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 x 2 +y 2 =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 mindsetCarol 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

19. Q&A Thanks! Questions Max Warshauer at max@txstate.edumax@txstate.edu Hiroko Warshauer at hw02@txstate.eduhw02@txstate.edu Julie Acosta at jacosta1@mcallenisd.orgjacosta1@mcallenisd.org