Two non-traditional content courses for in-service high school teachers at the Harvard Extension School
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We describe the Harvard Extension School's ALM in Mathematics for Teaching program and in detail two courses taught in an inquiry-based learning (IBL) style
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Two non-traditional content courses for in-service high school teachers at the Harvard Extension School
- 1. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Two non-traditional content courses for in-service high school teachers at the Harvard Extension School Bret Benesh Thomas Judson Matthew Leingang Harvard University Department of Mathematics Critical Issues in Education: Teaching Teachers Mathematics Mathematical Sciences Research Institute Berkeley, California May 31, 2007 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 2. The ALM Program Rationale for the courses Implementation Evaluation Conclusions On Deck Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 3. The ALM Program Rationale for the courses Implementation Evaluation Conclusions On Deck The Harvard Extension School’s Master of Liberal Arts (ALM) in Mathematics for Teaching Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 4. The ALM Program Rationale for the courses Implementation Evaluation Conclusions On Deck The Harvard Extension School’s Master of Liberal Arts (ALM) in Mathematics for Teaching Geometry and Probability courses taught this year Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 5. The ALM Program Rationale for the courses Implementation Evaluation Conclusions On Deck The Harvard Extension School’s Master of Liberal Arts (ALM) in Mathematics for Teaching Geometry and Probability courses taught this year Evaluations and Reflections Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 6. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Outline Theme The ALM Program 1 Class Details Rationale for the courses 2 Probability Instructors’ background Evaluation 4 Goals Questions Results Implementation 3 Geometry Conclusions 5 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 7. The ALM Program Rationale for the courses Implementation Evaluation Conclusions History and Purpose of ALM Program Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 8. The ALM Program Rationale for the courses Implementation Evaluation Conclusions History and Purpose of ALM Program Paul Sally’s Seminars for Elementary Specialists and Mathematics Educators (SESAME) Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 9. The ALM Program Rationale for the courses Implementation Evaluation Conclusions History and Purpose of ALM Program Paul Sally’s Seminars for Elementary Specialists and Mathematics Educators (SESAME) Meet state standards for mathematics content Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 10. The ALM Program Rationale for the courses Implementation Evaluation Conclusions History and Purpose of ALM Program Paul Sally’s Seminars for Elementary Specialists and Mathematics Educators (SESAME) Meet state standards for mathematics content In-service secondary school teachers and people considering career change Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 11. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Whom are we teaching? In-service teachers come from all kinds of Boston area schools: Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 12. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Whom are we teaching? In-service teachers come from all kinds of Boston area schools: from Boston Latin Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 13. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Whom are we teaching? In-service teachers come from all kinds of Boston area schools: from Boston Latin to Boston Public Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 14. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Description of ALM Program Requirements Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 15. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Description of ALM Program Requirements Students must take 10 courses, up through one year of calculus Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 16. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Description of ALM Program Requirements Students must take 10 courses, up through one year of calculus One of the courses must be on pedagogy Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 17. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Description of ALM Program Requirements Students must take 10 courses, up through one year of calculus One of the courses must be on pedagogy Students must complete a master’s thesis Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 18. The ALM Program Rationale for the courses Implementation Evaluation Conclusions ALM Courses “Standardquot; math courses (calculus, discrete math, etc.) Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 19. The ALM Program Rationale for the courses Implementation Evaluation Conclusions ALM Courses “Standardquot; math courses (calculus, discrete math, etc.) Courses designed for the secondary school teacher Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 20. The ALM Program Rationale for the courses Implementation Evaluation Conclusions ALM Courses “Standardquot; math courses (calculus, discrete math, etc.) Courses designed for the secondary school teacher Math E-300 Math for Teaching Arithmetic Math E-301 Math for Teaching Number Theory Math E-302 Math for Teaching Geometry Math E-303 Math for Teaching Algebra Math E-304 Inquiries into Probability and Combinatorics Math E-306 Theory and Practice of Teaching Statistics Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 21. The ALM Program Rationale for the courses Instructors’ background Implementation Goals Evaluation Conclusions Outline Theme The ALM Program 1 Class Details Rationale for the courses 2 Probability Instructors’ background Evaluation 4 Goals Questions Results Implementation 3 Geometry Conclusions 5 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 22. The ALM Program Rationale for the courses Instructors’ background Implementation Goals Evaluation Conclusions Bret’s background What living in Madison can do to you Graduate work was in finite group theory Minored in math education KTI Program Core Plus and Connected Mathematics Project (CMP) Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 23. The ALM Program Rationale for the courses Instructors’ background Implementation Goals Evaluation Conclusions Matt’s background How on Earth did I get so jaded? Geometer by training, teacher by trade Third time through a probability course for teachers First time: team taught, disconnected Second time: interesting for me, over their head Third time: ??? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 24. The ALM Program Rationale for the courses Instructors’ background Implementation Goals Evaluation Conclusions Goals for Math E-302 “Math for Teaching Geometry” Maximize student learning Improve communication skills Motivate students Provide a classroom model Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 25. The ALM Program Rationale for the courses Instructors’ background Implementation Goals Evaluation Conclusions Goals for Math E-304 “Inquiries into Probability and Combinatorics” Build a discipline from the ground up Teach students what they’re ready to learn Develop ability to read, write, and criticize mathematical arguments Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 26. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Outline Theme The ALM Program 1 Class Details Rationale for the courses 2 Probability Instructors’ background Evaluation 4 Goals Questions Results Implementation 3 Geometry Conclusions 5 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 27. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Platform for inquiry Taxicab geometry Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 28. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Platform for inquiry Taxicab geometry Compare and contrast with Euclidean Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 29. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Class Format Meet once per week Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 30. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Class Format Meet once per week Class length is two hours Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 31. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Class Format Meet once per week Class length is two hours Mostly in-service high school teachers Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 32. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Role of Instructor Moderate discussion Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 33. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Role of Instructor Moderate discussion Referee Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 34. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Role of Instructor Moderate discussion Referee Ask questions Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 35. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Role of Instructor Moderate discussion Referee Ask questions Not an authority Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 36. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical day Review Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 37. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical day Review Work on one problem Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 38. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical day Review Work on one problem 10% lecture Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 39. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical day Review Work on one problem 10% lecture 45% small group work Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 40. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical day Review Work on one problem 10% lecture 45% small group work 45% large group discussion Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 41. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical problem Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 42. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical problem What is the definition of a circle in Euclidean geometry? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 43. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical problem What is the definition of a circle in Euclidean geometry? What does a circle look like in taxicab geometry? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 44. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical problem What is the definition of a circle in Euclidean geometry? What does a circle look like in taxicab geometry? What is the diameter of a circle in taxicab geometry? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 45. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical problem What is the definition of a circle in Euclidean geometry? What does a circle look like in taxicab geometry? What is the diameter of a circle in taxicab geometry? What is the circumference in taxicab geometry? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 46. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical problem What is the definition of a circle in Euclidean geometry? What does a circle look like in taxicab geometry? What is the diameter of a circle in taxicab geometry? What is the circumference in taxicab geometry? What is π in taxicab geometry? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 47. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Another example A New Altitude A = 1 (2.3)(8.5) = 9.775 2 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 48. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Grading Mostly papers Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 49. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Grading Mostly papers Two exams Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 50. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Grading Mostly papers Two exams Class participation Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 51. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Probability course by the Moore Method Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 52. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Probability course by the Moore Method No textbooks at all; I write problems directed towards the course objectives Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 53. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Probability course by the Moore Method No textbooks at all; I write problems directed towards the course objectives Students submit written up problems Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 54. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Probability course by the Moore Method No textbooks at all; I write problems directed towards the course objectives Students submit written up problems Students present solutions Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 55. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Probability course by the Moore Method No textbooks at all; I write problems directed towards the course objectives Students submit written up problems Students present solutions I update notes with solutions Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 56. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 57. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents The Fundamental Counting Principle with without er ne Pr W n ov hiz er ne Wn z hi a a Am olo ic Am olo ic ov Pr Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 58. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents The Fundamental Counting Principle A A D B B D Permutations C C A A B B C C D D A A D D C C B B Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 59. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents The Fundamental Counting Principle 1 Permutations 1 1 Combinations 1 2 1 3 3 1 1 6 1 4 4 1 5 10 10 5 1 1 6 15 20 15 6 1 1 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 60. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents The Fundamental Counting Principle Permutations B Combinations Set theory A C A ∪ (B ∩ C) = (A ∪ B)∩(A ∪ C) Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 61. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents The Fundamental Counting Principle Permutations B Combinations Set theory A C Axioms of probability A ∪ (B ∩ C) = (A ∪ B)∩(A ∪ C) Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 62. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents The Fundamental Counting Principle Permutations B Combinations Set theory A C Axioms of probability Expected value A ∪ (B ∩ C) = (A ∪ B)∩(A ∪ C) Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 63. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents The Fundamental Counting Principle Permutations Combinations Set theory Axioms of probability Expected value Conditional probability Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 64. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Notes Table of Contents The Fundamental Counting Principle Permutations Combinations Set theory Axioms of probability Expected value Conditional probability Famous probability distributions Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 65. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Fun problems Give them a menu; ask how many combination plates can be ordered Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 66. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Fun problems Give them a menu; ask how many combination plates can be ordered Verify the published probabilities for winning various lottery games Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 67. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Fun problems Give them a menu; ask how many combination plates can be ordered Verify the published probabilities for winning various lottery games Why can we multiply probabilities of “consecutive” events? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 68. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions A typical day I will have assigned a chapter’s worth of problems I solicit volunteers to present We watch and question the presenters I stay seated (referee) Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 69. The ALM Program Rationale for the courses Geometry Implementation Probability Evaluation Conclusions Grading ≥ 1 problem written per week, 0-4 scale ≥ 1 problem presented per week, 0-4 scale Take-home final Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 70. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Outline Theme The ALM Program 1 Class Details Rationale for the courses 2 Probability Instructors’ background Evaluation 4 Goals Questions Results Implementation 3 Geometry Conclusions 5 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 71. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Questions We surveyed the E-302 and E-304 students. Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 72. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Questions We surveyed the E-302 and E-304 students. Influence thinking, teaching, or communicating? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 73. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Questions We surveyed the E-302 and E-304 students. Influence thinking, teaching, or communicating? Learn more than traditional format? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 74. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Questions We surveyed the E-302 and E-304 students. Influence thinking, teaching, or communicating? Learn more than traditional format? Challenging? Rewarding? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 75. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Questions We surveyed the E-302 and E-304 students. Influence thinking, teaching, or communicating? Learn more than traditional format? Challenging? Rewarding? Take another class? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 76. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Questions We surveyed the E-302 and E-304 students. Influence thinking, teaching, or communicating? Learn more than traditional format? Challenging? Rewarding? Take another class? Recommend class format? Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 77. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions The results: Question 1 How has this course affected the way you think about mathematics? 5=Very positively 4=Somewhat positively 3=No change 2=Somewhat negatively 1=Very negatively µ = 4.21 prob geom µ = 4.3 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 78. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions The results: Question 1 How has this course affected the way you think about mathematics? 5=Very positively 4=Somewhat positively 3=No change 2=Somewhat negatively 1=Very negatively µ = 4.21 prob geom µ = 4.3 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 79. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Question 2 How has this course affected the way you think about teaching mathematics? 5=Very positively 4=Somewhat positively 3=No change 2=Somewhat negatively 1=Very negatively µ = 4.12 prob geom µ = 3.9 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 80. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Question 3 How has this course affected the way you think about communicating in mathematics? 5=Very positively 4=Somewhat positively 3=No change 2=Somewhat negatively 1=Very negatively µ = 4.07 prob geom µ = 4.15 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 81. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Question 4 Do you think that you learned more, less, or as much as you would have in a more traditionally taught course? 5=Much, much more 4=A little more than usual 3=No change in learning 2=A little less than usual 1=A lot less than usual µ = 3.78 prob geom µ = 3.38 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 82. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Question 5 How challenging is this course? 3=Very challenging. I had to think much harder than I normally do. 2=Sort of challenging. 1=Not challenging at all. I could do this in my sleep. µ = 2.21 prob geom µ = 2.3 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 83. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Question 6 How rewarding is this course? 4=Ridiculously rewarding. Math is more fun than watching Dancing with the Stars! 3=Sort of rewarding 2=I don’t get anything out of it 1=I feel like this class saps my will to live. µ = 3.14 prob geom µ = 3.28 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 84. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Question 7 Would you like to take another course taught in this format? 5=Yes! Where do I sign up?!? 4=Yes, with some reservation 3=Undecided 2=No 1=Hell no µ = 3.85 prob geom µ = 4.17 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 85. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Question 8 Would you recommend a course taught in this format? 5=Yes! I want to share the love! 4=Sure, it was pretty good. 3=Undecided 2=No. 1=Yes, but only to my worst enemy. µ =4 prob geom µ = 4.15 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 86. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Some quotes from the probability class “I have always found proofs difficult and intimidating. Now I feel more comfortable with them.” “Either a problem is challenging/hard, or it is easy and the challenge is explaining it well. Either way, it is challenging.” “...it’s really the best way to learn math.” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 87. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions More quotes from the probability class “I think a little more teacher-based instruction would allow for a more rigorous pace, which pushes students and can lead to more of a need for interaction and discussion by necessity.” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 88. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions More quotes from the probability class “I think a little more teacher-based instruction would allow for a more rigorous pace, which pushes students and can lead to more of a need for interaction and discussion by necessity.” “Waiting for the other students to finish is a bit of a waste of time.” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 89. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions More quotes from the probability class “I think a little more teacher-based instruction would allow for a more rigorous pace, which pushes students and can lead to more of a need for interaction and discussion by necessity.” “Waiting for the other students to finish is a bit of a waste of time.” “I don’t necessarily like the experience, but at least it was pedagogically interesting.” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 90. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Some quotes from the geometry class “I see more value in working in groups as an ongoing strategy [for teaching]. It takes a while to build trust, but once its established the outcome in class thinking is fantastic!” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 91. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Some quotes from the geometry class “I see more value in working in groups as an ongoing strategy [for teaching]. It takes a while to build trust, but once its established the outcome in class thinking is fantastic!” “I have thought more about this ‘stuff’ than I have thought on other courses.” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 92. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Some quotes from the geometry class “I see more value in working in groups as an ongoing strategy [for teaching]. It takes a while to build trust, but once its established the outcome in class thinking is fantastic!” “I have thought more about this ‘stuff’ than I have thought on other courses.” “It is tiring to think this hard consistently, but good still.” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 93. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Some quotes from the geometry class “I see more value in working in groups as an ongoing strategy [for teaching]. It takes a while to build trust, but once its established the outcome in class thinking is fantastic!” “I have thought more about this ‘stuff’ than I have thought on other courses.” “It is tiring to think this hard consistently, but good still.” “I wish there was more concrete learning.” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 94. The ALM Program Rationale for the courses Questions Implementation Results Evaluation Conclusions Some quotes from the geometry class “I see more value in working in groups as an ongoing strategy [for teaching]. It takes a while to build trust, but once its established the outcome in class thinking is fantastic!” “I have thought more about this ‘stuff’ than I have thought on other courses.” “It is tiring to think this hard consistently, but good still.” “I wish there was more concrete learning.” “I leave excited and bewildered.” Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 95. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Outline Theme The ALM Program 1 Class Details Rationale for the courses 2 Probability Instructors’ background Evaluation 4 Goals Questions Results Implementation 3 Geometry Conclusions 5 Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 96. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Reflections Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 97. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Reflections Costs/benefits of IBL methods vs. lecturing Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 98. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Reflections Costs/benefits of IBL methods vs. lecturing Different kind of drama with a TMM course Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 99. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Reflections Costs/benefits of IBL methods vs. lecturing Different kind of drama with a TMM course The challenge of involving weaker students Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 100. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Reflections Costs/benefits of IBL methods vs. lecturing Different kind of drama with a TMM course The challenge of involving weaker students Reactions to the final exam Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 101. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Final Thoughts Please let us know about research into effectiveness of IBL (or analogous) methods Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 102. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Final Thoughts Please let us know about research into effectiveness of IBL (or analogous) methods ALM URL: http://www.extension.harvard.edu/math/ Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
- 103. The ALM Program Rationale for the courses Implementation Evaluation Conclusions Final Thoughts Please let us know about research into effectiveness of IBL (or analogous) methods ALM URL: http://www.extension.harvard.edu/math/ Great thanks to the Educational Advancement Foundation for support Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers