# learning mathematics in laboratory and small-group contexts â€“ and a few other...

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Learning mathematics in laboratory and small-group contexts and a few other ideas John A. Pelesko Slide 2 Problem Based Learning Innovative Courses Undergraduate Research Regular Mathematics Courses Outreach Research Bio-Calculus Math Fellows Math Modules Slide 3 Problem Based Learning A Central Theme Learning is initiated by a problem. Problems are based on complex, real-world situations. All information needed to solve problem is not initially given. Students identify, find, and use appropriate resources. Students work in permanent groups. Learning is active, integrated, cumulative, and connected. Slide 4 Overview Problem, Project, or Assignment Group Discussion Research Group Discussion Preparation of Group Product Whole Class Discussion Mini-lecture (as needed) Assessment (when desired) The Problem-Based Learning Cycle Slide 5 Problem Based Learning Innovative Courses Undergraduate Research Regular Mathematics Courses Outreach Research Bio-Calculus Math Fellows Math Modules Slide 6 The MEC Lab An Overview Founded in 2002 Experimental laboratory housed in the Department of Mathematical Sciences Modeled after similar labs at Gatech, UNC, UArizona, NJIT, NYU Home for innovative courses, undergraduate research, graduate research, outreach efforts, course enrichment Slide 7 Innovative Courses Math Modeling Math 512 Capstone course, required for all B.S. Majors in Mathematics Enrollment ~ 25 students More than are engineers Satisfies our writing requirement Project based Slide 8 Math Modeling Sample Projects Slide 9 Math Modeling Course Structure Work in a team of four students Improve speaking skills Improve writing skills Integrate mathematical knowledge Produce a journal style paper The Goals Slide 10 Math Modeling Course Structure Week One Projects described, small team activities, wiki createdwiki Week Two Projects chosen, teams assembled Week Three Mini-lectures, Team presentations begin Week Four Milestone #1 Key Events Slide 11 Math Modeling Course Structure MilestoneLit Review Assumptions Definitions Formulation Analysis Solutions Measuremen ts Parameter Estimation Simulations Comparison Strengths & weaknesses Synthesis Lab notes Style Clarity Presentation 180%5%0%15% 220%60%0%20% 35%40%25%30% 40%40%20%40% 50%20%30%50% Milestone structure keeps students moving forward! Revision is central! Slide 12 Math Modeling Future Innovations Students need better training in reading scientific literature Students need training in team work Mini-lecture structure needs revision Slide 13 A Lab Course Another Approach Students work on a sequence of classic problems Focus is on reading literature and reproducing classic experiments/mathematics Builds toward a final, short, self-chosen project Slide 14 A Lab Course Another Approach Course is divided into 4 week units Project introduced, experimental system described, relevant literature handed out Parallel lectures tied to topics Students present regular updates Product is a wiki page and presentations Basic Structure Slide 15 Interdisciplinary Undergraduate Research Summer months are our most active Various structures possible One-on-one research Small group projects Interdisciplinary teams Slide 16 Interdisciplinary Undergraduate Research A typical summer Identify advisor, project, join team Training in Matlab, Maple, Latex Weekly group meetings Lab rotation Final presentation at our symposium Present work elsewhere Slide 17 HHMI Initiative - Overview Supported by a $1.5 M grant from HHMI Joint effort between mathematics, biology, chemistry, chemical engineering NUCLEUS Undergraduate Research Quantitative Biology Initiative Slide 18 HHMI Initiative Quantitative Biology Revision of the calculus sequence, new bio-calc section New B.S. in Quantitative Biology Math Modules for math and bio courses Math Fellows Program Slide 19 HHMI Initiative Bio-Calculus Constraints: Consider local and global issues - Local: Bio-Calc must be open to all majors - Global: Must meet requirements of graduate and professional schools Goals: Why revise calculus? - Ensure all biology majors have right tools - Integrate and inspire Approach: Realign and revise - Calc sequence realigned to early transcendental - Special section created using biological examples Details: How to revise? - Connect calculus with first year biology sequence - Slowly create new library of examples and projects Slide 20 HHMI Initiative Bio-Calc Connect math faculty with bio faculty (Rossi- Hodson) Find common ground Share teaching goals, data, methods Integrate and iterate Slide 21 HHMI Initiative - Modules Goal: Build quantitative thinking into wide range of biology courses, build biological thinking into wide range of mathematics courses Approach: Build a library of instructional modules, loosely modeled on PBL Clearinghouse, that can be used widely Step One: Survey existing modules and make available to our faculty, develop new modules Step Two: Encourage collaborative development teams - Use existing efforts in math and biology (FRAP module) - Use undergraduate and graduate research students - Use educational funding opportunities (HHMI, CTE, NSF) The Future: Build a national clearinghouse Slide 22 HHMI Initiative Math Fellows Use talented math students to help inject mathematics into science labs Math Fellows serve as TAs for biology lab classes Math Fellows help coordinate between math and science faculty Slide 23 Problem Based Learning Innovative Courses Undergraduate Research Regular Mathematics Courses Outreach Research Bio-Calculus Math Fellows Math Modules Slide 24 An open invitation