Thinking about Learning, or Learning about Thinking

1
Thinking about Learning, or Learning about
Thinking

• Dr. Alan Zollman
• Mathematical Sciences
• MATH 610
• August 25, 2009

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Effective Strategies

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Effective Strategies

• One Important Concept

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Effective Strategies

• One Important Concept
• Two Dumb Stunts

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Effective Strategies

• One Important Concept
• Two Dumb Stunts
• Two Quick Actions

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Effective Strategies

• One Important Concept
• Two Dumb Stunts
• Two Quick Actions
• Three Big Ideas

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Effective Strategies

• One Important Concept
• Two Dumb Stunts
• Two Quick Actions
• Three Big Ideas
• Two Predictors of College Success

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Effective Strategies

• One Important Concept
• Two Dumb Stunts
• Two Quick Actions
• Three Big Ideas
• Two Predictors of College Success
• One Reflection

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A mayber was raling his temp. Saintly a durf
accotted some padis in his temp. Why did yind
accot padis in my blem temp? the mayber quassed
the durf. Arm varrly grendy, the durf trepped.
Ar hished yind merpled padis in your temp. Did
yind rale your temp blem?

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A mayber was raling his temp. Saintly a durf
accotted some padis in his temp. Why did yind
accot padis in my blem temp? the mayber quassed
the durf. Arm varrly grendy, the durf trepped.
Ar hished yind merpled padis in your temp. Did
yind rale your temp blem?

• Please answer the following question in complete
  sentences

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A mayber was raling his temp. Saintly a durf
accotted some padis in his temp. Why did yind
accot padis in my blem temp? the mayber quassed
the durf. Arm varrly grendy, the durf trepped.
Ar hished yind merpled padis in your temp. Did
yind rale your temp blem?

• Please answer the following question in complete
  sentences
• What did the durf accot in the maybers temp?

12
A mayber was raling his temp. Saintly a durf
accotted some padis in his temp. Why did yind
accot padis in my blem temp? the mayber quassed
the durf. Arm varrly grendy, the durf trepped.
Ar hished yind merpled padis in your temp. Did
yind rale your temp blem?

• Please answer the following question in complete
  sentences
• What did the durf accot in the maybers temp?
• What did the mayber quas the durf?

13
A mayber was raling his temp. Saintly a durf
accotted some padis in his temp. Why did yind
accot padis in my blem temp? the mayber quassed
the durf. Arm varrly grendy, the durf trepped.
Ar hished yind merpled padis in your temp. Did
yind rale your temp blem?

• Please answer the following question in complete
  sentences
• What did the durf accot in the maybers temp?
• What did the mayber quas the durf?
• Was the durf grendy?

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A mayber was raling his temp. Saintly a durf
accotted some padis in his temp. Why did yind
accot padis in my blem temp? the mayber quassed
the durf. Arm varrly grendy, the durf trepped.
Ar hished yind merpled padis in your temp. Did
yind rale your temp blem?

• Please answer the following question in complete
  sentences
• What did the durf accot in the maybers temp?
• What did the mayber quas the durf?
• Was the durf grendy?
• Why did the mayber rale his temp?

15
A mayber was raling his temp. Saintly a durf
accotted some padis in his temp. Why did yind
accot padis in my blem temp? the mayber quassed
the durf. Arm varrly grendy, the durf trepped.
Ar hished yind merpled padis in your temp. Did
yind rale your temp blem?

• Please answer the following question in complete
  sentences
• What did the durf accot in the maybers temp?
• What did the mayber quas the durf?
• Was the durf grendy?
• Why did the mayber rale his temp?
• Is there a difference between knowing an answer
  
• and understanding a solution in mathematics?
• Adapted from Kenneth Goodmans
• The Psycholinguistic Nature of the Reading
  Process

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The Difference Between Teaching and Learning
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The Difference Between Teaching and Learningor
How to Teach a Dog French
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Two Dumb Stunts

• Of all the demographic data collected on
  students taking standardized tests, which one
  has the highest correlation with scoring the
  highest mathematics test scores?

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Two Dumb Stunts

• 1) Give the Father Lottery Tickets

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Two Dumb Stunts

• 1) Give the Father Lottery Tickets
• 2) Give the Parents Honorary Degrees

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Two Dumb Stunts

• In applying the empirical research to the
  practical classroom, there is a difference
  between
• correlations

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Two Dumb Stunts

• In applying the empirical research to the
  practical classroom, there is a difference
  between
• correlations
• and
• causations.

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Two Quick Actions
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Two Quick Actions

• Have lecture, individual, cooperative group
  activities

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Two Quick Actions

• Have lecture, individual, cooperative group
  activities
• Have a daily reflection

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Effective Strategies

• Big Ideas
• Jean Piagets Reflective Abstraction

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Effective Strategies

• Big Idea 1
• Jean Piagets Reflective Abstraction
• Generalization (Association)

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Generalization (Association) Memorize the
following 12 items in orderMake sure you
can read the whole screen
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SKY
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SKYRADIO
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SKYRADIOGAS STATION
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SKYRADIOGAS STATIONBOX
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SKYRADIOGAS STATIONBOXCUP
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SKYRADIOGAS STATIONBOXCUPDOOR
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SKYRADIOGAS STATIONBOXCUPDOORKNIFE
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SKYRADIOGAS STATIONBOXCUPDOORKNIFETOY
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SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROAD

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SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROAD
SIGN
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SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROAD
SIGNTOWEL
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SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROAD
SIGNTOWELRAISINS
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wait ..
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Without looking
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Without looking whats the full name of this
course?
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OK, nowwrite the 12 nouns in order.
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SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROAD
SIGNTOWELRAISINS
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Effective Strategies

• Big Idea 2
• Jean Piagets Reflective Abstraction
• Generalization (Association)
• Coordination (Assimilation)

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Coordination (Assimilation)

• How do we add
• 2 tens 3 ones

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Coordination (Assimilation)

• How do we add
• 2 tens 3 ones
• 2 thirds 3 fourths

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Coordination (Assimilation)

• How do we add
• 2 tens 3 ones
• 2 thirds 3 fourths
• (2x 4y) (3x y)

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Effective Strategies

• Big Idea 3
• Jean Piagets Reflective Abstraction
• Generalization (Association)
• Coordination (Assimilation)
• Encapsulation

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Encapsulation Example4th Grade Question How
many different ways can you arrange 3 objects
with 2 objects, 2 at a time?
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• Encapsulation Example
• 4th Grade Question
• A. How many different ways can you arrange 3
  objects with 2 objects, 2 at a time?
  or
• B. How many ways can you make a gym outfit if
  you have red, blue, or white tee shirts and red
  or white shorts?
• (remember the movie Clueless?)

(question from Dr. John Sleisky, Authenticity
and Test Items In Large Scale Assessment SSMA
Centennial Conference, Downers Grove, IL, Nov. 1,
2001)
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Predictors of College Success

• 7.8 of high school students who take
• ALGEBRA I get a college degree

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Predictors of College Success

• 23.1 of high school students who take
• GEOMETRY get a college degree
• 7.8 of high school students who take
• ALGEBRA I get a college degree

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Predictors of College Success

• 39.5 of high school students who take
• ALGEBRA II get a college degree
• 23.1 of high school students who take
• GEOMETRY get a college degree
• 7.8 of high school students who take
• ALGEBRA I get a college degree

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Predictors of College Success

• 62.2 of high school students who take
• TRIGONOMETRY get a college degree
• 39.5 of high school students who take
• ALGEBRA II get a college degree
• 23.1 of high school students who take
• GEOMETRY get a college degree
• 7.8 of high school students who take
• ALGEBRA I get a college degree

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Predictors of College Success

• 74.3 of high school students who take
• PRE CALCULUS get a college degree
• 62.2 of high school students who take
• TRIGONOMETRY get a college degree
• 39.5 of high school students who take
• ALGEBRA II get a college degree
• 23.1 of high school students who take
• GEOMETRY get a college degree
• 7.8 of high school students who take
• ALGEBRA I get a college degree

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Predictors of College Success

• 79.8 of high school students who take
• CALCULUS get a college degree
• 74.3 of high school students who take
• PRE CALCULUS get a college degree
• 62.2 of high school students who take
• TRIGONOMETRY get a college degree
• 39.5 of high school students who take
• ALGEBRA II get a college degree
• 23.1 of high school students who take
• GEOMETRY get a college degree
• 7.8 of high school students who take
• ALGEBRA I get a college degree

Answers in the Tool Box, U.S. Department of
Education by Clifford Adelman
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Predictors of College Success

• Answers in the Tool Box, a study by U.S.
  Department of Education researcher Clifford
  Adelman, examined more than 20 variables--includin
  g high school courses, educational aspirations,
  race, socioeconomic status (SES), on-time versus
  late high school graduation, and parenthood prior
  to age 22--to determine what really influenced
  the college completion rates of over 10,000
  students.

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Predictors of College Success

• Of all the high school indicators of academic
  preparation, the one that is the strongest is
  taking rigorous and intense courses in high
  school.

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Predictors of College Success

• Of all the high school indicators of academic
  preparation, the one that is the strongest is
  taking rigorous and intense courses in high
  school.
• Taking rigorous and intense high school courses
  has a greater impact on African-American and
  Latino students than on white students.
• ?

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Predictors of College Success

• Of all the high school indicators of academic
  preparation, the one that is the strongest is
  taking rigorous and intense courses in high
  school.
• Taking rigorous and intense high school courses
  has a greater impact on African-American and
  Latino students than on white students.
• Of all the high school courses, the highest level
  of mathematics taken is the most important for
  college success. The odds that a student who
  enters college will complete a bachelor's degree
  more than doubles if that student completed a
  mathematics course beyond Algebra II (e.g.,
  trigonometry or pre-calculus) while in high
  school.
• ?

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Predictors of College Success

• Of all the high school indicators of academic
  preparation, the one that is the strongest is
  taking rigorous and intense courses in high
  school.
• Taking rigorous and intense high school courses
  has a greater impact on African-American and
  Latino students than on white students.
• Of all the high school courses, the highest level
  of mathematics taken is the most important for
  college success. The odds that a student who
  enters college will complete a bachelor's degree
  more than doubles if that student completed a
  mathematics course beyond Algebra II (e.g.,
  trigonometry or pre-calculus) while in high
  school.
• Socioeconomic status had some impact (but it was
  minimal after the first year of college), and
  race did not have a statistically significant
  impact at all.

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One Reflection
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The 80 Solution

• Know 80 (We dont know it all)

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The 80 Solution

• Know 80 (We dont know it all)
• Teach 80 (We cant teach all we know)

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The 80 Solution

• Know 80 (We dont know it all)
• Teach 80 (We cant teach all we know)
• Learn 80 (All students dont learn all
• thats taught)

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The 80 Solution

• Know 80 (We dont know it all)
• Teach 80 (We cant teach all we know)
• Learn 80 (All students dont learn all
• thats taught)
• Retain 80 (All material isnt retained)

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The 80 Solution

• Know 80 (We dont know it all)
• Teach 80 (We cant teach all we know)
• Learn 80 (All students dont learn all
• thats taught)
• Retain 80 (All material isnt retained)
• Whats the result?

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The 80 Solution

• Know 80 (We dont know it all)
• Teach 80 (We cant teach all we know)
• Learn 80 (All students dont learn all
• thats taught)
• Retain 80 (All material isnt retained)
• 80 of 80 of 80 of 80 41

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The 80 Solution

• Know 80 (We dont know it all)
• Teach 80 (We cant teach all we know)
• Learn 80 (All students dont learn all
• thats taught)
• Retain 80 (All material isnt retained)
• The Result 80 of 80 of 80 of 80 41
• Is this a passing grade?

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The 80 Solution

• We dont teach the content

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The 80 Solution

• We dont teach the content
• We do teach students

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• Dr. Alan Zollman
• Department of Mathematical Sciences
• Northern Illinois University
• DeKalb, IL 60115-2888
• 815/753-6750
• zollman_at_math.niu.edu
• http//www.math.niu.edu/zollman