redesign of precalculus mathematics

Redesign of Redesign of Precalculus MathematicsPrecalculus Mathematics

THE UNIVERSITY OF ALABAMATHE UNIVERSITY OF ALABAMACollege of Arts and SciencesCollege of Arts and Sciences

Course Redesign WorkshopCourse Redesign WorkshopOctober 21, 2006October 21, 2006

Redesign of Precalculus Redesign of Precalculus MathematicsMathematics

Setting/Problem Course History Course Format Outcomes

Implementation issues

Cost-Savings Conclusions

SettingSetting

• 6 Precalculus math courses• 6500 students per year• Taught in traditional, lecture-based

setting• Taught entirely by instructors and

GTAs

Course FormatCourse Format

• Courses taught in rigid format• Common syllabus

• Common presentation schedule

• Common tests

ProblemsProblems• Courses teacher centered• No support for multiple learning styles• Inconsistent coverage of topics• No flexibility in instructional pace• Lack of student success

• D/F/W rates as high as 60%• Very high course repeat percentage• Negative impact on student retention• Significant drain on resources

IssuesIssues

• Tenure-track faculty not invested in precalculus courses

• Courses damaging to department’s reputation

• Solutions proposed required significant resources• Smaller class size• Increased support (graders, tutors)

SolutionSolution

• Identify an alternative structure that:• Had faculty and instructor support• Was learner centered• Supported multiple learning styles• Provided consistent presentation of

material• Allowed students to work at own pace• Increased student success• Reduced resource demands

Approach SelectedApproach Selected

• “Math Emporium” model developed by Virginia Tech

• Initial application to Intermediate Algebra (Math 100)• Approximately 1300 students per year

CourseCourseHistoryHistory

Course HistoryCourse History

• Fall 1999Fall 1999

• Visited Virginia Tech

• Began initial planning for course

• course text/software - Intermediate Algebra by Martin-Gay/MyMathLab (Prentice-Hall)

Course HistoryCourse History

• Spring 2000Spring 2000

• Piloted redesigned format in 3 sections of Math 100 (100 students)

Course HistoryCourse History

• Summer 2000Summer 2000• Received $200,000 Pew grant• Assigned a 70-seat computer lab to

course• Established the Mathematics Mathematics

Technology Learning Center (MTLC)Technology Learning Center (MTLC)• Taught 5 sections of Math 100 (130

students) using redesigned format

Course HistoryCourse History

• Fall 2000Fall 2000

• Taught 18 sections of Math 100 in MTLC (1140 students)

1140

Course HistoryCourse History

Sp 00 F00 Sp 01 F 01 Sp 02 F 02 Sp 03 F 03 Sp 04 F 04 Sp 05 F 05 Sp 06

Math 005 P

Math 100 P

Math 110 P P

Math 112 P P P P

Math 121 P P P P P P

Pilot Sections PFull Implementation

Course HistoryCourse History

Sp 00 F00 Sp 01 F 01 Sp 02 F 02 Sp 03 F 03 Sp 04 F 04 Sp 05 F 05 Sp 06

Math 005 P

Math 100 P

Math 110 P P

Math 112 P P P P

Math 121 P P P P P P

Pilot Sections PFull Implementation

CourseCourseFormatFormat

Course FormatCourse Format 30-50 minute “classes” that introduce

students to topics and integrate the topics into the overall course objectives

3-4 hours in MTLC or elsewhere working independently using course software that presents a series of topics covering specific learning objectives

Instructors and tutors available in MTLC 71 hours/week to provide individualized assistance

Course Format (continued)Course Format (continued) Students work homework problems that

cover defined learning objectives Homework is graded immediately by the

computer providing the student with instant feedback on their performance

After completing homework, students take quizzes that cover learning objectives

Course Format (continued)Course Format (continued) Students can do homework and take

quizzes multiple times and receive instant feedback

After completing homework and quizzes on a series of topics, students take a section test

Tests are given only in the MTLC Tests available on demand with a

specified completion date

Fundamental PremiseFundamental Premise

Students learn mathematics by doing mathematics

Advantages of Course FormatAdvantages of Course Format

• Learner centered• Software supports multiple learning

styles• Consistent presentation of material• Individualized tutorial support available

Advantages of Course FormatAdvantages of Course Format

• Students can work at own pace• Students can work in lab or at home• Software provides instant feedback on

work• Homework, quizzes, tests, & exam

computer graded• Software records all student activity

Implementation Implementation IssuesIssues

• Instructor Buy-In• Instructor Training• Detachment From Students• Student Engagement• “No Teacher” Syndrome• Staff Scheduling• Scheduling Deadlines, Tests, Etc.• Data Management

Implementation IssuesImplementation Issues

OutcomesOutcomes

Success RatesSuccess RatesSemester Success Rate Semester Success RateSemester Success Rate Semester Success Rate

Fall 1998 47.1% Spring 1999 44.2% Fall 1999 40.6% Spring 2000 53.5%

Success RatesSuccess RatesSemester Success Rate Semester Success RateSemester Success Rate Semester Success Rate

Fall 1998 47.1% Spring 1999 44.2% Fall 1999 40.6% Spring 2000 53.5%

Fall 2000 50.2% Spring 2001 35.8%

Fall 2001 60.5% Spring 2002 49.8%

Fall 2002 63.0% Spring 2003 41.8%

Fall 2003 78.9% Spring 2004 55.4%

Fall 2004 76.2% Spring 2005 60.1%

Success RatesSuccess RatesSemester Success Rate Semester Success RateSemester Success Rate Semester Success Rate

Fall 1998 47.1% Spring 1999 44.2% Fall 1999 40.6% Spring 2000 53.5%

Fall 2000 50.2% Spring 2001 35.8%

Fall 2001 60.5% Spring 2002 49.8%

Fall 2002 63.0% Spring 2003 41.8%

Fall 2003 78.9% Spring 2004 55.4%

Fall 2004 76.2% Spring 2005 60.1%

Fall 2005 66.7% Spring 2006 56.5%

Outcomes – Outcomes – Grade Distribution*Grade Distribution* SemesterSemester A A B B C CFall 1999 13.1% 32.6% 54.2% Spring 2000 12.7% 34.0% 53.3%Fall 2000 18.0% 41.6% 40.4%Spring 2001 11.0% 24.8% 64.2%Fall 2001 17.4% 41.7% 40.9%Spring 2002 11.0% 36.7% 52.2%Fall 2002 21.5% 40.1% 38.4%Spring 2003 17.0% 28.6% 54.4%Fall 2003 42.3% 38.1% 19.6%Spring 2004 22.1% 36.2% 41.7%

*Percentages of students successful

Math 121Math 121Grade DistributionsGrade Distributions

(Fall 2005 Semester)(Fall 2005 Semester)

A B C D F W

Math 121 T 10.8% 18.6% 21.9% 5.4% 11.9% 31.4%

Math 121 C 17.4% 20.4% 26.9% 11.4% 9.6% 14.4%

Pass Rate Pass Rate (Subsequent Courses)(Subsequent Courses)

CohortCohort MTLCMTLC OverallOverall

F98-Sp99 57.4% 44.3%

F99-Sp00 54.6% 40.0%

F00-Sp01 58.0% 44.5%

F01-Sp02 74.6% 53.8%

F02-Sp03 81.4% 46.6%

Math 112 - PrecalculusMath 112 - Precalculus

Underserved GroupsUnderserved Groups

Pass Rates by Math Pass Rates by Math Placement CategoryPlacement Category

Math Placement Score

Year <200 200-250 >250

98/99 31.5% 45.5% 66.6%

99/00 40.3% 43.8% 63.2%

00/01 32.8% 42.0% 60.6%

01/02 48.9% 53.8% 71.2%

02/03 48.4% 54.9% 62.0%

Pass Rates by GenderPass Rates by Gender(Fall Semesters)(Fall Semesters)

F 98 F 99 F 00 F 01 F 02

Females 54.7% 48.9% 53.0% 66.7% 68.2%

Males 39.1% 31.8% 45.9% 55.8% 57.6%

Overall 47.1% 40.6% 50.2% 60.5% 63.0%

Outcomes By EthnicityOutcomes By Ethnicity

Demographics

Caucasian – 81%

African-American – 15%

Other – 4%

Math Placement ScoresMath Placement Scores

Fall 2001 Placement Level

Mean <200 200-250 >250

African-American 208 41% 31% 28%

Caucasian 230 20% 45% 35%

Pass Rates by EthnicityPass Rates by Ethnicity(Fall Semesters)(Fall Semesters)

F 98 F 99 F 00 F 01 F 02

African-American 46.2% 35.0% 59.4% 60.4% 63.6%

Caucasian 46.9% 41.1% 46.5% 60.7% 62.3%

Overall 47.1% 40.6% 50.2% 60.5% 63.0%

Course PersistenceCourse Persistence

Course PersistenceCourse Persistence(Math 100)(Math 100)

Test 1 Test 2 Test 3 Test 4 Final

Fall 2001 92.4% 89.3% 83.8% 81.6% 78.6%

Fall 2002 92.3% 89.7% 84.7% 79.4% 77.2%

Fall 2003 92.1% 91.2% 88.6% 86.3% 85.8%

Fall 2004 94.4% 92.2% 90.0% 86.6% 86.4%

Fall 2005 93.6% 89.7% 82.7% 79.7% 80.1%

Math 121Math 121Course PersistenceCourse Persistence

(Fall 2005 Semester)(Fall 2005 Semester)

Test 1 Test 2 Test 3 Test 4 Final

Math 121T 88.4% 83.0% 67.0% 64.9% 67.3%

Math 121C 94.6% 92.2% 85.6% 82.6% 81.4%

Cost SavingsCost Savings

2001-2002 Academic Year - 1480 Students43 Sections of 35 Students Each

2 FTTI (16 sections) @ $36,250 $72,5005 GTAs (20 sections) @ $17,565 $87,825 7 PTTI (7 sections) @ $1,655 $11,585

Total Cost $171,910Cost Per Student $116

Traditional Course CostTraditional Course Cost

Redesigned Course CostRedesigned Course Cost

2001-2002 Academic Year - 1480 Students1 Section Each Semester

2 FTTI @ $36,250 $72,5006 PTTI @ $1,655 $9,930UG Tutors 5760 hrs @ $7/hr $40,320

Total Cost $122,750Cost Per Student $83

Cost SavingsCost Savings

Traditional Course $116/studentRedesigned Course $83/studentSavings $33/student (28%)

Cost SavingsCost Savings(Economy of Scale)(Economy of Scale)

955 Students in Math 005 & 112

1 FTTI @ $36,250 $36,250 4 PTTI @ $1,655 $6,620

Total $42,870

$45/student

Cost SavingsCost Savings(Reduction of Course Repeats)(Reduction of Course Repeats)

1480 Students in Math 100

20% increase in success rate = 296 students

296 students @ $116/student = $34,336

Student Perceptions of Student Perceptions of Computer-Based InstructionComputer-Based Instruction

Perceived AdvantagesPerceived Advantages Flexibility in scheduling Ability to move at own pace Instant feedback Availability of individual help Equality of presentation Equality of testing Elimination of language problems

Perceived DisadvantagesPerceived Disadvantages Technical problems frustrating Confusion regarding course policies Lack of a “teacher” Inconsistent availability and quality of

help Necessity of self-discipline

Worked More or Less Worked More or Less Than Traditional CourseThan Traditional Course

Semester More Same Less

Sp 01 33.3% 30.3% 36.4%

Fall 01 46.1% 29.3% 24.6%

Sp 02 43.2% 28.6% 28.2%

Fall 02 42.6% 37.0% 20.4%

Sp 03 37.0% 38.9% 24.1%

For each section, what do For each section, what do you typically do first.you typically do first.

Percent

Learning Activities 5.0%

Practice Problems 9.4%

Graded Homework 81.8%

Quiz 1.7%

Talk With Tutor 1.8%

Learning Compared to Learning Compared to Traditional ClassTraditional Class

Semester Less Same MoreFall 00 18.3% 68.5% 13.2%

Sp 01 40.8% 31.6% 27.6%

Fall 01 28.8% 34.8% 36.4%

Sp 02 32.7% 40.9% 26.4%

Fall 02 24.6% 39.0% 36.4%

Sp 03 35.2% 35.2% 29.6%

Correlation to Active LearningCorrelation to Active Learning

Question Strongly Agree

Tend to Agree

Tend to Disagree

StronglyDisagree

1. This course helped me learn to work through a process to solve math problems

32.5% 47.2% 14.8% 5.5%

2. This course encourages me to take responsibility for my own learning

45.2% 42.3% 8.9% 3.6%

3. This course encourages me to search for answers myself rather than asking others

38.9% 49.9% 7.4% 3.8%

4. It is easy to pay attention in this class

34.0% 46.4% 14.5% 5.1%

University of North Carolina SurveyUniversity of North Carolina Survey

“This course is a good fit with my “This course is a good fit with my learning preferences.”learning preferences.”

Redesign

Strongly Disagree 45.3%

Disagree 21.8%

Neutral 17.3%

Agree 11.7%

Strongly Agree 3.9%

University of North Carolina SurveyUniversity of North Carolina Survey

“This course is a good fit with my “This course is a good fit with my learning preferences.”learning preferences.”

Redesign Traditional

Strongly Disagree 45.3% 26.6%

Disagree 21.8% 54.0%

Neutral 17.3% 17.3%

Agree 11.7% 2.1%

Strongly Agree 3.9% 0.0%

ConclusionsConclusions• Based on our experience, we are confident

that computer-based instruction in precalculus mathematics courses can:• Enhance student learning• Increase success rates, particularly for

underserved students• Reduce resource demands