Minnesota Mathematics Achievement Project (MNMAP)

1. Minnesota Mathematics Achievement Project (MNMAP) High School Mathematics Curricula and College Mathematics Achievement and Course Taking Tom Muchlinski Project Coordinator Michael Harwell and Tom Post Principal Investigators ASSM Meeting April 19, 2009 Alexandria, VA.

2. Overview of today’s comments:  Why we are here – previous efforts  Brief overview of five interrelated studies (All relate to the impact of high school mathematics curricula on student performance

3. Initial Two Years Minneapolis and St. Paul Area Merging to Achieve Standards Project – (MASP)2, NSF Award Number 9618741  During the four summers of (MASP)2, over 1100 teachers completed professional development related to one of the supported NSF funded curricula.

6. ASSESSMENT DESIGN - CONTEXT:A) Districts wanted confirmation that students using NSF curricula were not losing ground on nationally normed tests covering traditional content.B) Our response: Harwell, M.R., Post, T.P., Maeda, Y., Davis, J.D., Cutler, A. Andersen, E., & Kahan, J.A. (2007). Standards-based mathematics curricula and secondary students’ performance on standardized achievement tests. Journal of Research in Mathematics Education, 38, 71-101. Post, T.R.., Harwell, M.R., Davis, J. D., Maeda, Y., Cutler, A., Anderson, E., Kahan, J. A., & Norman, K. (2008) Standards-based mathematics and middle grade students’ performance on standardized achievement tests. Journal for Research in MathematicsEducation. 39(2), 184-212.

7. C) University mathematicians are lobbying parent groups and schools, saying that students in reform curricula will be ill equipped for university calculus. (Existing data do not support this position.)

8. Study Number 3 (AERJ – Spring 2009) “The preparation of students from National Science Foundation funded and commercially developed high school mathematics curricula for their FIRST UNIVERSITY MATHEMATICS course.”

9. All students in the following studies completed three or more years of high school mathematics using commercially developed, UCSMP, or NSF Funded curricula. • High school mathematics levels expressed in number of years of mathematics completed (i.e., 3, 4, or 5). Study 3

10. Difficulty Levels for University Mathematics Courses: [N=1296 CD; 371 NSFF] Level 1 – HS Mathematics Level 2 – College Algebra / Pre Calculus Math Level 3 – Calculus I Level 4 – Calculus II and beyond Study 3

11. HLM Findings: 1. With other predictors held constant, high school math curriculum is related to difficulty level of initial math course (expontiating curriculum slope of .717 = 2.04) i.e., NSF students twice as likely to enroll in less difficult math course relative to students from a CD curriculum. Study 3

12. HLM Findings (Continued): 2. HS mathematics curriculum not related to grade in initial course. But we believed that this is not always the most interesting or most important question(s) (see Studies 4 and 5). Study 3

13. Study Number 4 “The preparation of students completing various High School mathematics curricula for multiple post-secondary mathematics courses.” Students who had taken two or more post-secondary mathematics courses: A longitudinal perspective. Study 4

14. HS Mathematics Curricula • Impact on: • Difficulty level and grade in initial post- • secondary math course • Pattern of post-secondary math grades earned over time and student course taking patterns Study 4

15. Research Question: Among students completing at least two post-secondary mathematics courses - what is the nature and magnitude of the relationship between the high school mathematics curriculum a student completed (NSF funded, CD, UCSMP) and their subsequent performance in college level mathematics, i.e. their… Study 4

16. Research Question (Continued): 1. Patterns of grades earned in post-secondary mathematics classes over semesters when taking into account student background factors; 2. Patterns of course difficulty levels of post-secondary mathematics classes over semesters when taking into account student background factors? Study 4

17. Population: N = 2323 from 162 high schools. All were Freshmen who enrolled at a single large university during Fall 2002 and Fall 2003 – all took two or more math classes. Core+ N = 275 (MMOW (46), IMP (35) – MMOW and IMP students were omitted because of small N’s). Study 4

18. DifficultyLevels of University Mathematics Courses: Level 1 – HS Mathematics Level 2 – College Algebra / Pre Calculus Math Level 3 – Calculus I Level 4 – Calculus II and beyond 91% of students completed the minimum number of mathematics courses required in major. Study 4

19. Number of Mathematics Courses Completed (Percentages): 2 Courses 3 Courses 4 Courses CD 43 25 21 UCSMP 43 24 20 Core + 46 27 19 Study 4

20. HLM Findings: 1. No differences across High School mathematics curricula with respect to initial university mathematics grades or difficulty levels. 2. No relationship between HS math curriculum and university mathematics grade or difficulty level trajectories across multiple courses. Study 4

21. Conclusion: CD, USMP, and NSFF curricula do a comparable job of preparing students who complete multiple post-secondary mathematics courses. Study 4

22. Study Number 5 “The Impact of Prior Mathematics Achievement on the Relationship Between High School Mathematics Curricula and Post-Secondary Mathematics Performance, Course-taking, and Persistence.” High school curriculum and student achievement, course-taking patterns and persistence in college mathematics: Second longitudinal study (eight semesters of college work). Study 5

23. Research Question: • Are there differences among students with similar prior mathematical achievement who completed at least three years of high school mathematics in commercially developed, the University of Chicago School Mathematics Project, or NSF funded curricula in their: • University mathematics achievement • Course-taking patterns, and • Persistence in these classes? • If there are differences, what is their nature and magnitude? Study 5

24. Independent variable of primary interest: HS curriculum cohort (5 types: CD, UCSMP, Core+, IMP, and MMOW) Dependent (outcome) variables of primary interest: 1. Difficulty level of initial post-secondary mathematics course (HLM) 2. University mathematics course achievement over eight semesters (grades) (HLM) 3. Persistence – number of college mathematics courses completed (Poisson regression) 4. Course-taking patterns difficulty level of highest course completed (HLM) Study 5

25. Population: Total N = 4144 – all students had at least three years, most 4 or 5 years, of HS mathematics 266 high schools represented All students partitioned into thirds based on ACT math scores (lowest ACT ≤ 22; middle ACT 23-26; top ACT ≥27). Study 5

26. DifficultyLevels of Post-Secondary Mathematics Coursework : Level 1 – HS Mathematics Level 2 – College Algebra / Pre Calculus Math Level 3 – Calculus I Level 4 – Calculus II Level 5 – Beyond Calculus II – DEQ, Linear Algebra, Analysis, etc. Study 5

27. Statistics: Descriptive and Inferential analysis utilized (2 level HLM). Study 5

28. Study 5

29. Study 5

30. Study 5

31. Study 5

32. Conclusions from HLM Analysis: 1. For the middle and high ACT groups there were no curriculum differences in the difficulty level of the INITIAL post-secondary mathematics course. Study 5

33. Conclusions (Continued): 2. The same linear patterns were noted for post-secondary mathematics grades (achievement) students earned in multiple courses across the three ACT groups examined here. Study 5

34. Conclusions (Continued): 3. There was no evidence of significant differences in the numbers of college mathematics courses completed by students in the various high school curricula (persistence). Study 5

35. Conclusions (Continued): 4. Having examined eight semesters of post-secondary coursework, we conclude from the longitudinal analysis that students completing the NSFF, CD, and UCSMP curricula showed the same linear pattern of levels of difficulty of mathematics courses across eight semesters of college study (course taking patterns). Study 5

36. Summary: These results help to respond to the largely anecdotal criticism that NSFF curricula would leave middle and high ability students unprepared for post-secondary mathematics. Our findings suggest that this is not the case. Study 5

37. Study Number 6 (In Progress) Research Question: “Is there a relationship between the high school mathematics curriculum a student completed and their post-secondary mathematics achievement, course-taking, and persistence, and, is this relationship similar across post-secondary institutions varying in size and institutional mission?” Study 6

38. Sample: Approximately 27,000 students who enrolled in one of thirty-three four-year post-secondary institutions or six two-year institutions in the upper midwest of the U.S. All students graduated from a Minnesota high school. The four-year schools varied in size, educational mission (4 private and 29 public schools), and location (urban, suburban, rural). Data: High school variables (e.g., Minnesota high school attended, math courses and associated grades, percentile rank, overall GPA, gender, ethnicity) and post-secondary variables (math/statistics/physics courses and associated grades, major) provided by post-secondary institutions. Study 6

39. So why would anyone want students enrolled in NSF curricula when these students only perform as well as traditional students on college mathematics? Recall that all NSF curricula were designed to embody the content and principles of the 1989 NCTM Curriculum Standards document. This represents the sum total of the current thinking and best practices in our field. At the high school level, “…the Core-Plus curriculum seems to be particularly effective in developing students conceptual understanding, quantitative thinking, and ability to solve contextualized problems. They also perform well on tasks involving statistics and probability.” (Schoen and Hirsch in Senk and Thompson, 2003, p. 340-41.)

40. “It is not that students in NSF curricula learn traditional content better, but that they develop other skills and understandings while not falling behind on traditional content.” (Swafford in Senk and Thompson, 2003, p. 468.)

41. Five classroom events that were associated with “Standards-based instruction.” These included: • student opportunity for mathematical conjectures, • b) focus on conceptual understanding, • c) use of student verbal explanations, • d) utilizing multiple mathematical perspectives, and • e) teacher valuing student comments • (Romberg and Shafer, 2003, and Tarr, Reys, Reys, Chávez, Shih, and Osterlind, 2008.)

42. Some other other characteristics of NSFF curricula to consider: • Provide problems which actually occur in, or are derived from, real world experiences, often involving multiple strategies, and content domains in their solution (i.e., discrete mathematics, probability and statistics more prominent). • Provide many more opportunities for group discussion and problem solving; • Routinely consider problems whose solution requires more than a few minutes and more than simply the application of previously learned procedures (often over several days);

43. Place a premium on student explanation and investigation; • Provide more comprehensive models for the evaluation of student performance; • Utilize various forms of technology when and where appropriate; and • Lastly, the curricula funded with NSF support are vastly more consistent with the cognitive perspective of the nature of human learning as it is understood today.

44. Closing Thoughts: • It is unfortunate that mathematics has become politicized and polarized. • The ubiquitous goal is to have more kids learn more mathematics more effectively (ostensibly). • Cannot continue with the status quo. Currently losing too many students to mathematics and its associated future oriented benefits. • When schools make adoption decisions, no longer appropriate to make those decisions on the basis that students will not do well in college mathematics if they participate in one of the NSF funded high school curricula.