Thinking about Learning, or Learning about Thinking Dr. Alan Zollman Mathematical Sciences MATH 610...

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


• One Important Concept


• One Important Concept• Two Dumb Stunts


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


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


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

Success


• 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?”


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?






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



or How to Teach a Dog French


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?


1) Give the Father Lottery Tickets


1) Give the Father Lottery Tickets

2) Give the Parents Honorary Degrees


In applying the empirical research to the practical classroom,

there is a difference betweencorrelations


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


• Big Ideas• Jean Piaget’s Reflective Abstraction


• 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

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



• Generalization (Association)• Coordination (Assimilation)

Coordination (Assimilation)

How do we add:

2 tens + 3 ones


How do we add:

2 tens + 3 ones

2 thirds + 3 fourths


How do we add:

2 tens + 3 ones

2 thirds + 3 fourths

(2x + 4y) + (3x + y)



• 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


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


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




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





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







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




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.



• 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.


• 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.


• 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) Learn 80% (All students don’t learn all

that’s taught)

The 80% Solution



that’s taught) Retain 80% (All material isn’t retained)

The 80% Solution




What’s the result?

The 80% Solution




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


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

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