1. INVESTIGATING STUDENT OUTCOMES IN BEGINNING ALGEBRA Kevin L. McCandless, Ed.D San Jose City College Kevin.mccandless@sjcc.edu

2. WHAT FACTORS AFFECT STUDENT LEARNING IN BEGINNING ALGEBRA? Examples: effort, teacher style, class times, etc…

3. OBJECTIVES Identify factors that may affect student learning Define and analyze two contrasting methods of instruction and consider a new way of lesson planning Describe research methods that may be used to assess the effectiveness of instruction Describe the demographics of Beginning Algebra students at SJCC and discover that basic-skills mathematics instruction is an equity issue Define personal and situation interest and assess your own levels of interest Define and evaluate two types of mathematical knowledge and consider new ways of assessing your students Define and assess transfer of mathematical knowledge Offer plausible explanations for the results of this study

4. 3-PHASE MODEL OF INSTRUCTION Development (45%) Practice (45%) Closing (10%) LectureIndividualLecture Interactive LecturePairsInteractive Lecture Cooperative Activity Writing Activity

5. VARIED METHOD OF INSTRUCTION Phase2.12.22.3 Development Lecture X Interactive Lecture XX Cooperative Activity X Practice Problems Individually X Problems in Pairs X Cooperative Activity X Closing Lecture X Interactive Lecture X Cooperative Activity Writing Activity X X

6. NON-VARIED METHOD OF INSTRUCTION Phase2.12.22.3 Development Lecture X X X Interactive Lecture Cooperative Activity Practice Problems Individually X X X Problems in Pairs Cooperative Activity Closing Lecture X X X Interactive Lecture Cooperative Activity Writing Activity

7. RESEARCH DESIGN TimeMondayTuesdayWednesdayThursday 9:15 am - 11:40 am Varied 1 Instructor 1 Non-Varied 1 Instructor 1 Varied 1 Instructor 1 Non-Varied 1 Instructor 1 10:45 am - 1:10 pm Non-Varied 2 Instructor 2 Varied 2 Instructor 2 Non-Varied 2 Instructor 2 Varied 2 Instructor 2 12:15 pm - 2:40 pm Varied 3 Instructor 3 Non-Varied 3 Instructor 3 Varied 3 Instructor 3 Non-Varied 3 Instructor 3

8. RESEARCH DESIGN

9. Variable Units 108 6 – 8129 9 - 123335 12 – 154540 > 1509 Employment Unemployed4034 Part-time4544 Full-time1522 Learning Disability78 Retaking Class4552 Completed Prerequisite 4560 Placed in Class3835 Last Math Class 5763 1 – 2 years2117 3 – 4 years1011 > 4 years169

10. Variable Gender Female 44676566 Male 56333534 Age < 20 years old 18293835 20 - 24 years old 3435 25 - 39 years old 33312125 15565 Ethnicity African American 891110 American Indian 1132 Asian 22967 Filipino 4201 Hispanic 39605658 Pacific Islander 1243 White 1716 Unknown 8143

11. SOCIAL PREFERENCES 1. I like working by myself during math class. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 7 6 5 4 3 21 2. Solving math problems in a group is more motivating than working alone. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 1 2 3 4 5 67 3. Working in math groups often wastes my time. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 7 6 5 4 3 2 1 4. During math class, I enjoy working in small groups. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 1 2 3 4 5 67

12. PERSONAL INTEREST 1. Compared to other subjects, I feel relaxed studying mathematics. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 1 2 3 4 5 67 2. Compared to other subjects, mathematics is exciting to me. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 1 2 3 4 5 67 3. I like learning new mathematics concepts. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 1 2 3 4 5 67 4. I do not enjoy working on mathematics problems. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 7 6 5 4 3 21

13. REASONING INTELLIGENCE 1. Letter Series: a b a c a d a e a ____ 2. Letter Sets: Which set does not belong? NOPQ DEFL ABCD HIJK UVWX 3. Figure Analogy:

14. VERBAL INTELLIGENCE 1. Synonyms: IRRATIONAL 2. Sentence Completion: Weather conditions around the world are constantly ________ by satellites.

15. BACKGROUND VARIABLE SUMMARY Variable Social Preference18.35.028.0 Personal Interest 14.95.628.0 Gf Letter Series 5.22.710.0 Letter Sets 8.63.515.0 Figure Analogies5.82.311.0 Gc Synonyms6.62.512.0 Sentence Completions5.72.210.0 Prior Knowledge 34.66.948.0

16. BEGINNING ALGEBRA LEARNING OUTCOMES Upon completion of this course, students should be able to: 1.Perform operations on real numbers using properties of real numbers and appropriate symbols. 2.Simplify and evaluate algebraic expressions, including exponential, polynomial, and rational expressions. 3.Find the equation of a line, graph it, and determine whether two lines are parallel or perpendicular. 4.Solve linear, quadratic, and rational equations and inequalities in one variable, and represent the solution set of the linear inequalities on the number line and using interval notation. 5.Solve systems of linear equations in two variables by graphing, substitution, and addition methods. 6.Solve application problems using systems of linear equations, quadratic, and rational equations.

17. ACHIEVEMENT VARIABLES

18. EXAMPLE ITEMS

19. TRANSFER OF KNOWLEDGE

20. Far Transfer: The ability to apply knowledge to a novel problem in a new context.

21. SITUATIONAL INTEREST 1. Our math class is fun. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 1 2 3 4 5 67 2. I actually look forward to attending math class this semester. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 1 2 3 4 5 67 3. I have not enjoyed going to math class this semester. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 7 6 5 4 3 21

22. PREDICTIONS?!

23. Variable Varied M SD Non-Varied M SD Unit 1 CU 4.22.1 4.02.2 LCPA 7.41.7 7.11.8 HCPA 14.25.2 14.04.8 Unit 2 CU 4.42.1 5.02.5 LCPA 7.02.0 7.42.2 HCPA 9.95.1 11.14.9 Unit 3 CU 3.42.3 3.72.3 LCPA 5.61.6 5.71.6 HCPA 9.15.5 10.26.5 Transfer Near 1.00.9 0.8 Far 2.10.9 2.00.8 Situational Interest 13.13.8 15.13.4

24. CONCLUSIONS Both methods of instruction produced the same (poor) results Students slightly preferred the non-varied method of instruction Preferences for group work and interest in math were uncorrelated with achievement Perhaps we need to consider more significant reforms than methods of instruction? Should we teach the way we like and then bring in support services? Thoughts?

25. LIMITATIONS Study lasted 8 weeks, we may have seen different outcomes after 16 weeks No random assignment, so results don’t necessarily generalize beyond Beginning Algebra courses at SJCC Near and Far Transfer measures each contained one item, so they may no be a robust assessment of knowledge transfer

26. Variable (Varied) 123456789101112 1. Social Preference -- 2. Personal Interest -.18-- 3. Reasoning Ability-.01.05-- 4. Verbal Ability.03-.20.00-- 5. Prior Knowledge-.17-.04.43.17-- 6. Unit 1 Achievement -.22.20.23.27.54-- 7. Unit 2 Achievement -.26.07.24.25.50.78-- 8. Unit 3 Achievement -.05.00.33.31.52.60.70-- 9. Near Transfer.02.04.23.21.38.37.29.49-- 10. Far Transfer-.13.05.19.13.12.30.21.23.32-- 11. Situational Interest.10.27.00-.08.08.04.06.12-.12-.13-- 12. Retention.05 -.07-.12.10.28.29.09.30-.19-.07 --

27. Variable (Non-varied) 123456789101112 1. Social Preference -- 2. Personal Interest.13-- 3. Reasoning Ability.03.10-- 4. Verbal Ability-.35-.32.01-- 5. Prior Knowledge-.15.12.28.25-- 6. Unit 1 Achievement -.07.04.39.25.59-- 7. Unit 2 Achievement -.01-.04.29.30.51.77-- 8. Unit 3 Achievement -.14-.02.38.33.52.71.70-- 9. Near Transfer-.01.02.21.42.34.42.39.44-- 10. Far Transfer-.02-.04-.06.28.03.02.04.00.21-- 11. Situational Interest.02.03.18.01.09.39.32.47.22-.06-- 12. Retention.02.09.07-.19.25.39.36.24.03.08.31 --

28. Variable 1234567891011121314151617181920 21 1. Social Preference.80 2. Personal Interest -.05.87 3. Letter Series-.04-.02.77 4. Letter Sets-.02.10.60.80 5. Figure Analogies.02.01.50.52.56 6. Synonyms-.20-.18.22.19.18.65 7. Sentence Comp-.15-.26.39.25.22.57.67 8. Prior Knowledge -.16.05.36.32.27.21.26.85 9. CU1-.10.03.33.12.31.20.23.32-- 10. LCPA1-.18.14.34.16.32.29.24.56.48.31 11. HCPA1-.10.12.29.18.32.19.22.56.64.66-- 12. CU2-.20.01.21.09.08.14.23.31.56.51.55-- 13. LCPA2-.06.01.33.20.29.36.23.50.51.49.53.49.63 14. HCPA2-.05.01.23.19.23.22.20.45.60.52.68.64 -- 15. CU3-.04-.02.41.35.37.22.37.46.49.41.47.45.56.52-- 16. LCPA3-.10-.09.33.24.20.40.32.36.35.39.38.27.41.30.43.49 17. HCPA3-.12.06.17.15.19.15.42.53.41.59.58.56.71.62.41-- 18. Near Transfer.00.03.30.19.21.30.36.35.33.34.20.34.30.44.29.36-- 19. Far Transfer -.06.01.09.05.09.13.25.07.22.12.07.12.09.12.05.26-- 20. Situational Interest.02.16.02.00.04.01.10.14.17.23.15.22.24.21.26.37.04.08.71 21. Retention.04.07-.05-.03.02.07-.21.18.24.23.33.23.22.38.17.10.19.18-.08.15--