ibl approaches to geometry and probability for high school ... filerationale implementation...
TRANSCRIPT
RationaleImplementation
EvaluationSelf-evaluation and conclusions
IBL approaches to Geometry and Probabilityfor High School Teachers
Bret Benesh Matthew Leingang
Harvard UniversityDepartment of Mathematics
Legacy of R.L. Moore ConferenceAustin, TexasApril 12, 2007
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Outline
1 RationaleInstructors’ backgroundGoals
2 ImplementationGeometry
ThemeClass Details
Probability
3 EvaluationQuestionsResults
4 Self-evaluation and conclusions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Instructors’ backgroundGoals
Outline
1 RationaleInstructors’ backgroundGoals
2 ImplementationGeometry
ThemeClass Details
Probability
3 EvaluationQuestionsResults
4 Self-evaluation and conclusions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Instructors’ backgroundGoals
Bret’s backgroundWhat living in Madison can do to you
Graduate work was in finite group theoryMinored in math educationKTI ProgramCore Plus and Connected Mathematics Project (CMP)
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Instructors’ backgroundGoals
Matt’s backgroundHow on Earth did I get so jaded?
Geometer by training, teacher by tradeThird time through a probability course for teachersFirst time: team taught, disconnectedSecond time: interesting for me, over their headThird time: ???
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Instructors’ backgroundGoals
Outline
1 RationaleInstructors’ backgroundGoals
2 ImplementationGeometry
ThemeClass Details
Probability
3 EvaluationQuestionsResults
4 Self-evaluation and conclusions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Instructors’ backgroundGoals
Goals for Math E-302“Math for Teaching Geometry”
Maximize student learningImprove communication skillsMotivate studentsProvide a classroom model
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Instructors’ backgroundGoals
Goals for Math E-304“Inquiries into Probability and Combinatorics”
Build a discipline from the ground upTeach students what they’re ready to learnDevelop ability to read, write, and criticize mathematicalarguments
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Outline
1 RationaleInstructors’ backgroundGoals
2 ImplementationGeometry
ThemeClass Details
Probability
3 EvaluationQuestionsResults
4 Self-evaluation and conclusions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Platform for inquiry
Taxicab geometry
Compare and contrast with Euclidean
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Platform for inquiry
Taxicab geometryCompare and contrast with Euclidean
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Class Format
Meet once per week
Class length is two hoursMostly in-service high school teachers
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Class Format
Meet once per weekClass length is two hours
Mostly in-service high school teachers
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Class Format
Meet once per weekClass length is two hoursMostly in-service high school teachers
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Role of Instructor
Moderate discussion
RefereeAsk questionsNot an authority
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Role of Instructor
Moderate discussionReferee
Ask questionsNot an authority
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Role of Instructor
Moderate discussionRefereeAsk questions
Not an authority
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Role of Instructor
Moderate discussionRefereeAsk questionsNot an authority
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
Review
Work on one problem10% lecture45% small group work45% large group discussion
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
ReviewWork on one problem
10% lecture45% small group work45% large group discussion
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
ReviewWork on one problem10% lecture
45% small group work45% large group discussion
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
ReviewWork on one problem10% lecture45% small group work
45% large group discussion
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
ReviewWork on one problem10% lecture45% small group work45% large group discussion
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical problem
What is the definition of acircle in Euclidean geometry?What does a circle look like intaxicab geometry?What is the diameter of acircle in taxicab geometry?What is the circumference intaxicab geometry?What is π in taxicabgeometry?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical problem
What is the definition of acircle in Euclidean geometry?
What does a circle look like intaxicab geometry?What is the diameter of acircle in taxicab geometry?What is the circumference intaxicab geometry?What is π in taxicabgeometry?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical problem
What is the definition of acircle in Euclidean geometry?What does a circle look like intaxicab geometry?
What is the diameter of acircle in taxicab geometry?What is the circumference intaxicab geometry?What is π in taxicabgeometry?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical problem
What is the definition of acircle in Euclidean geometry?What does a circle look like intaxicab geometry?What is the diameter of acircle in taxicab geometry?
What is the circumference intaxicab geometry?What is π in taxicabgeometry?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical problem
What is the definition of acircle in Euclidean geometry?What does a circle look like intaxicab geometry?What is the diameter of acircle in taxicab geometry?What is the circumference intaxicab geometry?
What is π in taxicabgeometry?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical problem
What is the definition of acircle in Euclidean geometry?What does a circle look like intaxicab geometry?What is the diameter of acircle in taxicab geometry?What is the circumference intaxicab geometry?What is π in taxicabgeometry?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Another example
A New Altitude
A = 12(2.3)(8.5) = 9.775
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Grading
Mostly papers
Two examsClass participation
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Grading
Mostly papersTwo exams
Class participation
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Grading
Mostly papersTwo examsClass participation
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Outline
1 RationaleInstructors’ backgroundGoals
2 ImplementationGeometry
ThemeClass Details
Probability
3 EvaluationQuestionsResults
4 Self-evaluation and conclusions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Probability course is TMM
I write problems
Students submit written up problemsStudents present solutionsI update notes with solutions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Probability course is TMM
I write problemsStudents submit written up problems
Students present solutionsI update notes with solutions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Probability course is TMM
I write problemsStudents submit written up problemsStudents present solutions
I update notes with solutions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Probability course is TMM
I write problemsStudents submit written up problemsStudents present solutionsI update notes with solutions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probabilityExpected valueConditional probability. . .
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting Principle
PermutationsCombinationsSet theoryAxioms of probabilityExpected valueConditional probability. . .
with
Provolo
ne
America
nW
hiz
without
Provolo
ne
America
nW
hiz
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting PrinciplePermutations
CombinationsSet theoryAxioms of probabilityExpected valueConditional probability. . .
AB
CD
AC
BD
AC
DB
AD
CB
AD
BC
AB
DC
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting PrinciplePermutationsCombinations
Set theoryAxioms of probabilityExpected valueConditional probability. . .
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting PrinciplePermutationsCombinationsSet theory
Axioms of probabilityExpected valueConditional probability. . .
A
B
C
A∪ (B∩C) = (A∪B)∩(A∪C)
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probability
Expected valueConditional probability. . .
A
B
C
A∪ (B∩C) = (A∪B)∩(A∪C)
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probabilityExpected value
Conditional probability. . .
A
B
C
A∪ (B∩C) = (A∪B)∩(A∪C)
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probabilityExpected valueConditional probability
. . .
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Notes TOC
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probabilityExpected valueConditional probability. . .
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Fun problems
Give them a menu; askhow many combinationplates can be ordered
Verify the publishedprobabilities for winningvarious lottery gamesWhy can we multiplyprobabilities of“consecutive” events?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Fun problems
Give them a menu; askhow many combinationplates can be orderedVerify the publishedprobabilities for winningvarious lottery games
Why can we multiplyprobabilities of“consecutive” events?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Fun problems
Give them a menu; askhow many combinationplates can be orderedVerify the publishedprobabilities for winningvarious lottery gamesWhy can we multiplyprobabilities of“consecutive” events?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
I will have assigned a chapter’s worth of problems
I solicit volunteers to presentWe watch and question the presentersI stay seated
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
I will have assigned a chapter’s worth of problemsI solicit volunteers to present
We watch and question the presentersI stay seated
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
I will have assigned a chapter’s worth of problemsI solicit volunteers to presentWe watch and question the presenters
I stay seated
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
A typical day
I will have assigned a chapter’s worth of problemsI solicit volunteers to presentWe watch and question the presentersI stay seated
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Grading
≥ 1 problem written per week, 0-4 scale
≥ 1 problem presented per week, 0-4 scaleTake-home final to come
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Grading
≥ 1 problem written per week, 0-4 scale≥ 1 problem presented per week, 0-4 scale
Take-home final to come
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
GeometryProbability
Grading
≥ 1 problem written per week, 0-4 scale≥ 1 problem presented per week, 0-4 scaleTake-home final to come
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Outline
1 RationaleInstructors’ backgroundGoals
2 ImplementationGeometry
ThemeClass Details
Probability
3 EvaluationQuestionsResults
4 Self-evaluation and conclusions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Questions
Influence thinking, teaching, or communicating?
Learn more than traditional format?Challenging? Rewarding?Take another class?Recommend class format?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Questions
Influence thinking, teaching, or communicating?Learn more than traditional format?
Challenging? Rewarding?Take another class?Recommend class format?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Questions
Influence thinking, teaching, or communicating?Learn more than traditional format?Challenging? Rewarding?
Take another class?Recommend class format?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Questions
Influence thinking, teaching, or communicating?Learn more than traditional format?Challenging? Rewarding?Take another class?
Recommend class format?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Questions
Influence thinking, teaching, or communicating?Learn more than traditional format?Challenging? Rewarding?Take another class?Recommend class format?
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Outline
1 RationaleInstructors’ backgroundGoals
2 ImplementationGeometry
ThemeClass Details
Probability
3 EvaluationQuestionsResults
4 Self-evaluation and conclusions
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
The results: Question 1
How has this course affected the way you think aboutmathematics?
5=Very positively4=Somewhat positively3=No change2=Somewhat negatively1=Very negatively
prob
geom
µ = 4.21
µ = 4.3
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
The results: Question 1
How has this course affected the way you think aboutmathematics?
5=Very positively4=Somewhat positively3=No change2=Somewhat negatively1=Very negatively
prob
geom
µ = 4.21
µ = 4.3
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Question 2
How has this course affected the way you think about teachingmathematics?
5=Very positively4=Somewhat positively3=No change2=Somewhat negatively1=Very negatively
prob
geom
µ = 4.12
µ = 3.9
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Question 3
How has this course affected the way you think aboutcommunicating in mathematics?
5=Very positively4=Somewhat positively3=No change2=Somewhat negatively1=Very negatively
prob
geom
µ = 4.07
µ = 4.15
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Question 4
Do you think that you learned more, less, or as much as youwould have in a more traditionally taught course?
5=Much, much more4=A little more than usual3=No change in learning2=A little less than usual1=A lot less than usual
prob
geom
µ = 3.78
µ = 3.38
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Question 5
How challenging is this course?3=Very challenging. I had to think much harder than Inormally do.2=Sort of challenging.1=Not challenging at all. I could do this in my sleep.
prob
geom
µ = 2.21
µ = 2.3
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Question 6
How rewarding is this course?4=Ridiculously rewarding. Math is more fun than watchingDancing with the Stars!3=Sort of rewarding2=I don’t get anything out of it1=I feel like this class saps my will to live.
prob
geom
µ = 3.14
µ = 3.28
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Question 7
Would you like to take another course taught in this format?5=Yes! Where do I sign up?!?4=Yes, with some reservation3=Undecided2=No1=Hell no
prob
geom
µ = 3.85
µ = 4.17
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
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=Undecided2=No.1=Yes, but only to my worst enemy.
prob
geom
µ = 4
µ = 4.15
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the probability class
“I have always found proofs difficult and intimidating. Now Ifeel more comfortable with them.”
“Either a problem is challenging/hard, or it is easy and thechallenging is explaining it well. Either way, it ischallenging.”“...it’s really the best way to learn math.”“I think a little more teacher-based instruction would allowfor a more rigorous pace, which pushes students and canlead to more of a need for interaction and discussion bynecessity.”“Waiting for the other students to finish is a bit of a waste oftime.”“I don’t necessarily like the experience, but at least it waspedagogically interesting.”
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the probability class
“I have always found proofs difficult and intimidating. Now Ifeel more comfortable with them.”“Either a problem is challenging/hard, or it is easy and thechallenging is explaining it well. Either way, it ischallenging.”
“...it’s really the best way to learn math.”“I think a little more teacher-based instruction would allowfor a more rigorous pace, which pushes students and canlead to more of a need for interaction and discussion bynecessity.”“Waiting for the other students to finish is a bit of a waste oftime.”“I don’t necessarily like the experience, but at least it waspedagogically interesting.”
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the probability class
“I have always found proofs difficult and intimidating. Now Ifeel more comfortable with them.”“Either a problem is challenging/hard, or it is easy and thechallenging is explaining it well. Either way, it ischallenging.”“...it’s really the best way to learn math.”
“I think a little more teacher-based instruction would allowfor a more rigorous pace, which pushes students and canlead to more of a need for interaction and discussion bynecessity.”“Waiting for the other students to finish is a bit of a waste oftime.”“I don’t necessarily like the experience, but at least it waspedagogically interesting.”
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the probability class
“I have always found proofs difficult and intimidating. Now Ifeel more comfortable with them.”“Either a problem is challenging/hard, or it is easy and thechallenging is explaining it well. Either way, it ischallenging.”“...it’s really the best way to learn math.”“I think a little more teacher-based instruction would allowfor a more rigorous pace, which pushes students and canlead to more of a need for interaction and discussion bynecessity.”
“Waiting for the other students to finish is a bit of a waste oftime.”“I don’t necessarily like the experience, but at least it waspedagogically interesting.”
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the probability class
“I have always found proofs difficult and intimidating. Now Ifeel more comfortable with them.”“Either a problem is challenging/hard, or it is easy and thechallenging is explaining it well. Either way, it ischallenging.”“...it’s really the best way to learn math.”“I think a little more teacher-based instruction would allowfor a more rigorous pace, which pushes students and canlead to more of a need for interaction and discussion bynecessity.”“Waiting for the other students to finish is a bit of a waste oftime.”
“I don’t necessarily like the experience, but at least it waspedagogically interesting.”
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the probability class
“I have always found proofs difficult and intimidating. Now Ifeel more comfortable with them.”“Either a problem is challenging/hard, or it is easy and thechallenging is explaining it well. Either way, it ischallenging.”“...it’s really the best way to learn math.”“I think a little more teacher-based instruction would allowfor a more rigorous pace, which pushes students and canlead to more of a need for interaction and discussion bynecessity.”“Waiting for the other students to finish is a bit of a waste oftime.”“I don’t necessarily like the experience, but at least it waspedagogically interesting.”
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the geometry class
“I see more value in working in groups as an ongoingstrategy [for teaching]. It takes a while to build trust, butonce its established the outcome in class thinking isfantastic!”
“I have thought more about this ’stuff’ than I have thoughton 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, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the geometry class
“I see more value in working in groups as an ongoingstrategy [for teaching]. It takes a while to build trust, butonce its established the outcome in class thinking isfantastic!”“I have thought more about this ’stuff’ than I have thoughton 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, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the geometry class
“I see more value in working in groups as an ongoingstrategy [for teaching]. It takes a while to build trust, butonce its established the outcome in class thinking isfantastic!”“I have thought more about this ’stuff’ than I have thoughton 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, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the geometry class
“I see more value in working in groups as an ongoingstrategy [for teaching]. It takes a while to build trust, butonce its established the outcome in class thinking isfantastic!”“I have thought more about this ’stuff’ than I have thoughton 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, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
QuestionsResults
Some quotes from the geometry class
“I see more value in working in groups as an ongoingstrategy [for teaching]. It takes a while to build trust, butonce its established the outcome in class thinking isfantastic!”“I have thought more about this ’stuff’ than I have thoughton 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, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Our own reactions: Probability
Teaching TMM is harder than lecturing
When “drama” happens outside of class, class can beboringweakest students are involved
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Our own reactions: Probability
Teaching TMM is harder than lecturingWhen “drama” happens outside of class, class can beboring
weakest students are involved
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Our own reactions: Probability
Teaching TMM is harder than lecturingWhen “drama” happens outside of class, class can beboringweakest students are involved
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Our own reactions: Geometry
IBL is more difficult to teach
IBL is more rewarding to teachStill difficult to keep weaker students involved
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability
RationaleImplementation
EvaluationSelf-evaluation and conclusions
Our own reactions: Geometry
IBL is more difficult to teachIBL is more rewarding to teach
Still difficult to keep weaker students involved
Bret Benesh, Matthew Leingang IBL approaches to geometry and probability