Precalculus to Calculus: Insights & Innovations

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2 MATHEMATICAL ASSOCIATION OF AMERICA CSPCC, NSF # Precalculus to Calculus: Insights & Innovations David Bressoud St. Paul, MN University of Saint Thomas Saint Paul, MN June 16, 2016 PDF file of these slides available at

3 Today we teach greater numbers of students, who are less prepared, using fewer resources, and with increased expectations for student success.

4 insights andrecommendations fromthe maa nationalstudyof college calculus Bressoud, Mesa, & Rasmussen (eds.) Insights and Recommendations from the MAA National Study of College Calculus. EDITORS DAVID BRESSOUD VILMA MESA CHRIS RASMUSSEN Chapters describing best practices in Placement Student support maa.org/cspcc Pedagogy Departmental dynamics Preparation for teaching for graduate students

5 8 Features of Successful Calculus Programs 1- Attention to placement issues 2- Attention to local data 3- Support for active learning 4- Coordination of courses 5- Regular meetings of course instructors 6- Solid GTA professional development 7- Strong student support services 8- Rigorous courses

6 DUE I-USE # PI: David Bressoud co-pi s and senior personnel: Chris Rasmussen San Diego State Jess Ellis Colorado State Estrella Sean Johnson Larsen Virginia Portland Tech State Linda Braddy Tarrant County College

7 Spring 2015, surveys on the precalculus through single variable calculus sequence sent to all 330 US math departments offering a graduate degree in mathematics. Response rates: PhD departments: 134/178 = 75% MA departments: 89/152 = 59% Overall: 223/330 = 68%

8 DFW rates PhD Masters Precalculus 27% 28% Calculus I 21% 24% Calculus II 18% 24% = = 0.42

9 Varia-on PhD (133) MA(89) Precalc over 2 semesters as option Precalc contemporaneous with calculus 2 1 Stretched out Calculus I 13 7 Stretched out Calculus 1 & Calculus infused with precalculus 7 4 Mainstream Calculus for biology 11 4 Mainstream Calculus for engineering 14 0 Mainstream Calc for another subject 3 0 Calculus for first-timers 1 0 Accelerated/AP Calculus 12 2 Transition to mainstream 2 1

10 Successful CC UCC GTAT SSP 0.20 UoD 0.10 AL RIM Important Weighted average of responses: very important or successful, +1 somewhat, 0 not important or successful, 1 SP UCC = uniform course components CC = challenging courses GTAT = graduate teaching assistant training SSP = student support programs SP = student placement RIM = regular instructor meezngs UoD = use of data AL = aczve learning

11 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% What is important vs where they are successful PhD programs very important very successful

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13 Percentage of respondents using placement tool (could select multiple placement tools) 70% 60% 50% 40% 30% 20% 10% 0% PhD Masters

14 From 2010 to 2015, use of ALEKS for placement at universities with PhD programs has jumped from 10% to 28%. Adaptive questioning Includes focused instructional modules Opportunities for retesting Does not use multiple choice questions

15 120 Number (out of 223) using each placement tool With degree of overall satisfaction with placement SaZsfied Adequate, could be improved DissaZsfied

16 Across all placement instruments 9% are not satisfied 39% consider them adequate, but could be improved 30% are currently replacing or have recently replaced their placement instrument(s) 29% are considering changing their placement instruments

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18 Tutoring centers (TCs) and support services PhD Masters University-run TC just for math 32% 46% Department run TC 82% 72% Space in math bldg for students 56% 56% Practice exams 46% 14% Optional supplemental instruction 40% 37% Online resources for review 38% 35% Resources for at-risk students 33% 30% Arrange study groups outside dept 22% 18% Online tutoring 9% 14%

19 Use of undergraduates in student support PhD Masters Tutors 74% 89% Graders 54% 54% Leaders of supplemental instruction 29% 36% Recitation leaders 24% 14% Leaders of review sessions 17% 12%

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21 Primary style of instruczon for Mainstream Calculus Lecture + CBI 3% Other 13% Mainly aczve learning 3% Some aczve learning 18% Lecture 63% 35% of surveyed universities are using active learning in at least some sections Some aczve learning (e.g. clickers), mostly lecture Mainly aczve learning (e.g. flipped classes), minimal lecture CBI = Computer based instruczon Other includes too much variazon to specify one style

22 Kober, N Reaching Students: What research says about effective instruction in undergraduate science and engineering. National Research Council Search for Reaching Students at nap.edu

23 Saxe, K., & Braddy, L A Common Vision for Undergraduate Mathematical Science Programs in Joint report of AMATYC, AMS, ASA, MAA, SIAM. Search for Common Vision at maa.org

24 Catherine Fry (ed.) Achieving Systemic Change: A sourcebook for advancing and funding undergraduate STEM education. AAC&U Outcome of a workshop organized by CRUSE*, hosted by AAAS, and supported by the Alfred P. Sloan Foundation and the Research Corporation for Science Advancement aacu.org/pkal/sourcebook *CRUSE: Coalition for the Reform of Undergraduate STEM Education

25 Graduate Teaching Assistant (GTA) training University-wide GTA training? PhD Masters Yes, required 35% 14% Yes, strongly recommended 15% 7% Yes, not strongly recommended 14% 2% Department-specfic GTA training at 83% of PhD and 47% of Masters universizes

26 When is GTA teacher training done? (mark all that apply) PhD Masters Before first time teaching 88% 85% During first term teaching 53% 53% During second term teaching 19% 20% Continues beyond first two terms 17% 28%

27 What is the primary format of the main GTA training aczvity? (mark all that apply) PhD Masters Short workshop/orientation 25% 36% One full-day workshop 13% 21% Multi-day workshop 35% 26% Term-long course or seminar 62% 44% Occasional seminars or workshops 17% 13%

28 What is the primary acizvty to provide GTA with feedback on teaching? (mark all that apply) PhD Masters Practice teaching 74% 50% Observation by experienced instructor 76% 73% Observation by experienced GTA 33% 9% Paired with mentor 35% 39% Video-taped for review by experienced instructor or mentor 20% 0%

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30 Access to and use of local data Department has: PhD Masters No access 5% 5% Not readily available 48% 52% Department regularly reviews: PhD Masters Grades 89% 86% Student evaluations 87% 76% Communication with client disciplines 50% 9% Correlation with previous grades 49% 43% Adherence to placement 45% 41% Persistence 41% 41% Student exit interviews 19% 17%

31 Access to and use of local data Department has: PhD Masters No access 5% 5% Not readily available 48% 52% Department regularly reviews: PhD Masters Grades 89% 86% Student evaluations 87% 76% Communication with client disciplines 50% 9% Correlation with previous grades 49% 43% Adherence to placement 45% 41% Persistence 41% 41% Student exit interviews 19% 17%

32 Next Stages: Creation of networks of universities sharing common concerns, insights, successes, and failures. Identification of twelve universities for detailed three-year study of efforts to improve the effectiveness of the precalculus/calculus sequence. A pdf file of this PowerPoint is available at