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Slide 1Thinking about Learning, or Learning about Thinking Dr. Alan Zollman Mathematical Sciences MATH 610 August 25, 2009 Slide 2 Effective Strategies Slide 3 One Important Concept Slide 4 Effective Strategies One Important Concept Two Dumb Stunts Slide 5 Effective Strategies One Important Concept Two Dumb Stunts Two Quick Actions Slide 6 Effective Strategies One Important Concept Two Dumb Stunts Two Quick Actions Three Big Ideas Slide 7 Effective Strategies One Important Concept Two Dumb Stunts Two Quick Actions Three Big Ideas Two Predictors of College Success Slide 8 Effective Strategies One Important Concept Two Dumb Stunts Two Quick Actions Three Big Ideas Two Predictors of College Success One Reflection Slide 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. Arm varrly grendy, the durf trepped. Ar hished yind merpled padis in your temp. Did yind rale your temp blem? Slide 10 Please answer the following question in complete sentences: Slide 11 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. Arm 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. 1. What did the durf accot in the maybers temp? Slide 12 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. Arm 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. 1. What did the durf accot in the maybers temp? 2. 2. What did the mayber quas the durf? Slide 13 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. Arm 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. 1. What did the durf accot in the maybers temp? 2. 2. What did the mayber quas the durf? 3. 3. Was the durf grendy? Slide 14 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. Arm 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. 1. What did the durf accot in the maybers temp? 2. 2. What did the mayber quas the durf? 3. 3. Was the durf grendy? 4. 4. Why did the mayber rale his temp? Slide 15 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. Arm 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. 1. What did the durf accot in the maybers temp? 2. 2. What did the mayber quas the durf? 3. 3. Was the durf grendy? 4. 4. Why did the mayber rale his temp? 5. 5. Is there a difference between knowing an answer and understanding a solution in mathematics? Adapted from Kenneth Goodmans The Psycholinguistic Nature of the Reading Process Slide 16 The Difference Between Teaching and Learning Slide 17 The Difference Between Teaching and Learning or How to Teach a Dog French Slide 18 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? Slide 19 Two Dumb Stunts 1) Give the Father Lottery Tickets Slide 20 Two Dumb Stunts 1) Give the Father Lottery Tickets 2) Give the Parents Honorary Degrees Slide 21 Two Dumb Stunts In applying the empirical research to the practical classroom, there is a difference between correlations Slide 22 Two Dumb Stunts In applying the empirical research to the practical classroom, there is a difference between correlations and causations. Slide 23 Two Quick Actions Slide 24 Have lecture, individual, cooperative group activities Slide 25 Two Quick Actions Have lecture, individual, cooperative group activities Have a daily reflection Slide 26 Effective Strategies Big Ideas Jean Piagets Reflective Abstraction Slide 27 Effective Strategies Big Idea # 1 Jean Piagets Reflective Abstraction Generalization (Association) Slide 28 Generalization (Association) Memorize the following 12 items in order Make sure you can read the whole screen Slide 29 SKY Slide 30 SKY RADIO Slide 31 SKY RADIO GAS STATION Slide 32 SKY RADIO GAS STATION BOX Slide 33 SKY RADIO GAS STATION BOX CUP Slide 34 SKY RADIO GAS STATION BOX CUP DOOR Slide 35 SKY RADIO GAS STATION BOX CUP DOOR KNIFE Slide 36 SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY Slide 37 SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD Slide 38 SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD SIGN Slide 39 SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD SIGN TOWEL Slide 40 SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD SIGN TOWEL RAISINS Slide 41 wait .. Slide 42 Without looking Slide 43 Without looking whats the full name of this course? Slide 44 OK, now write the 12 nouns in order. Slide 45 SKY RADIO GAS STATION BOX CUP DOOR KNIFE TOY ROAD SIGN TOWEL RAISINS Slide 46 Effective Strategies Big Idea # 2 Jean Piagets Reflective Abstraction Generalization (Association) Coordination (Assimilation) Slide 47 How do we add: 2 tens + 3 ones Slide 48 Coordination (Assimilation) How do we add: 2 tens + 3 ones 2 thirds + 3 fourths Slide 49 Coordination (Assimilation) How do we add: 2 tens + 3 ones 2 thirds + 3 fourths (2x + 4y) + (3x + y) Slide 50 Effective Strategies Big Idea # 3 Jean Piagets Reflective Abstraction Generalization (Association) Coordination (Assimilation) Encapsulation Slide 51 Encapsulation Example 4th Grade Question How many different ways can you arrange 3 objects with 2 objects, 2 at a time? Slide 52 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) Slide 53 7.8 % of high school students who take ALGEBRA I get a college degree Predictors of College Success Slide 54 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 Slide 55 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 Slide 56 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 Slide 57 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 Slide 58 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 Slide 59 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. Slide 60 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 Slide 61 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. Slide 62 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. Slide 63 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. Slide 64 One Reflection Slide 65 The 80% Solution Know 80% (We dont know it all) Slide 66 The 80% Solution Know 80% (We dont know it all) Teach 80% (We cant teach all we know) Slide 67 The 80% Solution Know 80% (We dont know it all) Teach 80% (We cant teach all we know) Learn 80% (All students dont learn all thats taught) Slide 68 The 80% Solution Know 80% (We dont know it all) Teach 80% (We cant teach all we know) Learn 80% (All students dont learn all thats taught) Retain 80% (All material isnt retained) Slide 69 The 80% Solution Know 80% (We dont know it all) Teach 80% (We cant teach all we know) Learn 80% (All students dont learn all thats taught) Retain 80% (All material isnt retained) Whats the result? Slide 70 The 80% Solution Know 80% (We dont know it all) Teach 80% (We cant teach all we know) Learn 80% (All students dont learn all thats taught) Retain 80% (All material isnt retained) 80% of 80% of 80% of 80% 41% Slide 71 The 80% Solution Know 80% (We dont know it all) Teach 80% (We cant teach all we know) Learn 80% (All students dont learn all thats taught) Retain 80% (All material isnt retained) The Result: 80% of 80% of 80% of 80% 41% Is this a passing grade? Slide 72 The 80% Solution We dont teach the content Slide 73 The 80% Solution We dont teach the content We do teach students Slide 74 Dr. Alan Zollman Department of Mathematical Sciences Northern Illinois University DeKalb, IL 60115-2888 815/753-6750 zollman@math.niu.edu http://www.math.niu.edu/ ~ zollman