INVESTIGATING STUDENT OUTCOMES IN BEGINNING ALGEBRA Kevin L. McCandless, Ed.D San Jose City College

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%) LectureIndividualLecture Interactive LecturePairsInteractive Lecture Cooperative Activity Writing Activity

VARIED METHOD OF INSTRUCTION Phase 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

NON-VARIED METHOD OF INSTRUCTION Phase 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

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

RESEARCH DESIGN

Variable Units – – > 1509 Employment Unemployed4034 Part-time4544 Full-time1522 Learning Disability78 Retaking Class4552 Completed Prerequisite 4560 Placed in Class3835 Last Math Class – 2 years – 4 years1011 > 4 years169

Variable Gender Female Male Age < 20 years old years old years old Ethnicity African American American Indian 1132 Asian Filipino 4201 Hispanic Pacific Islander 1243 White 1716 Unknown 8143

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

PERSONAL INTEREST 1. Compared to other subjects, I feel relaxed studying mathematics. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree Compared to other subjects, mathematics is exciting to me. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree I like learning new mathematics concepts. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree I do not enjoy working on mathematics problems. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree

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 Variable Social Preference Personal Interest Gf Letter Series Letter Sets Figure Analogies Gc Synonyms Sentence Completions Prior Knowledge

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

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 I actually look forward to attending math class this semester. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree I have not enjoyed going to math class this semester. Strongly Disagree Disagree Disagree Somewhat Neutral Agree Somewhat Agree Strongly Agree

PREDICTIONS?!

Variable Varied M SD Non-Varied M SD Unit 1 CU LCPA HCPA Unit 2 CU LCPA HCPA Unit 3 CU LCPA HCPA Transfer Near Far Situational Interest

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) Social Preference Personal Interest Reasoning Ability Verbal Ability Prior Knowledge Unit 1 Achievement Unit 2 Achievement Unit 3 Achievement Near Transfer Far Transfer Situational Interest Retention

Variable (Non-varied) Social Preference Personal Interest Reasoning Ability Verbal Ability Prior Knowledge Unit 1 Achievement Unit 2 Achievement Unit 3 Achievement Near Transfer Far Transfer Situational Interest Retention

Variable Social Preference Personal Interest Letter Series Letter Sets Figure Analogies Synonyms Sentence Comp Prior Knowledge CU LCPA HCPA CU LCPA HCPA CU LCPA HCPA Near Transfer Far Transfer Situational Interest Retention