Thinking about Learning,Thinking about Learning,oror
Learning about Learning about ThinkingThinking
Dr. Alan ZollmanDr. Alan Zollman
Mathematical SciencesMathematical Sciences
MATH 610MATH 610
August 25, 2009August 25, 2009
Effective Strategies
Effective Strategies
• One Important Concept
Effective Strategies
• One Important Concept• Two Dumb Stunts
Effective Strategies
• One Important Concept• Two Dumb Stunts• Two Quick Actions
Effective Strategies
• One Important Concept• Two Dumb Stunts• Two Quick Actions• Three Big Ideas
Effective Strategies
• One Important Concept• Two Dumb Stunts• Two Quick Actions• Three Big Ideas• Two Predictors of College
Success
Effective Strategies
• One Important Concept• Two Dumb Stunts• Two Quick Actions• Three Big Ideas• Two Predictors of College
Success• One Reflection
A mayber was raling his temp. Saintly a durf accotted A mayber was raling his temp. Saintly a durf accotted some padis in his temp. “Why did yind accot padis in my some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m varrly blem temp?” the mayber quassed the durf. “Ar’m varrly grendy,” the durf trepped. “Ar hished yind merpled padis grendy,” the durf trepped. “Ar hished yind merpled padis in your temp. Did yind rale your temp blem?”in your temp. Did yind rale your temp blem?”
A mayber was raling his temp. Saintly a durf accotted A mayber was raling his temp. Saintly a durf accotted some padis in his temp. “Why did yind accot padis in my some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m varrly blem temp?” the mayber quassed the durf. “Ar’m varrly grendy,” the durf trepped. “Ar hished yind merpled padis grendy,” the durf trepped. “Ar hished yind merpled padis in your temp. Did yind rale your temp blem?”in your temp. Did yind rale your temp blem?”
Please answer the following question in complete sentences:
A mayber was raling his temp. Saintly a durf accotted A mayber was raling his temp. Saintly a durf accotted some padis in his temp. “Why did yind accot padis in my some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m varrly blem temp?” the mayber quassed the durf. “Ar’m varrly grendy,” the durf trepped. “Ar hished yind merpled padis grendy,” the durf trepped. “Ar hished yind merpled padis in your temp. Did yind rale your temp blem?”in your temp. Did yind rale your temp blem?”
Please answer the following question in complete sentences:
1. What did the durf accot in the mayber’s temp?
A mayber was raling his temp. Saintly a durf accotted A mayber was raling his temp. Saintly a durf accotted some padis in his temp. “Why did yind accot padis in my some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m varrly blem temp?” the mayber quassed the durf. “Ar’m varrly grendy,” the durf trepped. “Ar hished yind merpled padis grendy,” the durf trepped. “Ar hished yind merpled padis in your temp. Did yind rale your temp blem?”in your temp. Did yind rale your temp blem?”
Please answer the following question in complete sentences:
1. What did the durf accot in the mayber’s temp?
2. What did the mayber quas the durf?
A mayber was raling his temp. Saintly a durf accotted A mayber was raling his temp. Saintly a durf accotted some padis in his temp. “Why did yind accot padis in my some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m varrly blem temp?” the mayber quassed the durf. “Ar’m varrly grendy,” the durf trepped. “Ar hished yind merpled padis grendy,” the durf trepped. “Ar hished yind merpled padis in your temp. Did yind rale your temp blem?”in your temp. Did yind rale your temp blem?”
Please answer the following question in complete sentences:
1. What did the durf accot in the mayber’s temp?
2. What did the mayber quas the durf?
3. Was the durf grendy?
A mayber was raling his temp. Saintly a durf accotted A mayber was raling his temp. Saintly a durf accotted some padis in his temp. “Why did yind accot padis in my some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m varrly blem temp?” the mayber quassed the durf. “Ar’m varrly grendy,” the durf trepped. “Ar hished yind merpled padis grendy,” the durf trepped. “Ar hished yind merpled padis in your temp. Did yind rale your temp blem?”in your temp. Did yind rale your temp blem?”
Please answer the following question in complete sentences:
1. What did the durf accot in the mayber’s temp?
2. What did the mayber quas the durf?
3. Was the durf grendy?
4. Why did the mayber rale his temp?
A mayber was raling his temp. Saintly a durf accotted A mayber was raling his temp. Saintly a durf accotted some padis in his temp. “Why did yind accot padis in my some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m varrly blem temp?” the mayber quassed the durf. “Ar’m varrly grendy,” the durf trepped. “Ar hished yind merpled padis grendy,” the durf trepped. “Ar hished yind merpled padis in your temp. Did yind rale your temp blem?”in your temp. Did yind rale your temp blem?”
Please answer the following question in complete sentences:
1. What did the durf accot in the mayber’s temp?
2. What did the mayber quas the durf?
3. Was the durf grendy?
4. Why did the mayber rale his temp?5. Is there a difference between knowing an answer
and understanding a solution in mathematics?Adapted from Kenneth Goodman’s
The Psycholinguistic Nature of the Reading Process
The Difference Between Teaching and Learning
The Difference Between Teaching and Learning
The Difference Between Teaching and Learning
or How to Teach a Dog French
The Difference Between Teaching and Learning
or How to Teach a Dog French
Two Dumb StuntsTwo 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?
Two Dumb StuntsTwo Dumb Stunts
1) Give the Father Lottery Tickets
Two Dumb StuntsTwo Dumb Stunts
1) Give the Father Lottery Tickets
2) Give the Parents Honorary Degrees
Two Dumb StuntsTwo Dumb Stunts
In applying the empirical research to the practical classroom,
there is a difference betweencorrelations
Two Dumb StuntsTwo Dumb Stunts
In applying the empirical research to the practical classroom,
there is a difference betweencorrelations
andcausations.
Two Quick Actions
Two Quick Actions• Have lecture, individual, cooperative
group activities
Two Quick Actions• Have lecture, individual, cooperative
group activities
• Have a daily reflection
Effective Strategies
• Big Ideas• Jean Piaget’s Reflective Abstraction
Effective Strategies
• Big Idea # 1• Jean Piaget’s Reflective Abstraction
• Generalization (Association)
Generalization (Association)
Memorize the following 12 items in order
Make sure you can read the whole screen
SKY
SKYRADIO
SKYRADIO
GAS STATION
SKYRADIO
GAS STATIONBOX
SKYRADIO
GAS STATIONBOXCUP
SKYRADIO
GAS STATIONBOXCUP
DOOR
SKYRADIO
GAS STATIONBOXCUP
DOORKNIFE
SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROAD
SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROADSIGN
SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROADSIGN
TOWEL
SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROADSIGN
TOWELRAISINS
wait …..
Without looking …
Without looking …what’s the full name of this course?
OK, nowwrite the 12 nouns in order.
SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROADSIGN
TOWELRAISINS
Effective Strategies
• Big Idea # 2• Jean Piaget’s Reflective Abstraction
• Generalization (Association)• Coordination (Assimilation)
Coordination (Assimilation)
How do we add:
2 tens + 3 ones
Coordination (Assimilation)
How do we add:
2 tens + 3 ones
2 thirds + 3 fourths
Coordination (Assimilation)
How do we add:
2 tens + 3 ones
2 thirds + 3 fourths
(2x + 4y) + (3x + y)
Effective Strategies
• Big Idea # 3• Jean Piaget’s Reflective Abstraction
• Generalization (Association)• Coordination (Assimilation)• Encapsulation
Encapsulation ExampleEncapsulation Example
4th Grade Question4th Grade Question
How many different ways can you How many different ways can you arrange 3 objects with 2 objects, 2 at arrange 3 objects with 2 objects, 2 at
a time?a time?
Encapsulation ExampleEncapsulation Example
4th Grade Question4th Grade Question
A. How many different ways can you A. How many different ways can you arrange 3 objects with 2 objects, 2 arrange 3 objects with 2 objects, 2 at a time? at a time? oror
B. How many ways can you make a B. How many ways can you make a gym outfit if you have red, blue, or gym outfit if you have red, blue, or white tee shirts and red or white white tee shirts and red or white shorts?shorts?
(remember the movie (remember the movie CluelessClueless?)?)(question from Dr. John Sleisky, “Authenticity and Test Items In Large Scale Assessment” SSMA Centennial Conference, Downers Grove, IL, Nov. 1, 2001)
7.8 %7.8 % of high school students who take of high school students who take ALGEBRA I ALGEBRA I get a college degreeget a college degree
Predictors of College SuccessPredictors of College Success
Predictors of College SuccessPredictors of College Success
23.1%23.1% of high school students who take of high school students who take GEOMETRY GEOMETRY get a college degreeget a college degree
7.8 %7.8 % of high school students who take of high school students who take ALGEBRA I ALGEBRA I get a college degreeget a college degree
39.5%39.5% of high school students who take of high school students who take ALGEBRA II ALGEBRA II get a college degreeget a college degree
23.1%23.1% of high school students who take of high school students who take GEOMETRY GEOMETRY get a college degreeget a college degree
7.8 %7.8 % of high school students who take of high school students who take ALGEBRA I ALGEBRA I get a college degreeget a college degree
Predictors of College SuccessPredictors of College Success
62.2%62.2% of high school students who take of high school students who take TRIGONOMETRY TRIGONOMETRY get a college degreeget a college degree
39.5%39.5% of high school students who take of high school students who take ALGEBRA II ALGEBRA II get a college degreeget a college degree
23.1%23.1% of high school students who take of high school students who take GEOMETRY GEOMETRY get a college degreeget a college degree
7.8 %7.8 % of high school students who take of high school students who take ALGEBRA I ALGEBRA I get a college degreeget a college degree
Predictors of College SuccessPredictors of College Success
74.3%74.3% of high school students who take of high school students who take PRE CALCULUS PRE CALCULUS get a college degreeget a college degree
62.2%62.2% of high school students who take of high school students who take TRIGONOMETRY TRIGONOMETRY get a college degreeget a college degree
39.5%39.5% of high school students who take of high school students who take ALGEBRA II ALGEBRA II get a college degreeget a college degree
23.1%23.1% of high school students who take of high school students who take GEOMETRY GEOMETRY get a college degreeget a college degree
7.8 %7.8 % of high school students who take of high school students who take ALGEBRA I ALGEBRA I get a college degreeget a college degree
Predictors of College SuccessPredictors of College Success
Predictors of College SuccessPredictors of College Success
Answers in the Tool BoxAnswers in the Tool Box, U.S. Department of Education by Clifford Adelman, U.S. Department of Education by Clifford Adelman
79.8%79.8% of high school students who take of high school students who take CALCULUSCALCULUS get a college degreeget a college degree
74.3%74.3% of high school students who take of high school students who take PRE CALCULUS PRE CALCULUS get a college degreeget a college degree
62.2%62.2% of high school students who take of high school students who take TRIGONOMETRY TRIGONOMETRY get a college degreeget a college degree
39.5%39.5% of high school students who take of high school students who take ALGEBRA II ALGEBRA II get a college degreeget a college degree
23.1%23.1% of high school students who take of high school students who take GEOMETRY GEOMETRY get a college degreeget a college degree
7.8 %7.8 % of high school students who take of high school students who take ALGEBRA I ALGEBRA I get a college degree get a college degree
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--including 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.
• Of all the high school indicators of academic preparation, the one that is the strongest is taking rigorous and intense courses in high school.
Predictors of College Success
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.
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.
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.
One ReflectionOne Reflection
The 80% Solution
Know 80% (We don’t know it all)
The 80% Solution
Know 80% (We don’t know it all) Teach 80% (We can’t teach all we
know)
The 80% Solution
Know 80% (We don’t know it all) Teach 80% (We can’t teach all we
know) Learn 80% (All students don’t learn all
that’s taught)
The 80% Solution
Know 80% (We don’t know it all) Teach 80% (We can’t teach all we
know) Learn 80% (All students don’t learn all
that’s taught) Retain 80% (All material isn’t retained)
The 80% Solution
Know 80% (We don’t know it all) Teach 80% (We can’t teach all we
know) Learn 80% (All students don’t learn all
that’s taught) Retain 80% (All material isn’t retained)
What’s the result?
The 80% Solution
Know 80% (We don’t know it all) Teach 80% (We can’t teach all we
know) Learn 80% (All students don’t learn all
that’s taught) Retain 80% (All material isn’t retained)
80% of 80% of 80% of 80% ≈ 41%
The 80% Solution
Know 80% (We don’t know it all) Teach 80% (We can’t teach all we know) Learn 80% (All students don’t learn all
that’s taught) Retain 80% (All material isn’t retained)
The Result: 80% of 80% of 80% of 80% ≈ 41%
Is this a passing grade?
The 80% Solution
• We don’t teach the content
The 80% Solution
• We don’t teach the content
• We do teach students
Dr. Alan ZollmanDepartment of Mathematical SciencesNorthern Illinois UniversityDeKalb, IL 60115-2888815/[email protected]://www.math.niu.edu/~zollman