1. Investigating student outcomes in beginning algebra
Kevin L. McCandless, Ed.D
San Jose City College

2. 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

3. 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

4. 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

5. 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

6. 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
years old
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

7. Research design

8. Social Preferences 1. I like working by myself during math class.
Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree  
2. Solving math problems in a group is more motivating than working alone.  
3. Working in math groups often wastes my time.  
4. During math class, I enjoy working in small groups.

9. Personal interest
1. Compared to other subjects, I feel relaxed studying mathematics.
Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree  
2. Compared to other subjects, mathematics is exciting to me.  
3. I like learning new mathematics concepts.
4. I do not enjoy working on mathematics problems.

10. 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:

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

12. Background Variable Summary𝑀 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

13. 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.

14. Achievement Variables

15. 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

16. 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

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

18. 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

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

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

21. 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

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

23. 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

24. 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

25. 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

26. 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?

27. 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