teaching for understanding: what will it take? jim stigler ucla may 29, 2015
TRANSCRIPT
![Page 1: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/1.jpg)
Teaching for Understanding:What Will It Take?
Jim Stigler
UCLA
May 29, 2015
![Page 2: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/2.jpg)
Plan for Today
• What’s at stake• Why it’s hard• What it will take• Understanding statistics
![Page 3: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/3.jpg)
WHAT’S AT STAKECommunity college developmental mathematics students
![Page 4: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/4.jpg)
Developmental Math Students: Views of Math
• View math as rules/procedures to be memorized;can’t “figure it out”
• When students were asked, “What does it mean to be good at math?” 77% gave answers like these:• “Math is just all these steps.”
• “In math, sometimes you have to just accept that that’s the way it is and there’s no reason behind it.”
• “I don't think [being good at math] has anything to do with reasoning. It's all memorization.”
![Page 5: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/5.jpg)
Developmental Math Students
Which is greater: or ?
• 53% correct, but very few could explain why
• Compulsion to calculate…
a5
a8
5a = a85 = 8 ✔
![Page 6: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/6.jpg)
Developmental Math Students
Interviewer: “Why did you subtract 253? Could you have subtracted 462 to check the answer?”
462 + 253
715Interviewer: “How could you check that your answer is correct?”
715 – 253 = 462
![Page 7: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/7.jpg)
What Do We Want Our Students to Learn?
• Flexible vs. routine expertise (Hatano & Inagaki)• What is flexible expertise?
• Procedural fluency• Conceptual understanding• Disposition to think/make sense of mathematics• Ability to nimbly bring knowledge to bear across a
wide array of new situations
![Page 8: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/8.jpg)
WHY IT’S HARDTeaching is a cultural activity
![Page 9: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/9.jpg)
TIMSS Video Studies: How We Teach Mathematics
![Page 10: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/10.jpg)
TIMSS Video: Teaching is Cultural
• Teaching is a cultural activity; varies more across than within cultures (TIMSS 1995 video study; goals/scripts)
![Page 11: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/11.jpg)
US: “Quick and snappy”Japan: “Slow and sticky”
SOURCE: Hess & Azuma (1991)
![Page 12: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/12.jpg)
TIMSS Video: Teaching is a Cultural Activity
• Cultural activities are:• Learned implicitly (ritual learning)• Multiply determined• Hard to see (e.g., confusion)• Hard to change: culture wins
![Page 13: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/13.jpg)
WHAT IT WILL TAKEA focus on learning opportunities
![Page 14: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/14.jpg)
What do high-achieving countries have in common?*
*Do they all teach like Japan?
![Page 15: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/15.jpg)
Hong Kong
![Page 16: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/16.jpg)
Netherlands
![Page 17: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/17.jpg)
Teaching looks different in every country – no one way to teach.
![Page 18: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/18.jpg)
But: despite using different strategies… …high-achieving countries create similar learning opportunities for students.
![Page 19: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/19.jpg)
Research Indicates Three Types of Learning Opportunities Required for Deep Understanding
For deep learning, with understanding, students need recurring and sustained opportunities for:• Productive struggle – with important mathematics• Explicit connections – among concepts, procedures,
problems, situations• Deliberate practice – increasing variation and
complexity over time
![Page 20: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/20.jpg)
1. PRODUCTIVE STRUGGLE
![Page 21: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/21.jpg)
Productive Struggleand Desirable Difficulties
Students randomly assigned to two conditions to study science text:• Four study periods
• Read passage 14.2 times• Predicted good recall
• One study / 3 recall periods• Read passage 3.4 times• Predicted poor recall
5 Minutes 1 Week0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SSSS SRRR
Recall Test Delay
Pro
port
ion
Idea
Uni
ts R
ecal
led
Source: Roediger & Karpicke (2006)
![Page 22: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/22.jpg)
Productive Struggleand Desirable Difficulties
Students randomly assigned to two conditions to study science text:• Four study periods
• Read passage 14.2 times• Predicted good recall
• One study / 3 recall periods• Read passage 3.4 times• Predicted poor recall
5 Minutes 1 Week0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SSSS SRRR
Recall Test Delay
Pro
port
ion
Idea
Uni
ts R
ecal
led
Source: Roediger & Karpicke (2006)
![Page 23: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/23.jpg)
Confucius
“I never enlighten anyone who has not been driven to distraction by trying to understand a difficulty or who has not got into a frenzy trying to put his ideas into words. When I have pointed out one corner of a square to anyone and he does not come back with the other three, I will not point it out to him a second time” ( 不愤不启 , 不悱不发 . 举一隅不以三隅反 , 则不复也 .) (Lau, 7:8)
![Page 24: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/24.jpg)
2. EXPLICIT CONNECTIONS
![Page 25: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/25.jpg)
Thinking Hard
![Page 26: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/26.jpg)
The Power of Connections
Few Connections Many Connections
A
E
DF
G H
BC
A
E
DF
G H
BC
![Page 27: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/27.jpg)
Example: Struggle to Make Connections
⅓
¼⅓
½
What fraction of the rectangle is shaded brown?
(a)
(b)
SOURCE: Deborah Ball (2013)
![Page 28: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/28.jpg)
3. DELIBERATE PRACTICE
![Page 29: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/29.jpg)
Deliberate Practice
• Different from repetitive practice
• Constantly increasing variation, complexity, challenge
• With feedback• Staving off premature
automaticity• Understanding takes
practice, too!
![Page 30: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/30.jpg)
Learning Opportunities
Step-By-Step
Procedures
Well-Formed Lecture
Discovery Learning ✪
Explicit Connections
ProductiveStruggle
− +
−
+
![Page 31: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/31.jpg)
✪Learning Opportunities
Step-By-Step Procedures
Well-Formed Lecture
Discovery Learning ✪
Explicit Connections
ProductiveStruggle
− +
−
+
✪✪✪
✪
Deliberate Practice
Maintainingstruggle and connections
through time
![Page 32: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/32.jpg)
UNDERSTANDING STATISTICSMaking connections to core concepts
![Page 33: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/33.jpg)
Igor Gregoriev: “Only 5 Chords”
![Page 34: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/34.jpg)
Connections Map
L3A
L3B
L3C
L1 L2 L3 L4 L5 L6 L7
Core Concept
1
Core Concept
2
Core Concept
3
Related Concep
t
Example: Connect concept of mean to that of best fitting regression line.
![Page 35: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/35.jpg)
Working Hypothesis
• Statistics is the study of distributions.
• The “five chords”: the Distribution Triad.
• Hypothesis: practicing these connections over time will result in more coherent and flexible understanding.
Distributions
Sample
PopulationSampling
![Page 36: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/36.jpg)
Developmental Progression
• The whole is more than the sum of the parts
• Describing/comparing distributions
Distributions Sample
![Page 37: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/37.jpg)
Developmental Progression
• Working from sample to population, and vice versa
• Random sampling, and bias
• Problem of inference; informal approaches
• Sampling variation
Distributions
Sample
Population
![Page 38: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/38.jpg)
Developmental Progression
• A very abstract idea, hard to understand with or without simulation
• Confidence intervals, hypothesis tests
• Wait: I thought there were only three distributions?
Distributions
Sample
PopulationSampling
![Page 39: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/39.jpg)
Final Question:How do you make this happen?
![Page 41: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/41.jpg)
Teacher’s Goal for the Lesson
Skills Thinking0
20
40
60
80
100
55
3125
7361
22
GermanyJapanUSA
Per
cen
t of
Tea
cher
s
“What was the main thing you wanted students to learn from today’s lesson?”
Back
![Page 42: Teaching for Understanding: What Will It Take? Jim Stigler UCLA May 29, 2015](https://reader030.vdocuments.site/reader030/viewer/2022032600/56649dbf5503460f94ab3265/html5/thumbnails/42.jpg)
“Every system is perfectly designed to achieve the results it gets.”
-Paul Bataldan