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What Do We Do With the Seniors?

What Do We Do With the Seniors?. Asilomar 2009 Bob Loew Foothill High School Pleasanton, CA. The Problem. If students take Algebra in Grade 8, they finish Pre-Calculus in Grade 11 Then what, if AP is not the answer? The effect is compounded if 8th Graders take Geometry.

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What Do We Do With the Seniors?

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  1. What Do We Do With the Seniors? Asilomar 2009 Bob Loew Foothill High School Pleasanton, CA

  2. The Problem • If students take Algebra in Grade 8, they finish Pre-Calculus in Grade 11 • Then what, if AP is not the answer? • The effect is compounded if 8th Graders take Geometry

  3. Different Students - Different Needs Honors Geometry - Algebra 2 - Pre-Calc Natural candidates for AP Calc or Stat Mainstream College Prep Geometry - Algebra 2 - Pre-Calc Want a Senior math class, but not necessarily AP Math I-IV Definitely need an AP Alternative

  4. This led us to design two new courses College Prep: Math Analysis One semester of “Calculus Lite”, plus one semester of other math topics UC-approved Elective: Problem Solving Techniques for solving problems that are not neatly defined Qualifies for graduation units, but not UC-approved

  5. Problem Solving: Try this one Take a two-digit number, reverse the digits, and then add them together. The result is 121. What is the original number?

  6. The new course specializes in dealing with this kind of problem Teaches logic and strategy, beyond computation Emphasizes both individual initiative and group collaboration Deals with fuzzy problems, not always well-defined “What to do when you don’t know what to do” Places a premium on creativity and divergent thinking

  7. Students are exposed to a broad array of problem solving strategies (I) Draw a Diagram Systematic Lists Eliminate Possibilities Matrix Logic Look for a Pattern Subproblems

  8. Students are exposed to a broad array of problem solving strategies (II) Unit Analysis Solve a Related Problem Work Backwards Finite Differences Change Your Focus Physical Models 6 other approaches

  9. By the end of the course, many of the problems are complex and non-obvious A man living in the South Pacific is planning a sailing trip. His boat will carry enough food for three weeks. Along his route are five islands, each a week’s travel apart. Four of the islands are uninhabited and have no food. The fifth island is his destination and is well-supplied. He thus realizes that he cannot make the trip in a single pass. Instead, he will have to ferry supplies to the intermediate islands sufficient to support him on the final sailing. How should he organize his food supplies? How many weeks will it take him to reach the fifth island?

  10. A non-traditional course calls for non-traditional assessment Group Problem sets Presentations of methods and results Individual Journal writing on assigned topics Quizzes and a final exam

  11. Learnings from the first two years (I) It is essential to set the ground rules and atmosphere at the start Open-ended inquiry, divergent thinking Tolerance for ambiguity Collaboration Sustained effort This is not a standard math class Some/many students will be uncomfortable Some students may need to be filtered out Initial selection (by application?) After the first few weeks

  12. Learnings from the first two years (II) Teachers too need to learn some new behaviors Guiding, not telling Resisting student pleas that come from discomfort Class size matters - 20-25 is about right Problems of too big and too small Course did not get UC approval Thus, is an Elective, not a Math course Limits participation by the strongest students Target audience: mid- to lower-range students

  13. A good textbook is available “Problem Solving Strategies” Ken Johnson et. al. Key Curriculum Press Designed for this type of course Strong on teacher guidance and advice Lots of good examples and problems Developed in actual use

  14. Let’s take some questionsbefore we go on to the second course

  15. The Math Analysis course was designed with dual objectives Introduction to Differential and Integral Calculus Heavy on applications, light on theory Focus on polynomials and Sin/Cos, but not Logs or Exponentials Survey of other math topics Negotiation, Game Theory, Time Value of Money, Critical Path Scheduling, Decision Analysis, others

  16. The Calculus semester covers the essential elements and their applications Continuity and Limits Average and instantaneous rates of change Derivative = Rate of change at a point = Tangent Basic rules for Differentiation, incl. Chain Rule Finding Extreme Values Meaning and use of First and Second Derivatives Integration = Cumulative effect of change = Area under curve Rules for Integration

  17. The second semestergives exposure to math topics not often covered in high school Management Science Euler and Hamiltonian Circuits Critical Path scheduling Game Theory and Negotiation Prisoner’s Dilemma Fair Division Time Value of Money Models for Savings and Investment Decision Analysis

  18. Good textbooks are available here too Calculus “Calculus With Applications”, Lial et. al Or, “Calculus and Its Applications”, Bittenger et. al. Both from Addison Wesley Other math topics “For All Practical Purposes”, COMAP W.H. Freeman

  19. Now let’s take some questionson this course,and find out what you’ve been doing

  20. Turn in an Evaluation Formto get the handout.

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