Improving Success Rates in Calculus Bridging and Testing Don Allen Department of Mathematics Texas A&M University College Station, TX

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 Remediational bridging – Getting under-prepared students ready for the collegiate level Min-Bridging2

General Outline College Readiness exam Math Placement exam The TAMU success story – Features – Results – Plans for the future Mini-bridging Min-Bridging3

College Readiness Basic Algebra Exam – rather technical Location: p?id=215 p?id=215 You can sign up for a section, and point your students to it. You will control access. Min-Bridging4

Math Placement Exam (MPE) 33 question test substantially on pre-calculus topics. Available through WebAssign – licensing contracts should be available soon. Used at Texas A&M since Thousands of students have taken this exam. Minimal score for placement into Calculus I is 22/33 – now required Min-Bridging5

Riddle Min-Bridging6 Suppose you have a wonderful remediation program for students, and they don’t take it. The riddle is why? Too busy? Don’t care? Don’t think they need it?

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 Min-Bridging7

Mini Bridging Targets – students receiving a grade of “C” or “B” in Calculus I. Recruiting – sent to all such students Sign-up – created a sign-up page for students to enroll. – Turnout was huge > 150 – Asked students to confirm. Min-Bridging8

Format – very interactive Instructor does about minutes of explaining with examples. Instructor gives the class about 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 minutes. Now give some more homework-type problems and a short break. reconvene for the second hour. Repeat with different materials. Min-Bridging9

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 Min-Bridging10

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 Min-Bridging11

Tutors Very experienced calculus teachers None from Texas A&M No professors Well versed in teaching methods online Important to have an overall manager Min-Bridging12 Our Tutors: Jill Nichols Ebru Ö zbay Sharon Sledge

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. Min-Bridging13

Results Min-Bridging14 Approximately how many hours did you spend this week either attending the sessions or watching the recorded sessions?

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. Min-Bridging15

Results Students overwhemingly 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. Min-Bridging16

Results Min-Bridging17 Last semester in Calculus (check all that apply)

Results Min-Bridging18 Technology issues

Engagement by Times Min-Bridging19 82% attendance rate!

Results Students overwhelmingly desire there should be a bridging program Calculus II → Calculus III At this point we do not know if this program will actually improve student scores. The difficulty of making this measurement is huge. Min-Bridging20

What You Need People with skill in math, technology, data analysis, survey creation, working with students An indefatigable director Skill with IRB’s Excellent tutors/peers Department/Administrative support Min-Bridging21

Questions? Min-Bridging22