Learning mathematics in laboratory and small-group

contexts – and a few other ideas

John A. PeleskoJohn A. Pelesko

Problem Based Problem Based LearningLearning

Innovative Innovative CoursesCourses

Undergraduate Undergraduate ResearchResearch

Regular Regular Mathematics Mathematics CoursesCourses

OutreachOutreach

ResearchResearch

Bio-CalculusBio-Calculus Math FellowsMath Fellows

Math ModulesMath Modules

Problem Based Learning – A Central ThemeProblem 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 Problem Based LearningLearning

Innovative Innovative CoursesCourses

Undergraduate Undergraduate ResearchResearch

Regular Regular Mathematics Mathematics CoursesCourses

OutreachOutreach

ResearchResearch

Bio-CalculusBio-Calculus Math FellowsMath Fellows

Math ModulesMath Modules

The MEC Lab – An OverviewThe 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 ModelingInnovative 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 ProjectsMath Modeling – Sample Projects

Math Modeling – Course StructureMath 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 StructureMath Modeling – Course Structure

•Week One – Projects described, small team activities, wiki created

•Week Two – Projects chosen, teams assembled

•Week Three – Mini-lectures, Team presentations begin

•Week Four – Milestone #1

Key Events

Math Modeling – Course StructureMath Modeling – Course Structure

Milestone Lit ReviewAssumptionsDefinitionsFormulation

AnalysisSolutionsMeasurementsParameter Estimation

SimulationsComparisonStrengths & weaknessesSynthesis

Lab notesStyleClarityPresentation

1 80% 5% 0% 15%

2 20% 60% 0% 20%

3 5% 40% 25% 30%

4 0% 40% 20% 40%

5 0% 20% 30% 50%

•Milestone structure keeps students moving forward!

•Revision is central!

Math Modeling – Future InnovationsMath 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 ApproachA 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 ApproachA 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 ResearchInterdisciplinary Undergraduate Research

•Summer months are our most active

•Various structures possible

•One-on-one research

•Small group projects

•Interdisciplinary teams

Interdisciplinary Undergraduate ResearchInterdisciplinary 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 - OverviewHHMI 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 BiologyHHMI 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-CalculusHHMI 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-CalcHHMI Initiative – Bio-Calc

•Connect math faculty with bio faculty (Rossi-Hodson)

•Find common ground

•Share teaching goals, data, methods

•Integrate and iterate

HHMI Initiative - ModulesHHMI 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 FellowsHHMI Initiative – Math Fellows

•Use talented math students to help inject mathematics into science labs

•Math Fellows serve as TA’s for biology lab classes

•Math Fellows help coordinate between math and science faculty

Problem Based Problem Based LearningLearning

Innovative Innovative CoursesCourses

Undergraduate Undergraduate ResearchResearch

Regular Regular Mathematics Mathematics CoursesCourses

OutreachOutreach

ResearchResearch

Bio-CalculusBio-Calculus Math FellowsMath Fellows

Math ModulesMath Modules

An open invitation