General Education Assessment in Mathematics Courses: Finding What Works

1. General Education Assessment in Mathematics Courses: Finding What Works Teri Rysz, EdD Teri .Rysz @uc.edu Margaret J. Hager, EdD Margaret.Hager@uc.edu University of Cincinnati Clermont AMATYC Las Vegas, 11/12/2009

2. Beginnings • Summer, 2004 – New Associate Dean of Academics • 6 General Education Math Courses were identified to be assessed. • General Education Course Assessment Plan designed by all attendees.

3. Individual Assignments • Individual Assessment Assignments • Designed for all courses. • Demonstrated Competence • Rubric given to each student along with the assignment.

4. High Hopes • Assignment was to be given to all students in every section. • Instructors would forward responses to Coordinator. • A random sample chosen to be ‘graded’ with rubric previously given to student.

5. Would a Random Sample Work? • My argument was to have the assignments given every quarter to every student, thereby making the process something that instructors would have as a regular part of their syllabus.

6. Feedback • Based on feedback from the first two rounds (with limited instructor buy-in): • Three assignments were tweaked. • It could work, but needed more consistency with all instructors.

7. Changing of the Guard • Current Associate Dean decided that random sections would be assessed. • Coordinator was inconsistent in getting this information to instructors in a timely manner (once given to me in last week of the quarter ).

8. What Happened Next? • Frustrated with the process, and deep into writing a dissertation, I could no longer be involved. • Coordinator was getting paid to do it, but wasn’t following through. • Needed ‘New Blood’: • Dr. Teri Rysz

9. General Education Mathematics Courses at Clermont • Math for Behavioral Sciences I (MATH 136) • Math for Behavioral Sciences II (MATH 137) • Statistics for Health Sciences (MATH 146) • College Algebra I (MATH 173) • Finite Math & Calculus I (MATH 225) • Calculus & Analytic Geometry I (MATH 261)

10. Pilot Study College Algebra I (MATH 173) Search for simple assessment question • 2 major concepts a successful College Algebra I student learns • 10 real world application questions for inverse functions • Colleague asked to choose question to ask students • Question to current College Algebra I instructors

11. First Assessment Question The table lists the total numbers of radio stations in the United States for certain years. a) Determine a linear function f (x) = ax + b that models these data, where x is the number of years since 1950. Plot f (x) and the data on the same coordinate axes. b) Find f-1 (x). Explain the significance of f-1. c) Use f-1 (x) to predict the year in which there were 7,744 radio stations. Compare it with the true value, which is 1975.

12. Rubric • 1 point – f (x)= 201.15x + 2,773 Slope could be anything close to 201.15. • 1 point – f -1 (x)= (x – 2,773)/201.15 If incorrect function in part a, 1 point for correct inverse function from stated function • 1 point – inverse function predicts the year for a given number of radio stations • 1 point – correct year for the inverse function determined or explanation of the process for a correct prediction • 0 points - no correct responses

13. Results Score Count 0 19 1 11 2 3 3 2 4 7 • 42 scores • Mean of 1.2 • 21.4% scored 3 or better

14. Revisions • Graphing extraneous, eliminate plot directions • Because the data was not exactly linear, some students decided a function could not be determined. “Use the number of radio stations in the first and last year to determine an average rate of change for the slope in the function.” • Question was asked with different risk factors • Two sections: question on final exam • One section: review for final exam

15. Expectations for Next Round • Mean of 1.5 (1.2) • 30% (21.4%) score a 3 or better • Subsequent reflection on further editions to the question and/or instruction.

16. Revised Question The table lists the total numbers of radio stations in the United States for certain years. a) Determine a linear function f (x) = ax + b that models these data, where x is the number of years since 1950. Use the first and last year to determine the average rate of change for the slope of the linear function. b) Find f-1 (x). Explain the significance of f-1. c) Use f-1 (x) to predict the year in which there were 7,744 radio stations. Compare it with the true value, which is 1975.

17. Revised Results Score Count 0 9 1 2 2 2 3 1 4 5 • 19 scores • one section “disappeared” • Mean of 1.52 (1.5) • 31.6% (30%) scored 3 or better

18. Plans Mathematics for Behavioral Sciences II • A student observes the spinner below and claims that the color red has the highest probability of appearing since there are two red areas on the spinner. What is your reply? • Rubric • 1 point – compares yellow area to red area • 1 point – yellow has 50% of the area • 1 point – yellow is greater area • 1 point – yellow has higher probability • 0 point – only false statement or no statement is made • Results Score Count 0 4 45 responses 1 8 2 10 Mean is 2.4 3 11 4 12 51.1% scored 3 or better

19. Plans (continued) • Academic Assessment Committee • Mathematics instructors meeting • Full time and adjunct • Improves instruction → improves learning • Collaborate and cooperate to learn from results • Continue building assessment coverage and on-time reports