Diana White Director National Association of Math Circles NAMC Mathematical Sciences Research Institute Associate Professor University of Colorado Denver Presented at International Math Outreach Workshop ID: 931430
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Math Circles – Mathematicians Fostering Habits of Mind in K12 Teachers and Students
Diana
White
Director, National Association of Math Circles (NAMC)
(Mathematical Sciences Research Institute)
Associate Professor, University of Colorado Denver
Presented at International Math Outreach Workshop
at Banff International Research Station
November 24, 2015
Slide2Mathematical Sciences Research Institute – Outreach Efforts
National Math Festival
Mathical
Book PrizeNumberphileNavajo Nation Math Circle FilmGuerilla Science – Fire OrganNational Association of Math Circles
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
Slide3National Association of Math Circles
Programs
to launch, support, mentor,
and sustain Math CirclesGrants – support and exchange visitsMath Circle - Mentorship and Partnership ProgramResources Online – website and handbook (in development)
AMS/MRSI Math Circle Library Series
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
Slide4What is a
MathCircle
?
Slide5Math Circles
Loosely defined, goal of inclusivity
Participants are K12 students or teachers
Focus is generally on learning to explore, conjecture, create, collaborate and communicate substantive mathematics --- All those things that a mathematician does while engaging in the practice of mathematical research
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide6Math Circles - Goals
Put mathematics professionals in direct
contact
with K12 students and teachersIncrease problems solving skillsDevelop enjoyment of mathematicsLearn disciplinary skills of mathematics
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide7Types of Math Circles
Math Teachers’ Circles
Started in 2006 at American Institute of Mathematics (AIM)
Math Students’ CirclesOriginated in Eastern EuropeSpread to U.S. in 1990’s
Both
Rapid growth in past decade due to intentional efforts by AIM and NAMC
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide8Math Circle Growth
Growth of Math Circles
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
Slide9Math Circles Across the Country
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
Slide10‘Knowing About’ and ‘Figuring Out’
V-E+F = 2
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
Slide11Problem
Write numbers from 1 to 100 on the board. Select any two of the numbers, erase them, and write on the board the sum plus the product of the two numbers. For example, if you erased 2 and 5, the sum plus the product is 7 plus 10, or 17, and so you write a 17 on the board. Now there are two 17s, but that’s OK. Repeat this process of selecting two numbers and replacing them with their sum plus their product. What are the possible outcomes
?
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students11
Slide12Problem Posing
Does there exist c such that there are a, b with
ab+a+b
=c?Can you unerase a number that you erase?How big does it get?Does order matter?Is there a smaller problem?Why not a trinary
relation?
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide13Key Aspects of Problem
Connections to K-12 Mathematics
Commutative and associative properties
Structure and symmetryAlgebraic representation: xy+x+yConnects to higher level mathematicsCombinatorics GeometryAlgebra
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide14Key Aspects of Problem
Low Threshold, High Ceiling
Ideal for Problem Posing, Flexibility with Pathways
Problem Solving Techniques/SkillsAsk a simpler questionUse fewer numbersUse simpler operationGeneralizeAsk related questions
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide15Teacher Professional Development
Tendency to teach how they were taught
Teachers being asked to teach in ways they have not experienced as learners
Need experiences as learners of mathematics that model mathematical habits of mind and the process of doing mathematics
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide16Out of school learning
Kids spend lots more time out of school than in school
Out of school STEM learning is known to have significant affects
ContentSense of belonging, identityWillingness to consider STEM careers
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide17Mathematicians
– benefits each way
Deep understanding of mathematics
ContentProcessQuestioning skillsAbility to respond in the moment to student directionsRole modelsCan affect our own
teaching
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
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Slide18NAMC Goals - Partial
Provide support to Math Circle leaders
Resources (materials, videos, funding, journal)
Training, mentoringProfessionalizationConnect to informal STEM education communityMath Circle/Informal Mathematics Education JournalBuild a community of practice Conferences and workshops
Catalyze research efforts
Math Circles – Mathematicians fostering habits of mind in k12 teachers and students
Slide19Thank you!!
Questions?
Dr. Diana White diana.white@ucdenver.edu
For info about NAMC:
info@mathcircles.org