4
© 2015 Great Minds
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
Grade 4
G4-M3-L13
© 2015 Great Minds
Solution C: x = 814, x + 4x + (4x – 143) = ?
Grade 7
G7-M3-L24
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
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.
Geometry
G9-M3-L1
Problem Set
© 2015 Great Minds
Algebra I
AI-M1-L4
Algebra I
AI-M1-L26
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
𝟐
𝟖
𝟖2∙∙𝟐𝟐++𝟓𝟓==𝟐𝟏
9
𝟐𝟏
𝟗
𝟐𝟏
9 ∙∙𝟐𝟐++𝟓𝟓==23
𝟒𝟕
𝟐𝟑
𝟒𝟕
𝟒𝟕
23∙∙ 𝟐𝟐 +
+ 𝟓𝟓 =
= 51,
𝟗𝟗,no!
no!
Algebra I
AI-M1-L26
𝑎0
𝑎𝑖+1 = 2𝑎𝑖 + 5, 𝑖 ≥ 0
Exercise 3
• Find a formula for 𝒂𝟏 , 𝒂𝟐 , 𝒂𝟑 , 𝒂𝟒 in terms of 𝒂𝟎 .
𝒂𝟏 = 𝟐𝒂𝟎 + 𝟓,
𝒂𝟐 = 𝟐𝒂𝟏 + 𝟓 = 𝟐 𝟐𝒂𝟎 + 𝟓 + 𝟓 = 𝟒𝒂𝟎 + 𝟏𝟓,
𝒂𝟑 = 𝟐𝒂𝟐 + 𝟓 = 𝟐 𝟐 ∙ 𝟐𝒂𝟎 + 𝟏𝟓 + 𝟓 = 𝟖𝒂𝟎 + 𝟑𝟓,
𝒂𝟒 = 𝟐𝒂𝟑 + 𝟓 = 𝟐 𝟐𝟑 ∙ 𝒂𝟎 + 𝟑𝟓 + 𝟓 = 𝟏𝟔𝒂𝟎 +
𝟕𝟓.
Attractive
Nuisances
Attractive Nuisances
in K-12 Mathematics Education
SMP
Commonalities Among the
practices in Math/Science/ELA
NGSS Appendix L
Standards for Mathematical Practice
in Common Core Standards
1. Make sense of problems & persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning
of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
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.
Attractive
Nuisances
Nuances
Attractive Nuances
in K-12 Mathematics Education
1. Solving “real-world and mathematical” problems
2. Interaction of OA and NBT
3. Fractions
1. Logical progressions
2. Start “+” with Common Denominator, Not LCD
3. Fractions before Decimals
4.
5.
6.
7.
Backbone of K-8 math
Improper fractions?
Number lines for #s & linear model of “+” & “-”
Area model for multiplication (and division)
Attractive Nuisances Nuances
in K-12 Math Education
9. Separation of Algebra and Functions in HS
10. Geometry based on transformations
11. HS Pathways and Courses (Appendix A)
12. (simple repeating) Patterns? To Teach or not to
teach in lower grades? Why and how?
13. Pedagogy neutral (with necessary exceptions,
e.g., 3 and 7)
14. Stresses fluency (even with ONE algorithm)
Lessons
Morpheus Yelled…
“Stop trying to hit me and
hit me."
Adywans Empire Strikes Back - Raising
the X-Wing Video 0:40 to 1:27
Alright, I’ll give it
a try.
No. Try not.
Do, or do not!!
There is no try.
I can't promise
I'll try, but I'll try
to try.
Adywans Empire Strikes Back - Raising
the X-Wing Video 3:40 to 5:13
I can’t…
I don’t believe it.
That is why you
fail.
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.]
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!
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.]
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
Duh! RIGOR! Productive Struggle
The Music is
NOT in the Guitar
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
The “Physics” of K-12 Math Education
Perfect
Standards
Perfect
Instructional
Materials
Instruction
• Teacher
Content
Knowledge
• Teaching
Practices
Perfect
Tests
PARCC
SBAC
PD on Content Knowledge
Coaching on Teaching Practices
Educator
Evaluation
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
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
Takeaways
Be Humble
Be Analytical
Have World-Class High
Expectations for all
Enjoy the Modules
Stay Sane (w/ Focus,
Coherence and Rigor)
Stay connected: [email protected]
Can I Teach Good Math
with ONLY Stick and Sand?
Stay connected: [email protected]
This Space For Rent