Results from a Randomized Trial of Two Algebra Sequences for Underprepared Freshmen

1. Results from a Randomized Trial of Two Algebra Sequences for Underprepared Freshmen Ruth Curran Neild Vaughan Byrnes Robert Balfanz

2. Motivation for the Study • States and districts increasingly consider Algebra 1 to be the “default” course for all 9th graders • AND YET – • In districts with “Algebra for All” policies, course failure rates in Algebra have been high (Los Angeles, Milwaukee, Chicago)

3. Large percentages of ninth graders in low-performing districts are underprepared for Algebra (Data from Philadelphia, adapted from Neild and Balfanz, 2005)

4. Where is “catch up” required? • Intermediate mathematics skills: fractions, decimals, signed numbers Complete the following statement with >, <, or = .56 _____ ¾

5. Where is “catch up” required? • Pre-algebra skills, including: • Graphing • One- and two-step equations • Inequalities • Mathematics reasoning skills • Does this answer/argument make sense? • What are the patterns?

6. “Double dosing” is a common ninth grade “catching up” strategy

7. Options for extended time • Provide an additional 45-50 minute Algebra support course during the school day (Philadelphia, Chicago) • Place students into a year-long Algebra course that meets ~90 minutes each day and allows time for catch up as needed • Provide a structured catch-up course first semester, followed by Algebra 1 second semester (class meets ~90 minutes each day)

8. The Conditions Catch Up Course Followed by Algebra 1 Course Year-LongAlgebrawith Embedded Catch Up Year-long 80-90 minute class, taught by the same teacher Algebra curriculum is of the district’s choosing Conceptualized as the “business as usual” condition • Year-long 80-90 minute classes, taught by the same teacher • First semester course is the Transition to Advanced Mathematics Curriculum, developed by Johns Hopkins • Second semester is Algebra curriculum of the district’s choosing

9. Transition to Advanced Math (TAM) Genesis of the curriculum was observation of a quandary: either fail most students or water down the content Recognizes material and human capital challenges in low-resource schools through student consumables, tightly organized curriculum, and classroom kits of materials.

10. Transition to Advanced Math (TAM) Five Units: Mathematical Reasoning, Data Analysis, and Probability Numbers and Integers Rational Numbers Measurement Patterns and Functions & Introduction to Algebra

11. Study Details • Two cohorts of districts: eight in 2008/09, five in 2009/10 (13 district in total) Implementation/data collection in each district for a single year • Randomization within districts, at the school level • Students who are 1-4 years below grade level in mathematics are eligible to participate

12. Study districts, 2008/09 and 2009/10

13. Research Questions Primary questions • Are there mid-year differences between the conditions in growth in intermediate mathematics skills? • Are there end-of-year differences between the conditions in Algebra proficiency? • Are there differences between the conditions in mathematics grades during semester 1 and semester 2?

14. September September End of first semester (~January) ALGEBRA PROFICIENCY (Orleans-Hanna & CTB Algebra) End of year (~May) Instrumentation INTERMEDIATE MATH SKILLS (CTBS)

15. Other Instrumentation • Student and teacher surveys: Beginning-of-year and end-of-year • Classroom observations, with quantitative measures and narrative: once each semester

16. Basic Models • Multi-level modeling (HLM) • 3-level model with students nested within teachers, within schools • Uncontrolled (empty) model • Model with student, teacher, and school controls • (4,941 Students – 131 Teachers – 46 Schools)

19. Growth in Intermediate Math:

20. Distribution of fall CTBS national percentiles

21. Distribution of winter CTBS national percentiles

22. Estimated treatment effect, Intermediate Mathematics

23. Direction of Effects is Consistent Across Districts

24. SEMESTER 1 MATH GRADES:

25. Estimated treatment effect, Semester 1 Math Grade, 2008/09

26. Distribution of 1st Semester Math GradesBy Condition

27. ALGEBRA PROFICIENCY:

28. Distribution of national percentiles

29. Estimated treatment effect, Algebra Proficiency

30. Direction of Effects Across Districts

31. SEMESTER 2 MATH GRADES:

32. Estimated treatment effect, Semester 2 Math Grade

33. Distribution of 2nd Semester Math GradesBy Condition

34. Robust Results Results for all achievement outcomes were consistent when re-tested using several supplementary methods, Including: • Best-Fit Models for each outcome • Analyses with only complete case data • Analyses with only those targeted students, 1-4 GE behind • Testing for interaction between treatment effect and prior achievement levels

35. INTERVENING FACTORS AND INTERMEDIATE OUTCOMES: Classroom PRACTICES & attitudes toward mathematics

36. Measure: Classroom Practices, including: • Students used objects or tools, such as rulers, protractors or algebra tiles • The teacher asks students to explain how they got their answers. • When I didn't understand something my teacher tried to help by asking questions • Students are asked to show more than one way of solving a math problem • I worked on math problems during class time with other students in my class • I was asked to write a few sentences about how I solved a math problem • Students worked in small groups or with a partner • My teacher uses real-life examples to help us understand math • The teacher made sure that everyone understood before moving on to another topic

37. Measure: Attitudes Toward Math Class, including: • I liked coming to math class • I paid attention in math class • I did my math homework • I felt that I could do almost all the work in math if I didn’t give up. • I felt confused in math class. • I worked hard in math class. • I studied for math tests and quizzes. • I felt successful in math. • I felt confident that I could do the math work.

38. Estimated Effect of Classroom Practices & Attitudes on Student Outcomes

39. Estimated treatment effect on Classroom Practices & Attitudes

40. Finally… • Fall to Winter Gains made in Intermediate Math were significantly related to spring Algebra scores when modeled • So, while TAM students may not have performed significantly higher in Spring Algebra, their 1st semester gains in basic math skills were related to improved Algebra performance

41. Conclusions • TAM students improved significantly more in terms of their intermediate math skills. • TAM students performed equally to Stretch students in Algebra, despite spending only half as much of the school year on the topics. • TAM students experienced higher levels of intermediate outcomes which indirectly lead to better Algebra outcomes (intermediate math gains, and better Classroom Practices).