improving success rates in calculus bridging and testing don allen texas a&m university college...

Improving Success Rates in CalculusBridging and Testing

Don AllenTexas A&M University

College Station, TX [email protected]

NSF STEP November 12, 2014

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


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


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.


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


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


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


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.


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


CurriculumHourly Plans for Bridge to Math 152• Day 1:

Hour 1 – Derivative rules with algebraic functionsHour 2 – Derivative rules with exponential and logarithmic functionsHour 3 – Derivative rules with trig functions

Day 2:Hour 1 – Derivative rules with inverse trig functionsHour 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 integrationHour 2 – Integration with u-substitutionHour 3 – Integration with trig, exponential and logarithmic functions

Day 4:Hour 1 – Partial fraction decompositionHour 2 – Integration with inverse trig functionsHour 3 – Definite integration with change of limits

Day 5:Hour 1 – Properties from derivatives (critical points, inc/dec, concavity, etc.)Hour 2 – Algebra for calculusHour 3 – Limit rule refresher


Tutors

• Very experienced calculus teachers• None from Texas A&M• No professors• Well versed in teaching methods online• Important to have an overall manager

Our Tutors:Jill Nichols

Ebru ÖzbaySharon 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.


Results

11.67%7

3.33%2

5%3

8.33%5

66.67%40

5%3

Total 60

0-3 hours (1 day)

4-6 hours (2 days)

7-9 hours (3 days)

10-12 hours (4 days)

13-15 hours (5 days)

more than 15 hours

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.


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


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.


?Questions

improving success rates in calculus bridging and testing don allen texas a&m university college...

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