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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
Citation preview
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Two non-traditional content courses forin-service high school teachers at the
Harvard Extension School
Bret Benesh Thomas Judson Matthew Leingang
Harvard UniversityDepartment of Mathematics
Critical Issues in Education: Teaching Teachers MathematicsMathematical Sciences Research Institute
Berkeley, CaliforniaMay 31, 2007
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
On Deck
The Harvard ExtensionSchool’s Master ofLiberal Arts (ALM) inMathematics forTeachingGeometry andProbability coursestaught this yearEvaluations andReflections
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
On Deck
The Harvard ExtensionSchool’s Master ofLiberal Arts (ALM) inMathematics forTeaching
Geometry andProbability coursestaught this yearEvaluations andReflections
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
On Deck
The Harvard ExtensionSchool’s Master ofLiberal Arts (ALM) inMathematics forTeachingGeometry andProbability coursestaught this year
Evaluations andReflections
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
On Deck
The Harvard ExtensionSchool’s Master ofLiberal Arts (ALM) inMathematics forTeachingGeometry andProbability coursestaught this yearEvaluations andReflections
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Outline
1 The ALM Program2 Rationale for the courses
Instructors’ backgroundGoals
3 ImplementationGeometry
ThemeClass Details
Probability4 Evaluation
QuestionsResults
5 Conclusions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
History and Purpose of ALM Program
Paul Sally’s Seminarsfor ElementarySpecialists andMathematics Educators(SESAME)Meet state standardsfor mathematics contentIn-service secondaryschool teachers andpeople consideringcareer change
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
History and Purpose of ALM Program
Paul Sally’s Seminarsfor ElementarySpecialists andMathematics Educators(SESAME)
Meet state standardsfor mathematics contentIn-service secondaryschool teachers andpeople consideringcareer change
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
History and Purpose of ALM Program
Paul Sally’s Seminarsfor ElementarySpecialists andMathematics Educators(SESAME)Meet state standardsfor mathematics content
In-service secondaryschool teachers andpeople consideringcareer change
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
History and Purpose of ALM Program
Paul Sally’s Seminarsfor ElementarySpecialists andMathematics Educators(SESAME)Meet state standardsfor mathematics contentIn-service secondaryschool teachers andpeople consideringcareer change
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Whom are we teaching?
In-service teachers come from all kinds of Boston area schools:
from Boston Latinto Boston Public
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Whom are we teaching?
In-service teachers come from all kinds of Boston area schools:
from Boston Latinto Boston Public
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Description of ALM Program Requirements
Students must take 10courses, up throughone year of calculusOne of the coursesmust be on pedagogyStudents mustcomplete a master’sthesis
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Description of ALM Program Requirements
Students must take 10courses, up throughone year of calculus
One of the coursesmust be on pedagogyStudents mustcomplete a master’sthesis
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Description of ALM Program Requirements
Students must take 10courses, up throughone year of calculusOne of the coursesmust be on pedagogy
Students mustcomplete a master’sthesis
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Description of ALM Program Requirements
Students must take 10courses, up throughone year of calculusOne of the coursesmust be on pedagogyStudents mustcomplete a master’sthesis
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
ALM Courses
“Standard" math courses (calculus, discrete math, etc.)
Courses designed for the secondary school teacher
Math E-300 Math for Teaching ArithmeticMath E-301 Math for Teaching Number TheoryMath E-302 Math for Teaching GeometryMath E-303 Math for Teaching AlgebraMath E-304 Inquiries into Probability and CombinatoricsMath E-306 Theory and Practice of Teaching Statistics
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
ALM Courses
“Standard" math courses (calculus, discrete math, etc.)Courses designed for the secondary school teacher
Math E-300 Math for Teaching ArithmeticMath E-301 Math for Teaching Number TheoryMath E-302 Math for Teaching GeometryMath E-303 Math for Teaching AlgebraMath E-304 Inquiries into Probability and CombinatoricsMath E-306 Theory and Practice of Teaching Statistics
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
ALM Courses
“Standard" math courses (calculus, discrete math, etc.)Courses designed for the secondary school teacher
Math E-300 Math for Teaching ArithmeticMath E-301 Math for Teaching Number TheoryMath E-302 Math for Teaching GeometryMath E-303 Math for Teaching AlgebraMath E-304 Inquiries into Probability and CombinatoricsMath E-306 Theory and Practice of Teaching Statistics
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Instructors’ backgroundGoals
Outline
1 The ALM Program2 Rationale for the courses
Instructors’ backgroundGoals
3 ImplementationGeometry
ThemeClass Details
Probability4 Evaluation
QuestionsResults
5 Conclusions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Instructors’ backgroundGoals
Goals for Math E-302“Math for Teaching Geometry”
Maximize student learningImprove communication skillsMotivate studentsProvide a classroom model
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Outline
1 The ALM Program2 Rationale for the courses
Instructors’ backgroundGoals
3 ImplementationGeometry
ThemeClass Details
Probability4 Evaluation
QuestionsResults
5 Conclusions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Platform for inquiry
Taxicab geometry
Compare and contrastwith Euclidean
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Platform for inquiry
Taxicab geometryCompare and contrastwith Euclidean
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Class Format
Meet once per week
Class length is two hoursMostly in-service high school teachers
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Class Format
Meet once per weekClass length is two hours
Mostly in-service high school teachers
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Class Format
Meet once per weekClass length is two hoursMostly in-service high school teachers
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Role of Instructor
Moderate discussion
RefereeAsk questionsNot an authority
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Role of Instructor
Moderate discussionReferee
Ask questionsNot an authority
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Role of Instructor
Moderate discussionRefereeAsk questions
Not an authority
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Role of Instructor
Moderate discussionRefereeAsk questionsNot an authority
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
A typical day
Review
Work on one problem10% lecture45% small group work45% large group discussion
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
A typical day
ReviewWork on one problem
10% lecture45% small group work45% large group discussion
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
A typical day
ReviewWork on one problem10% lecture
45% small group work45% large group discussion
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
A typical day
ReviewWork on one problem10% lecture45% small group work
45% large group discussion
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
A typical day
ReviewWork on one problem10% lecture45% small group work45% large group discussion
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Another example
A New Altitude
A = 12(2.3)(8.5) = 9.775
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Grading
Mostly papers
Two examsClass participation
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Grading
Mostly papersTwo exams
Class participation
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Grading
Mostly papersTwo examsClass participation
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Probability course by the Moore Method
No textbooks at all; Iwrite problems directedtowards the courseobjectivesStudents submit writtenup problemsStudents presentsolutionsI update notes withsolutions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Probability course by the Moore Method
No textbooks at all; Iwrite problems directedtowards the courseobjectives
Students submit writtenup problemsStudents presentsolutionsI update notes withsolutions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Probability course by the Moore Method
No textbooks at all; Iwrite problems directedtowards the courseobjectivesStudents submit writtenup problems
Students presentsolutionsI update notes withsolutions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Probability course by the Moore Method
No textbooks at all; Iwrite problems directedtowards the courseobjectivesStudents submit writtenup problemsStudents presentsolutions
I update notes withsolutions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Probability course by the Moore Method
No textbooks at all; Iwrite problems directedtowards the courseobjectivesStudents submit writtenup problemsStudents presentsolutionsI update notes withsolutions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probabilityExpected valueConditional probabilityFamous probabilitydistributions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting Principle
PermutationsCombinationsSet theoryAxioms of probabilityExpected valueConditional probabilityFamous probabilitydistributions
with
Provolo
ne
America
nW
hiz
without
Provolo
ne
America
nW
hiz
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting PrinciplePermutations
CombinationsSet theoryAxioms of probabilityExpected valueConditional probabilityFamous probabilitydistributions
AB
CD
AD
CB
AC
DB
AB
DC
AC
BD
AD
BC
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting PrinciplePermutationsCombinations
Set theoryAxioms of probabilityExpected valueConditional probabilityFamous probabilitydistributions
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting PrinciplePermutationsCombinationsSet theory
Axioms of probabilityExpected valueConditional probabilityFamous probabilitydistributions
A
B
C
A∪ (B∩C) = (A∪B)∩(A∪C)
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probability
Expected valueConditional probabilityFamous probabilitydistributions
A
B
C
A∪ (B∩C) = (A∪B)∩(A∪C)
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probabilityExpected value
Conditional probabilityFamous probabilitydistributions
A
B
C
A∪ (B∩C) = (A∪B)∩(A∪C)
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probabilityExpected valueConditional probability
Famous probabilitydistributions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Notes Table of Contents
The FundamentalCounting PrinciplePermutationsCombinationsSet theoryAxioms of probabilityExpected valueConditional probabilityFamous probabilitydistributions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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 (referee)
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
GeometryProbability
Grading
≥ 1 problem written per week, 0-4 scale≥ 1 problem presented per week, 0-4 scaleTake-home final
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
Outline
1 The ALM Program2 Rationale for the courses
Instructors’ backgroundGoals
3 ImplementationGeometry
ThemeClass Details
Probability4 Evaluation
QuestionsResults
5 Conclusions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
Questions
We surveyed the E-302 andE-304 students.
Influence thinking,teaching, orcommunicating?Learn more thantraditional format?Challenging?Rewarding?Take another class?Recommend classformat?
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
Questions
We surveyed the E-302 andE-304 students.
Influence thinking,teaching, orcommunicating?
Learn more thantraditional format?Challenging?Rewarding?Take another class?Recommend classformat?
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
Questions
We surveyed the E-302 andE-304 students.
Influence thinking,teaching, orcommunicating?Learn more thantraditional format?
Challenging?Rewarding?Take another class?Recommend classformat?
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
Questions
We surveyed the E-302 andE-304 students.
Influence thinking,teaching, orcommunicating?Learn more thantraditional format?Challenging?Rewarding?
Take another class?Recommend classformat?
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
Questions
We surveyed the E-302 andE-304 students.
Influence thinking,teaching, orcommunicating?Learn more thantraditional format?Challenging?Rewarding?Take another class?
Recommend classformat?
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
Questions
We surveyed the E-302 andE-304 students.
Influence thinking,teaching, orcommunicating?Learn more thantraditional format?Challenging?Rewarding?Take another class?Recommend classformat?
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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 thechallenge 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
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
More quotes from the probability class
“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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
More quotes from the probability class
“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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
QuestionsResults
More quotes from the probability class
“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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Outline
1 The ALM Program2 Rationale for the courses
Instructors’ backgroundGoals
3 ImplementationGeometry
ThemeClass Details
Probability4 Evaluation
QuestionsResults
5 Conclusions
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Reflections
Costs/benefits of IBLmethods vs. lecturingDifferent kind of dramawith a TMM courseThe challenge ofinvolving weakerstudentsReactions to the finalexam
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Reflections
Costs/benefits of IBLmethods vs. lecturing
Different kind of dramawith a TMM courseThe challenge ofinvolving weakerstudentsReactions to the finalexam
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Reflections
Costs/benefits of IBLmethods vs. lecturingDifferent kind of dramawith a TMM course
The challenge ofinvolving weakerstudentsReactions to the finalexam
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Reflections
Costs/benefits of IBLmethods vs. lecturingDifferent kind of dramawith a TMM courseThe challenge ofinvolving weakerstudents
Reactions to the finalexam
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Reflections
Costs/benefits of IBLmethods vs. lecturingDifferent kind of dramawith a TMM courseThe challenge ofinvolving weakerstudentsReactions to the finalexam
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
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 Foundationfor support
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Final Thoughts
Please let us know about research into effectiveness of IBL(or analogous) methodsALM URL:http://www.extension.harvard.edu/math/
Great thanks to the Educational Advancement Foundationfor support
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers
The ALM ProgramRationale for the courses
ImplementationEvaluation
Conclusions
Final Thoughts
Please let us know about research into effectiveness of IBL(or analogous) methodsALM URL:http://www.extension.harvard.edu/math/
Great thanks to the Educational Advancement Foundationfor support
Bret Benesh, Thomas Judson, Matthew Leingang Non-traditional content courses for in-service teachers