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Evolution of Math Undergraduate Education for the Physical Sciences Peter Turner, Clarkson University John Bailer, Miami University Paul Zorn, St. Olaf College The First Two Years of College Math: Building Student Success STEM Readiness, Modeling, Computational Science Statistics and statistical modeling INGenIOuS and workforce issues

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Evolution of Math Undergraduate Education for the Physical Sciences STEM Readiness, Modeling and Computational Science The First Two Years of College Math: Building Student Success Peter Turner SIAM Vice President for Education Dean of Arts & Sciences, Professor of Mathematics and Computer Science, Clarkson University pturner@clarkson.edupturner@clarkson.edu vpeducation@siam.orgvpeducation@siam.org

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Key issues: Some of them PCAST Engage to Excel The Math Gap Preparation & Readiness for STEM majors CU STEM admissions data Outdated curricula and delivery methods Math 2025 “Real-life” relevant content Student “demands” for relevant education BUT with care over “training vs. education” CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 3

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Background to STEM Readiness Problem Budget is dominated by tuition Close to 90% STEM majors Long-established demanding curriculum had little flexibility No remedial/catch up courses available in regular program Calculus, Physics and Chemistry (I & II) all in First Year Started to change in early 2000’s Predictor-Corrector-Refinement model CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 4 Retention is a high priority Near-unique institution facing common issues Small scale makes us nimble

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The elevator pitch! CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 5 “Dismissed” means for academic reasons only What we’re doing is working! Note that “treatments” have been focused primarily on ENG/STEM majors so far.

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STEM Readiness Major issue even for highly selective, STEM- intensive colleges Clarkson has close to 65% of incoming STEM majors under-prepared in Math Based on diagnostic test of pre-calc skills Expectation of starting in Calc I (or higher) Used in conjunction with a Physics concept survey (FCI) to give a highly predictive two- dimensional model of STEM readiness Advising tool for “placement” CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 6

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STEM Readiness Just a part of a comprehensive retention program Includes Spatial Visualization Writing assessment Counseling and non-academic advising, too 92% first-year retention in Fall 2013 cohort Adding more hands-on experiences in first year Teach the students you have Add relevance and “real-life” projects Connect the dots CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 7

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The Curriculum: What is being done? Multiple initiatives in the Math Sciences community Modeling across the Curriculum TPSE-Math MAA-led Common Vision for Undergraduate Math in 2025 Computational Science & Engineering Future Workshop GAISE (Statistics assessment) SIAM & COMAP are collaborating on a similar initiative in Math Modeling, GAIMME CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 8

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Modeling across the Curriculum CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 9 NSF/EHR/DUE Awards 1206230 & 1352973, Education and Human Resources Directorate

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MaC I Recommendations Undergraduate programs Develop modeling-based undergraduate curricula Advocate an infusion model, “Trojan mice” Addresses the PCAST Math Gap Opportunities for coordinated approach to math and science teaching Studio Calculus project CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 10

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MaC I Recommendations Undergraduate programs Develop a repository of materials for math modeling instruction and understanding No organized progress yet Similar theme emerged at TPSE Math Distinction between Models and Modeling Not just math majors CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 11

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Some MaC II undergrad recommendations* Proposal for NRC Study/Report Response to Joan Ferrini-Mundy’s Challenge to think about effective ways to educate students at the crossroads of: Mathematical modeling Data science Information science Computational science Computational thinking CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 12 * Credit to Jeff Humpherys for some of this content

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CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 13 SIAM Working Group On CSE Undergraduate Education (Turner and Petzold, co-chairs) Undergraduate Computational Science and Engineering Education, SIAM REVIEW Vol. 53, No. 3, pp. 561–574 http://epubs.siam.org/doi/pdf/10.1137/07070406Xhttp://epubs.siam.org/doi/pdf/10.1137/07070406X

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Modeling and the Pipeline: Attracting and retaining STEM students How to achieve the 34% increase in Engage to Excel. Recruitment and retention Appeal to diverse population Multiple entryways? A non-calculus track for freshman modeling? Use of computation/ discrete calculus Data-based models as well as “physics-based” models CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 14

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Modeling and the Pipeline: Attracting and retaining STEM students Multiple math science major programs Not uniform across institutions Increased statistics and data science Modeling and solution of models Computational, analytic, simulation-based What if scenarios Linkage/ coordination with applications domains Require a minor? CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 15

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What are “new” key areas for undergrad math? A modern math sciences undergraduate education should include at least some introduction to Algorithms and Analysis (Data Structures, Approximation Theory, Numerical Analysis, Computational Science) Distributed Computing and Big Data (MPI, Hadoop, noSQL) Data Analytics (Regression, Estimation, SQL, R/Python) Modeling with Probability and Stochastic Processes Bayesian Statistics and Machine Learning Dynamical Systems (ODE, PDE, SDE) Optimization and Control CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 16

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Future of CS&E Education CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 17 SIAM-EESI Workshop Breckenridge, CO August 2014

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CSE Future Workshop Graduate and Undergraduate Education Future research directions, too Potential updates to Petzold report on CSE Grad Education SIAM Working Group on CSE Education (Linda Petzold, Chair) Graduate Education in CSE, SIAM Review 43 (2001) 163-177 Turner/ Petzold report on Undergrad CSE Education SIAM Working Group On CSE Undergraduate Education (Turner and Petzold, co-chairs) Undergraduate Computational Science and Engineering Education, SIAM REVIEW 53 (2011) 561–574 http://epubs.siam.org/doi/pdf/10.1137/07070406X http://epubs.siam.org/doi/pdf/10.1137/07070406X CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 18

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Computational Science and Engineering CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 19 CSE is larger than the pure intersection of the three component pieces, but is nonetheless included in their union. That is to say CSE provides, and strengthens, the bridges connecting those components but should not become a separate "island".

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Why is CSE education relevant here? The basic models – and philosophy – of CSE programs apply equally well to programs in the Math Sciences as a whole, especially in transitional years Using relevant learning experiences Making connections to other STEM fields, while Introducing sound mathematical concepts and reasoning Focus on integration of knowledge to develop problem-solving methodologies & tools Needs input/collaboration from application domains Advocating for internships and career preparation Simultaneous development of vital “soft skills” Building bridges, not silos CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 20

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Can this work in the transition years? Emphatic “Yes” I was personally involved for some 15 years at USNA with the Computer Calculus sequence Satisfied both Calc and CS requirements Coordinated throughout Deeper understanding of many fundamental concepts Included rigorous proofs and applications of uniform continuity and development of the Riemann integral at freshman level University of Oslo (Knut Mørken) Computational projects in early courses for both STEM and non-STEM CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 21

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Common Curriculum Content Modeling and Simulation Data and science-based Programming and algorithms Applied math Numerical methods Parallel programming Scientific visualization Analysis of results Does my answer make sense? CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 22 Application domain content Team-based projects Technical analysis and presentation Research or “Professional” Experience

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Motivational Factors for Developing CSE Programs Future jobs of technical nature require new skills directly related to computational, including data and statistical, science Computer science graduates do not have the modeling, mathematics and science background needed for future technical employment STEM fields are becoming more computational; science and engineering are now commonly done in silico Boeing aircraft design process for example Provides relevance to mathematics programs CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 23

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Undergraduate Math Sci Education Must Address Professional Experience or Internships Projects Interdisciplinary, Team-based, including team teaching Extended projects develop perseverance for workplace Breadth vs. Depth Communication Presentations at meetings Educational outreach activities Career awareness is critical to recruitment CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 24

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An Industry perspective: What Industry Needs Strong foundation in a discipline Need computational skills Not just MATLAB Understand Error, Stability, Performance Need second discipline “expertise” Speak another “language” Provide added breadth Transition to other problem areas Willingness to Change – and to DRIVE CHANGE CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 25 Kirk Jordan, IBM

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Conclusions and Recommendations Many different models of undergraduate math sciences programs can work Many curricular items in common Many different objectives Other STEM disciplines at both undergrad and grad student levels Education, Graduate Schools, Labs, Industry Interdisciplinary collaboration an integral part of the curriculum and thesis research CBMS Forum October 2014 The First Two Years of College Math: Building Student Success 26

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