1. Improving Success Rates in Calculus Bridging and Testing Don Allen Texas A&M University College Station, TX 77843 dallen@math.tamu.edu

2. Types of Bridging Conceptual bridging – Creating interest, e.g. non-STEM → STEM, summer camps Transitional bridging – Preparing students for the next venue, e.g. as in a continuation courses, as in transferring from community college to 4 yr college Remedial bridging – Getting under-prepared students ready for the collegiate level NSF STEP November 12, 2014

3. Mini Bridging, Calc I →Calc II Concept: Run an online one week session reviewing Calculus I concepts for under performing students enrolled in Calculus II. – Target – Recruiting – Sign up – Format – Tutors – Curriculum – Results NSF STEP November 12, 2014

4. Mini Bridging Targets – students receiving a grade of “C” or “B” in Calculus I. Recruiting – email sent to all such students Sign-up – created a sign-up page for students to enroll. – Turnout was huge > 150 – Asked students to confirm. NSF STEP November 12, 2014

5. Challenges to Bridging Convincing students they need to improve mathematics skills Students with borderline scores especially at risk Less than half the qualified students choose to participate NSF STEP November 12, 2014

6. Texas A&M Bridge Programs History Precalculus Summer Bridge Program – 36 hours over 6 weeks – 6 hours per week of live online tutoring – 4 categories of algebra & precalculus topics – Imitation primary method of solving problems – 500 students participated over 4 years, with average scores increases about 7 points on a total of 33 points Bridge to Engineering Calculus II – 15 hours of online tutoring in one week – Focused on derivative rules, integration, partial fractions, optimization – Grades increased for those who spent >820 minutes – More analysis to be done NSF STEP November 12, 2014

7. New Bridge to Engineering Calculus I Students who met MPE cut score eligible Students from longer precalculus bridge eligible 15 hours live online tutoring in one week Focused on trigonometry, parametric equations, and vectors Critical online features: – Live online tutoring – Ability of tutors and students to talk online – Online breakout rooms for collaborative groups to solve problems – Recordings of sessions for students to watch – Additional problems sets for practice – Videos over topics made available NSF STEP November 12, 2014

8. Format – very interactive Instructor does about 15-20 minutes of explaining with examples. Instructor gives the class about 10-15 minutes to work on similar problems. One can be routine and the other more challenging. Students return to the class online, and instructor elicits what she can from the students and what they did, but then gives a clear solution to all. (Many students do not understand other students. ) This should take about 45-50 minutes. Now give some more homework-type problems and a short break. reconvene for the second hour. Repeat with different materials. NSF STEP November 12, 2014

9. Format – very interactive Fully online mediated by WebMeeting Three hour sessions – Two in the morning 9-12 – Two in the afternoon 2-5 Live tutor Students given full instructions on how to log in. All sessions are recorded. Facebook active NSF STEP November 12, 2014

10. Curriculum Hourly Plans for Bridge to Math 152 Day 1: Hour 1 – Derivative rules with algebraic functions Hour 2 – Derivative rules with exponential and logarithmic functions Hour 3 – Derivative rules with trig functions Day 2: Hour 1 – Derivative rules with inverse trig functions Hour 2 – Trig identity rewrites (recognize trig derivatives as part of trig statements/expressions) Hour 3 – Right triangle trig prep for trig sub integrals Day 3: Hour 1 – Basic integration Hour 2 – Integration with u-substitution Hour 3 – Integration with trig, exponential and logarithmic functions Day 4: Hour 1 – Partial fraction decomposition Hour 2 – Integration with inverse trig functions Hour 3 – Definite integration with change of limits Day 5: Hour 1 – Properties from derivatives (critical points, inc/dec, concavity, etc.) Hour 2 – Algebra for calculus Hour 3 – Limit rule refresher NSF STEP November 12, 2014

11. Tutors Very experienced calculus teachers None from Texas A&M No professors Well versed in teaching methods online Important to have an overall manager NSF STEP November 12, 2014 Our Tutors: Jill Nichols Ebru Ö zbay Sharon Sledge

12. Notes Students were remarkably weak on how to work with trig functions – esp. for integration – Formulas – Identities It was sometimes difficult to get students to interact. There was a constant chat during the sessions. NSF STEP November 12, 2014

13. Results NSF STEP November 12, 2014 Approximately how many hours did you spend this week either attending the sessions or watching the recorded sessions?

14. Results The class was about evenly split between C and B Calculus I students. Students overwhelmingly were complimentary of their tutor. Students overwhelming feel better prepared for Calculus II. There was enhanced awareness of the need for study. NSF STEP November 12, 2014

15. New Bridge to Engineering Calculus I Students who met MPE cut score eligible Students from longer precalculus bridge eligible 15 hours live online tutoring in one week Focused on trigonometry, parametric equations, and vectors Critical online features: – Live online tutoring – Ability of tutors and students to talk online – Online breakout rooms for collaborative groups to solve problems – Recordings of sessions for students to watch – Additional problems sets for practice – Videos over topics made available NSF STEP November 12, 2014

16. New Bridge to Engineering Calculus I Students who met MPE cut score eligible Students from longer precalculus bridge eligible 15 hours live online tutoring in one week Focused on trigonometry, parametric equations, and vectors Critical online features: – Live online tutoring – Ability of tutors and students to talk online – Online breakout rooms for collaborative groups to solve problems – Recordings of sessions for students to watch – Additional problems sets for practice – Videos over topics made available NSF STEP November 12, 2014

17. Results Students overwhelmingly felt the Bridging programs helped them – Refine their knowledge – Recall previous skills. Students were equally split on whether they would be willing to enroll if a fee was charged. NSF STEP November 12, 2014

18. ? Questions