math 402 methods of instruction in the mathematics curriculum for the elementary school (k–6)
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MATH 402 Methods of Instruction in the Mathematics Curriculum for the Elementary School (K–6). Dr. Alan Zollman Mathematical Sciences NIU Teaching Effectiveness Institute January 24, 2013. Effective Strategies. Two Important Concepts. - PowerPoint PPT PresentationTRANSCRIPT
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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
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Effective Strategies
Two Important Concepts
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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. “Ar’m 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. “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:
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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. “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?
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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. “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?
![Page 7: MATH 402 Methods of Instruction in the Mathematics Curriculum for the Elementary School (K–6)](https://reader037.vdocuments.site/reader037/viewer/2022103101/56814356550346895dafd393/html5/thumbnails/7.jpg)
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?
![Page 8: MATH 402 Methods of Instruction in the Mathematics Curriculum for the Elementary School (K–6)](https://reader037.vdocuments.site/reader037/viewer/2022103101/56814356550346895dafd393/html5/thumbnails/8.jpg)
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?
![Page 9: MATH 402 Methods of Instruction in the Mathematics Curriculum for the Elementary School (K–6)](https://reader037.vdocuments.site/reader037/viewer/2022103101/56814356550346895dafd393/html5/thumbnails/9.jpg)
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
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The Difference Between Teaching and Learning
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The Difference Between Teaching and Learning
or How to Teach a Dog French
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Effective Strategies
• Big Ideas• Jean Piaget’s Reflective Abstraction
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Effective Strategies
• Big Idea # 1• Jean Piaget’s Reflective Abstraction
• Generalization (Association)
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Generalization (Association)
Memorize the following 12 items in order
Make sure you can read the whole screen
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SKY
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SKYRADIO
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SKYRADIO
GAS STATION
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SKYRADIO
GAS STATIONBOX
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SKYRADIO
GAS STATIONBOXCUP
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SKYRADIO
GAS STATIONBOXCUP
DOOR
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SKYRADIO
GAS STATIONBOXCUP
DOORKNIFE
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SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
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SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROAD
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SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROADSIGN
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SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROADSIGN
TOWEL
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SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROADSIGN
TOWELRAISINS
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wait …..
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Without looking …
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Without looking …what’s my name?
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OK, nowwrite the 12 nouns in order.
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SKYRADIO
GAS STATIONBOXCUP
DOORKNIFETOY
ROADSIGN
TOWELRAISINS
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Effective Strategies
• Big Idea # 2• Jean Piaget’s 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 Piaget’s Reflective Abstraction
• Generalization (Association)• Coordination (Assimilation)• Encapsulation
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Encapsulation Example
4th 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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7.8 % of high school students who take ALGEBRA I get a college degree
Predictors of College Success
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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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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
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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
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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
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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
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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--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.
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• 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
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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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Closure
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The 80% Solution
Know 80% (We don’t know it all)
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The 80% Solution
Know 80% (We don’t know it all) Teach 80% (We can’t teach all we
know)
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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)
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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)
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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?
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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%
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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?
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The 80% Solution
• We don’t teach the content
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The 80% Solution
• We don’t teach the content
• We do teach students
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Thank you!
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Dr. Alan ZollmanDepartment of Mathematical SciencesNorthern Illinois UniversityDeKalb, IL 60115-2888815/[email protected]://www.math.niu.edu/~zollman