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