INVESTIGATING STUDENT OUTCOMES

IN BEGINNING ALGEBRA

Kevin L. McCandless, Ed.DSan Jose City CollegeKevin.mccandless@sjcc.edu

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

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

3-PHASE MODEL OF INSTRUCTION

Development(45%)

Practice(45%)

Closing(10%)

Lecture Individual Lecture

Interactive Lecture Pairs Interactive Lecture

Cooperative Activity Cooperative Activity Cooperative Activity

Writing Activity

VARIED METHOD OF INSTRUCTION

Phase 2.1 2.2 2.3DevelopmentLecture X    Interactive Lecture   X XCooperative Activity X    PracticeProblems Individually   X  Problems in Pairs X    Cooperative Activity     XClosingLecture   X  Interactive Lecture     XCooperative Activity      Writing Activity X   X

NON-VARIED METHOD OF INSTRUCTION

Phase 2.1 2.2 2.3DevelopmentLecture X  X  XInteractive Lecture  Cooperative Activity    PracticeProblems Individually X  X  XProblems in Pairs    Cooperative Activity    ClosingLecture X  X  XInteractive Lecture    Cooperative Activity      Writing Activity  

RESEARCH DESIGNTime Monday Tuesday Wednesday Thursday

9:15 am - 11:40 am

Varied 1Instructor 1

Non-Varied 1Instructor 1

Varied 1Instructor 1

Non-Varied 1Instructor 1

10:45 am - 1:10 pm

Non-Varied 2Instructor 2

Varied 2Instructor 2

Non-Varied 2Instructor 2

Varied 2Instructor 2

12:15 pm - 2:40 pm

Varied 3Instructor 3

Non-Varied 3Instructor 3

Varied 3Instructor 3

Non-Varied 3 Instructor 3

RESEARCH DESIGN

VariableVaried Non-Varied

Units     5 10 8

6 – 8 12 99 - 12 33 35

12 – 15 45 40> 15 0 9

EmploymentUnemployed 40 34

Part-time 45 44Full-time 15 22

Learning Disability 7 8

Retaking Class 45 52CompletedPrerequisite 45 60

Placed in Class 38 35Last Math Class    

1 year 57 631 – 2 years 21 173 – 4 years 10 11

> 4 years 16 9

Variable

College-Wide Varied

Non-Varied

Total Sample

Gender        Female 44 67 65 66Male 56 33 35 34

Age        < 20 years old 18 29 38 35

20 - 24 years old 34 35 35 35

25 - 39 years old 33 31 21 25

40 years old 15 5 6 5Ethnicity        African American 8 9 11 10

American Indian 1 1 3 2

Asian 22 9 6 7Filipino 4 2 0 1Hispanic 39 60 56 58Pacific Islander 1 2 4 3

White 17 16 16 16Unknown 8 1 4 3

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.

Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree

  1 2 3 4 5 6 7

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 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. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree

  1 2 3 4 5 6 7

3. I like learning new mathematics concepts. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree

  1 2 3 4 5 6 7

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 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

VariableSocial Preference 18.3 5.0 28.0Personal Interest 14.9 5.6 28.0

Gf      Letter Series 5.2 2.7 10.0

Letter Sets 8.6 3.5 15.0

Figure Analogies 5.8 2.3 11.0Gc      Synonyms 6.6 2.5 12.0Sentence Completions 5.7 2.2 10.0

Prior Knowledge 34.6 6.9 48.0

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.

 

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

Solve for

Solve

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.

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

  1 2 3 4 5 6 7

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 6 7

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 2 1

PREDICTIONS?!

 Variable 

VariedM SD

  

Non-Varied

M SDUnit 1            CU   4.2 2.1   4.0 2.2LCPA   7.4 1.7   7.1 1.8HCPA   14.2 5.2   14.0 4.8

Unit 2            CU   4.4 2.1   5.0 2.5LCPA   7.0 2.0   7.4 2.2HCPA   9.9 5.1   11.1 4.9

Unit 3            CU   3.4 2.3   3.7 2.3LCPA   5.6 1.6   5.7 1.6HCPA   9.1 5.5   10.2 6.5

Transfer            Near   1.0 0.9   0.9 0.8Far   2.1 0.9   2.0 0.8

Situational Interest

  13.1 3.8   15.1 3.4

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?

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

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 .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 .05 -.07 -.12 .10 .28 .29 .09 .30 -.19 -.07 --

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 .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 --

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 -.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 .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 .15 .42 .53 .41 .59 .58 .56 .71 .62 .41 --        

                                           18. Near Transfer .00 .03 .30 .19 .21 .30 .30 .36 .35 .33 .34 .20 .34 .30 .44 .29 .36 --      

19. Far Transfer

-.06

.01 .09 .05 .09 .13 .25 .07 .07 .22 .12 .07 .12 .12 .09 .12 .05 .26 --    

20. Situational Interest

.02 .16 .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 -.0

8 .15 --