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Algebra, Problem Solving, and Higher-level Mathematics for
Middle School Students
April 25, 2009
2009 Annual Conference & Exposition
National Council of Teachers of Mathematics
Max L. Warshauer
Hiroko K. Warshauer
Julie AcostaA member of The Texas State University System
Overview
• Problems and activities• Strategies • Equity and accessibility• International perspective• Contests and Camps• Q/A
Creating Interesting Problems
• Engaging
• Relevant
• Requires making connections
• Develop student understanding
A Dry Problem
Solve for xy if
• x+y=8 and
• x2+y2=36
Different approaches
• Substitution
• Graphing
• Making connections
Refining the problem
• A rectangle has perimeter 16 and diagonal of length 6. Find its area.
Key Principles
• Compute simple examples• Look for patterns• Make conjectures• Test and prove why things work
Focus on
• What is the student asking?
• The problems, not just answers.
• How to open the communication.
• Different ways to approach the problem.
• Different ways to pose questions.
Equity and Accessibility
• “To think deeply of simple things”
• Challenge with rich problems
• Develop a growth mindset—Carol Dweck
• Early Access to algebraic thinking
Summer Programs
• Awesome
• Ross (Ohio State)
• PROMYS (Boston University)
• Texas Mathworks Junior Summer Math Camp, Honors Summer Math Camp
Implications for preparing future teachers
• Engage in examining problems
• Examine student questions
• Develop independent, confident problem solvers
• Think deeply about the mathematics.
• Communicate by writing mathematics
Combining with Teacher Training
• Structure—– Observe Camp– Graduate Course– Conduct Camp– School year follow-up
School Support
• Long-term relationships
• Curriculum Director
• Principal Support
• Teacher Buy-In
School-District Perspective
• Curriculum Pilots
• Parental support
• Family Math Nights
• Community support
University and School District Partnership
• Superintendent, Curriculum Director, Principal, Teacher
• Understanding district needs
• Coordinating with undergraduate teacher preparation
Contests
• MathCounts
• American Math Competition – (AMC) 8, 10, 12
• Primary Math World Contest (PMWC)
• American Regions Math League (ARML)
• American Invitational Math Exam (AIME)
International Perspective
• Primary Math World Contest
• Bulgaria
• Japan
• Australia
• China
Q&A
Thanks!
Questions
Max Warshauer at [email protected]
Hiroko Warshauer at [email protected]
Julie Acosta at [email protected]