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MATH 402 Methods of Instruction in the Mathematics Curriculum for the Elementary School (K–6)

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.

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MATH 402 Methods of Instruction in the Mathematics Curriculum for the Elementary School (K–6)

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  1. 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

  2. Effective Strategies Two Important Concepts

  3. 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?”

  4. 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:

  5. 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?

  6. 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?

  7. 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?

  8. 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?

  9. 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

  10. The Difference Between Teaching and Learning

  11. The Difference Between Teaching and Learningor How to Teach a Dog French

  12. Effective Strategies • Big Ideas • Jean Piaget’s Reflective Abstraction

  13. Effective Strategies • Big Idea # 1 • Jean Piaget’s Reflective Abstraction • Generalization (Association)

  14. Generalization (Association)Memorize the following 12 items in orderMake sure you can read the whole screen

  15. SKY

  16. SKYRADIO

  17. SKYRADIOGAS STATION

  18. SKYRADIOGAS STATIONBOX

  19. SKYRADIOGAS STATIONBOXCUP

  20. SKYRADIOGAS STATIONBOXCUPDOOR

  21. SKYRADIOGAS STATIONBOXCUPDOORKNIFE

  22. SKYRADIOGAS STATIONBOXCUPDOORKNIFETOY

  23. SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROAD

  24. SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROADSIGN

  25. SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROADSIGNTOWEL

  26. SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROADSIGNTOWELRAISINS

  27. wait …..

  28. Without looking …

  29. Without looking …what’s my name?

  30. OK, nowwrite the 12 nouns in order.

  31. SKYRADIOGAS STATIONBOXCUPDOORKNIFETOYROADSIGNTOWELRAISINS

  32. Effective Strategies • Big Idea # 2 • Jean Piaget’s Reflective Abstraction • Generalization (Association) • Coordination (Assimilation)

  33. Coordination (Assimilation) How do we add: 2 tens + 3 ones

  34. Coordination (Assimilation) How do we add: 2 tens + 3 ones 2 thirds + 3 fourths

  35. Coordination (Assimilation) How do we add: 2 tens + 3 ones 2 thirds + 3 fourths (2x + 4y) + (3x + y)

  36. Effective Strategies • Big Idea # 3 • Jean Piaget’s Reflective Abstraction • Generalization (Association) • Coordination (Assimilation) • Encapsulation

  37. Encapsulation Example4th Grade QuestionHow many different ways can you arrange 3 objects with 2 objects, 2 at a time?

  38. 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)

  39. Predictors of College Success 7.8 % of high school students who take ALGEBRA I get a college degree

  40. 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

  41. Predictors of College Success 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

  42. 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

  43. 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

  44. Predictors of College Success 79.8% of high school students who take CALCULUSget 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 Answers in the Tool Box, U.S. Department of Education by Clifford Adelman

  45. 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.

  46. 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.

  47. 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. 

  48. 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. 

  49. 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.

  50. Closure

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