Learning mathematics in laboratory and small-group contexts – and a few other ideas John A. Pelesko

Problem Based Learning Innovative Courses Undergraduate Research Regular Mathematics Courses Outreach Research Bio-Calculus Math Fellows Math Modules

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.

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

Problem Based Learning Innovative Courses Undergraduate Research Regular Mathematics Courses Outreach Research Bio-Calculus Math Fellows Math Modules

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

Innovative Courses – Math Modeling Math 512 – Capstone course, required for all B.S. Majors in Mathematics Enrollment ~ 25 students More than ½ are engineers Satisfies our writing requirement Project based

Math Modeling – Sample Projects

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

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

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!

Math Modeling – Future Innovations Students need better training in reading scientific literature Students need training in team work Mini-lecture structure needs revision

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

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

Interdisciplinary Undergraduate Research Summer months are our most active Various structures possible One-on-one research Small group projects Interdisciplinary teams

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

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

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

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

HHMI Initiative – Bio-Calc Connect math faculty with bio faculty (Rossi- Hodson) Find common ground Share teaching goals, data, methods Integrate and iterate

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

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

Problem Based Learning Innovative Courses Undergraduate Research Regular Mathematics Courses Outreach Research Bio-Calculus Math Fellows Math Modules

An open invitation