Algebra, Problem Solving, and Higher-level Mathematics for Middle School Students April 25, 2009 2009 Annual Conference & Exposition National Council of.

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]