MATH 402 Methods of Instruction in the Mathematics Curriculum for the Elementary School (K–6) Dr. Alan Zollman Mathematical Sciences NIU Teaching Effectiveness Institute August 24, 2009

Effective Strategies

One Important Concept

Effective Strategies One Important Concept Two Dumb Stunts

Effective Strategies One Important Concept Two Dumb Stunts Four Quick Actions

Effective Strategies One Important Concept Two Dumb Stunts Four Quick Actions Three Big Ideas

Effective Strategies One Important Concept Two Dumb Stunts Four Quick Actions Three Big Ideas Two Predictors of College Success

Effective Strategies One Important Concept Two Dumb Stunts Four Quick Actions Three Big Ideas Two Predictors of College Success Closure

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: 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: What did the durf accot in the mayber’s temp? 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: What did the durf accot in the mayber’s temp? What did the mayber quas the durf? 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: What did the durf accot in the mayber’s temp? What did the mayber quas the durf? Was the durf grendy? 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: What did the durf accot in the mayber’s 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 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

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?

Two Dumb Stunts 1) Give the Father Lottery Tickets

Two Dumb Stunts 1) Give the Father Lottery Tickets 2) Give the Parents Honorary Degrees

Two Dumb Stunts In applying the empirical research to the practical classroom, there is a difference between correlations

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

Four Quick Actions

Take daily attendance

Four Quick Actions Take daily attendance Have lecture, individual, cooperative group activities

Four Quick Actions Take daily attendance Have lecture, individual, cooperative group activities T, M, E, A duties

Four Quick Actions Take daily attendance Have lecture, individual, cooperative group activities T, M, E, A duties 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

SKY RADIO

SKY RADIO GAS STATION

SKY RADIO GAS STATION BOX

SKY RADIO GAS STATION BOX CUP

SKY RADIO GAS STATION BOX CUP DOOR

SKY RADIO GAS STATION BOX CUP DOOR KNIFE

SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY

SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD

SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD SIGN

SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD SIGN TOWEL

SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD SIGN TOWEL RAISINS

wait …..

Without looking …

Without looking … what’s my name?

OK, now write the 12 nouns in order.

SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD SIGN TOWEL RAISINS

Effective Strategies Big Idea # 2 Jean Piaget’s Reflective Abstraction Generalization (Association) 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

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 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

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

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 Zollman Department of Mathematical Sciences Northern Illinois University DeKalb, IL / ~ zollman