Investigating student outcomes in beginning algebra Kevin L. McCandless, Ed.D San Jose City College Kevin.mccandless@sjcc.edu

Varied method of instruction Phase 2.1 2.2 2.3 Development Lecture X   Interactive Lecture Cooperative Activity Practice Problems Individually Problems in Pairs Closing Writing Activity

Non-Varied method of instruction Phase 2.1 2.2 2.3 Development Lecture X  X Interactive Lecture   Cooperative Activity Practice Problems Individually Problems in Pairs Closing Writing Activity

Research design Time Monday Tuesday Wednesday Thursday 9:15 am - 11:40 am Varied 1 Instructor 1 Non-Varied 1 10:45 am - 1:10 pm Non-Varied 2 Instructor 2 Varied 2 12:15 pm - 2:40 pm Varied 3 Instructor 3 Non-Varied 3

Variable Varied (𝑛=61) Non-Varied (𝑛=78) Units   ≤ 5 10 8 6 – 8 12 9 9 - 12 33 35 12 – 15 45 40 > 15 Employment Unemployed 34 Part-time 44 Full-time 15 22 Learning Disability 7 Retaking Class 52 Completed Prerequisite 60 Placed in Class 38 Last Math Class < 1 year 57 63 1 – 2 years 21 17 3 – 4 years 11 > 4 years 16

Variable College-Wide (𝑛=13,750) Varied (𝑛=61) Non-Varied (𝑛=78) Total Sample (𝑛=139) Gender   Female 44 67 65 66 Male 56 33 35 34 Age < 20 years old 18 29 38 20 - 24 years old 25 - 39 years old 31 21 25 ≥ 40 years old 15 5 6 Ethnicity African American 8 9 11 10 American Indian 1 3 2 Asian 22 7 Filipino 4 Hispanic 39 60 58 Pacific Islander White 17 16 Unknown

Research design

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 2 1 2. Solving math problems in a group is more motivating than working alone.   1 2 3 4 5 6 7 3. Working in math groups often wastes my time.   7 6 5 4 3 2 1 4. During math class, I enjoy working in small groups. 1 2 3 4 5 6 7

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 6 7 2. Compared to other subjects, mathematics is exciting to me.   1 2 3 4 5 6 7 3. I like learning new mathematics concepts. 4. I do not enjoy working on mathematics problems. 7 6 5 4 3 2 1

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:

Verbal intelligence 1. Synonyms: IRRATIONAL 2. Sentence Completion: Weather conditions around the world are constantly ________ by satellites.

Background Variable Summary 𝑀 𝑆𝐷 𝑀𝑎𝑥 Social Preference 18.3 5.0 28.0 Personal Interest 14.9 5.6 Gf   Letter Series 5.2 2.7 10.0 Sets 8.6 3.5 15.0 Figure Analogies 5.8 2.3 11.0 Gc Synonyms 6.6 2.5 12.0 Sentence Completions 5.7 2.2 Prior Knowledge 34.6 6.9 48.0

Beginning Algebra learning outcomes Upon completion of this course, students should be able to: Perform operations on real numbers using properties of real numbers and appropriate symbols. Simplify and evaluate algebraic expressions, including exponential, polynomial, and rational expressions. Find the equation of a line, graph it, and determine whether two lines are parallel or perpendicular. 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. Solve systems of linear equations in two variables by graphing, substitution, and addition methods. Solve application problems using systems of linear equations, quadratic, and rational equations.  

Achievement Variables

Example Items Conceptual Understanding Give an example of a linear equation in one variable whose solution is 2. Explain the difference between a solution to a linear equation in one variable and a solution to a linear equation in two variables. Procedural Application (low complexity and high complexity) Solve for 𝑤. (multiple-choice) 𝐴=𝑙𝑤 Solve. (short-answer) 4 3𝑥−2 −32=8𝑥−4

Transfer of Knowledge Near Transfer: The ability to apply knowledge to a novel problem in a similar context. Solve the system of equations by graphing and justify your answer in one or two sentences. 𝑦=5−2𝑥 𝑦=3𝑥−1 𝑦= 1 2 𝑥−3

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

Situational interest 1. Our math class is fun. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree   2. I actually look forward to attending math class this semester. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 3. I have not enjoyed going to math class this semester. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree

Modified Situational interest 1. This presentation has been fun. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree   1 2 3 4 5 6 7 2. I actually look forward to attending another presentation by this speaker. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree   1 2 3 4 5 6 7 3. I have not enjoyed this guy’s presentation. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree 7 6 5 4 3 2 1

Non-Varied Instruction PREDICTIONS?! Varied Instruction >, <, or =? Non-Varied Instruction Conceptual Understanding Low-Complexity Procedural High-Complexity Procedural Near Transfer Far Transfer Situational Interest

  Variable  Varied M SD Non-Varied M SD Max Unit 1 CU 4.2 2.1 4.0 2.2 10 LCPA 7.4 1.7 7.1 1.8 HCPA 14.2 5.2 14.0 4.8 20 Unit 2 4.4 5.0 2.5 7.0 2.0 9.9 5.1 11.1 4.9 Unit 3 3.4 2.3 3.7 5.6 1.6 5.7 8 9.1 5.5 10.2 6.5 22 Transfer Near 1.0 0.9 0.8 3 Far Situational Interest 13.1 3.8 15.1 21

Non-Varied Instruction Results Varied Instruction >, <, or =? Non-Varied Instruction Conceptual Understanding = Low-Complexity Procedural High-Complexity Procedural Near Transfer Far Transfer Situational Interest <

Variable (Varied) 1 2 3 4 5 6 7 8 9 10 11 12 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 .33 .31 .52 .60 .70 9. Near Transfer .02 .04 .21 .38 .37 .29 .49 10. Far Transfer -.13 .19 .13 .12 .30 .32 11. Situational Interest .10 -.08 .08 .06 -.12 12. Retention -.07 .28 .09 -.19

Variable (Non-varied) 1 2 3 4 5 6 7 8 9 10 11 12 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 .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 .02 .21 .42 .34 .44 10. Far Transfer -.06 .00 11. Situational Interest .18 .09 .32 .47 .22 12. Retention .07 -.19 .36 .24 .08 .31

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 Prior knowledge was best predictor of success

discussion 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 and pathways? Thoughts?

Variable 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 1. Social Preference .80   2. Personal Interest -.05 .87 3. Letter Series -.04 -.02 .77 4. Letter Sets .10 .60 5. Figure Analogies .02 .01 .50 .52 .56 6. Synonyms -.20 -.18 .22 .19 .18 .65 7. Sentence Comp -.15 -.26 .39 .25 .57 .67 8. Prior Knowledge -.16 .05 .36 .32 .27 .21 .26 .85 9. CU1 -.10 .03 .33 .12 .31 .20 .23 -- 10. LCPA1 .14 .34 .16 .29 .24 .48 11. HCPA1 .64 .66 12. CU2 .09 .08 .51 .55 13. LCPA2 -.06 .49 .53 .63 14. HCPA2 .45 .68 15. CU3 .41 .35 .37 .46 .47 16. LCPA3 -.09 .40 .38 .30 .43 17. HCPA3 -.12 .06 .17 .15 .42 .59 .58 .71 .62 18. Near Transfer .00 .44 19. Far Transfer .13 .07 20. Situational Interest .04 21. Retention -.03 -.21 -.08