MATH 402 Methods of Instruction in

the Mathematics Curriculum for the

Elementary School (K–6)Dr. Alan Zollman

Mathematical SciencesNIU Teaching Effectiveness Institute

January 24, 2013

Effective Strategies

Two Important Concepts

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. “Ar’m varrly grendy,” the durf trepped. “Ar hished yind merpled padis in your temp. Did yind rale your temp blem?”

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. “Ar’m 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:

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. “Ar’m 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:1. What did the durf accot in the mayber’s temp?

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. “Ar’m 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: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 some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m 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: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 some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m 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: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 some padis in his temp. “Why did yind accot padis in my blem temp?” the mayber quassed the durf. “Ar’m 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: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

or How to Teach a Dog French

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 my name?

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 Example

4th Grade Question

How many different ways can you arrange 3 objects with 2 objects, 2 at

a time?

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)

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

Predictors of College Success

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

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

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

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

Predictors of College Success

Predictors of College Success

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

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

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.

Closure

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

Thank you!

Dr. Alan ZollmanDepartment of Mathematical SciencesNorthern Illinois UniversityDeKalb, IL 60115-2888815/753-6750zollman@math.niu.eduhttp://www.math.niu.edu/~zollman