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Algebra, Problem Solving, and Higher-level Mathematics for Middle School Students

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 Acosta. A member of The Texas State University System. Overview.

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Algebra, Problem Solving, and Higher-level Mathematics for Middle School Students

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  1. 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 Acosta A member of The Texas State University System

  2. Overview • Problems and activities • Strategies • Equity and accessibility • International perspective • Contests and Camps • Q/A

  3. Creating Interesting Problems • Engaging • Relevant • Requires making connections • Develop student understanding

  4. A Dry Problem Solve for xy if • x+y=8 and • x2+y2=36

  5. Different approaches • Substitution • Graphing • Making connections

  6. Refining the problem • A rectangle has perimeter 16 and diagonal of length 6. Find its area.

  7. Key Principles • Compute simple examples • Look for patterns • Make conjectures • Test and prove why things work

  8. 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.

  9. Equity and Accessibility • “To think deeply of simple things” • Challenge with rich problems • Develop a growth mindset—Carol Dweck • Early Access to algebraic thinking

  10. Summer Programs • Awesome • Ross (Ohio State) • PROMYS (Boston University) • Texas Mathworks Junior Summer Math Camp, Honors Summer Math Camp

  11. 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

  12. Combining with Teacher Training • Structure— • Observe Camp • Graduate Course • Conduct Camp • School year follow-up

  13. School Support • Long-term relationships • Curriculum Director • Principal Support • Teacher Buy-In

  14. School-District Perspective • Curriculum Pilots • Parental support • Family Math Nights • Community support

  15. University and School District Partnership • Superintendent, Curriculum Director, Principal, Teacher • Understanding district needs • Coordinating with undergraduate teacher preparation

  16. Contests • MathCounts • American Math Competition • (AMC) 8, 10, 12 • Primary Math World Contest (PMWC) • American Regions Math League (ARML) • American Invitational Math Exam (AIME)

  17. International Perspective • Primary Math World Contest • Bulgaria • Japan • Australia • China

  18. Q&A Thanks! Questions Max Warshauer at max@txstate.edu Hiroko Warshauer at hw02@txstate.edu Julie Acosta at jacosta1@mcallenisd.org

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