Proficient but not College Ready: Bridging the Gap in Mathematics

1. Proficient but not College Ready: Bridging the Gap in Mathematics Woodrow Wilson Seminar October 21, 2009 Princeton, NJ Zalman Usiskin The University of Chicago z-usiskin@uchicago.edu

2. Outline of remarks • Transitions • Linearity • Prerequisites for success • National data • The dream

3. 1. Transitions before the Transition into College

4. Algebra and calculus are both • fixtures of the curriculum; the first course at a new level; a sign of arrival • prerequisites to a great deal of future work • filters • normally offered at a variety of levels of difficulty • normally taken one year earlier by the best students.

5. Other common features of algebra and calculus • Some people think that the basic ideas can be learned much earlier than one year before. • But hurdles are in place to discourage early work.

6. Transitions in schooling • from home to school • from elementary to middle school • from middle to high school • from high school to college

7. 2. Linearity in Mathematics

8. 3. Prerequisites for Success in College Mathematics

9. Mathematics Core Academic Knowledge and Skills (Conley) (1) Most important for success in college math is a thorough understanding of the basic concepts, principles, and techniques of algebra. This is different than simply having been exposed to these ideas. Much of the subsequent mathematics they will encounter draw upon or utilize these principles. (2) In addition, having learned these elements of mathematical thinking at a deep level, they understand what it means to understand mathematical concepts deeply and are more likely to do so in subsequent areas of mathematical study.

10. Mathematics Core Academic Knowledge and Skills (edited) (1) Most important for success in college math is a thorough understanding of the basic (concepts)skills, principles, applications, and representations (e.g., graphs)of algebra, geometry, statistics, and functions. ((2)In addition, having learned these elements of mathematical thinking at a deep level, they understand what it means to understand mathematical concepts deeply and are more likely to do so in subsequent areas of mathematical study.)

11. Mathematics Core Academic Knowledge and Skills (Conley) (3) College-ready students possess more than a formulaic understanding of mathematics. They have the ability to apply conceptual understandings in order to extract a problem from a context, use mathematics to solve the problem, and then interpret the solution back into the context.

12. Mathematics Core Academic Knowledge and Skills (edited) (4) They know when and how to estimate to determine the reasonableness of answers and can use a calculator appropriately as a tool, not a crutch. They are able to move back and forth among the doing of simple mathematics in their heads, the use of paper and pencil technology for short exercises, and the employment of sophisticated calculator and computer technology to handle more complex tasks and explorations; when one method does not solve a problem they can use another method.

13. 4. Some National Data

14. Percents of 8th graders studying various levels of mathematics curricula Alg Enr. Typ Rem. • SIMS 13 11 66 10 Alg PreA Reg Other • NAEP 16 19 61 5 • NAEP 20 36 39 5 G/AA Alg PreA Reg Other • NAEP 3 25 31 37 5 2003 NAEP 5 28 29 33 5 2007 NAEP 7 34 30 25 4 SIMS = Second International Mathematics Study NAEP = National Assessment of Educational Progress Alg = Algebra; Enr = Enriched; Typ = Typical; Rem = Remedial; PreA = Pre-algebra; Reg = Regular; G/AA = Geometry or Advanced Algebra.

18. Number of AP Calculus Exams 2000-2008 Year AB BC 2000 137,276 34,142 2001 146,771 38,134 2002 157,524 41,785 2003 166,821 45,973 2004 175,094 50,134 2005 185,992 54,415 2006 197,181 58,603 2007 211,693 64,311 2008 222,83569,103 Source: The College Board, AP Report to the Nation 2005-06-07-08

19. Source: David Bressoud: www.macalester.edu/~bressoud/talks/CBMS.pdf

20. Percents of students with each score on AP Calculus Exams ABBC Year 2004 2005 2006 2007 2004 2005 2006 2007 Score 5 20.4 20.9 22.3 21.0 39.8 43.8 41.9 43.5 4 19.9 19.5 20.5 18.7 18.8 17.0 19.7 17.9 3 19.0 17.7 18.6 19.1 20.9 20.1 19.7 18.8 2 17.6 16.7 15.5 15.4 7.7 6.8 6.4 6.4 1 23.0 25.2 23.2 25.7 12.8 12.3 12.3 13.5 ≥3 59.3 58.1 61.3 58.8 79.6 80.9 81.3 80.2 mean 2.97 2.94 3.03 2.94 3.65 3.73 3.72 3.71 Source: The College Board, AP Reports to the Nation 2005-06-07-08

21. 5. An Impossible Dream?

22. Giving up the dream • Do not have calculus in high school as a goal. • Teach a restricted curriculum that aims only towards calculus. • Expect only a small percent of students to have the time and diligence to successfully handle the work load of a demanding curriculum.

23. Realizing the dream • Start at least as early as grade 6 with double periods for mathematics to catch students up. • Teach a full curriculum that aims at the full spectrum of college preparatory mathematics. • Expect almost all students to successfully handle the work load of a demanding curriculum by providing time in school. • Reduce the economic hardship that requires some students to work or have family responsibilities many hours each week.

24. Thank you!