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# Designing Math Courses: Pedagogical Issues PowerPoint PPT Presentation

Designing Math Courses: Pedagogical Issues. Glenn Ledder Department of Mathematics University of Nebraska-Lincoln gledder@math.unl.edu http://www.math.unl.edu/~gledder1/Talks/. Key Issues to Consider. Course Goal Main purpose and place in curriculum Constraints

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Designing Math Courses: Pedagogical Issues

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### Designing Math Courses: Pedagogical Issues

Glenn Ledder

Department of Mathematics

gledder@math.unl.edu

http://www.math.unl.edu/~gledder1/Talks/

### Key Issues to Consider

• Course Goal

• Main purpose and place in curriculum

• Constraints

• Hours, class size, student background/ability

• Objectives

• What you want the students to learn

• Outcomes

• What you want the students to do to demonstrate their learning

• Goal:

• Empower engineering students with useful mathematics beyond linear algebra and differential equations

• Constraints:

• So many topics, so little time

50% vector calculus, 50% complex variables

### Complex Variables (half-course)

• Objective:

• Be able to use the residue theorem to invert Laplace transforms

• Outcomes:

• Students will do homework problems and write solutions with explanations.

• Students will demonstrate techniques on exams.

### Complex Variables (half-course)

• Course Content:

• Complex numbers

• Integration in the complex plane

• Laurent series and residues

• The residue theorem

### A Challenge

I wrote an NSF grant for an interdisciplinary undergraduate research program in mathematical biology.

The proposal included “a 3-credit course to introduce young students to interdisciplinary research.”

In effect, I jumped off the Sears Tower with a bag of cloth and hardware, expecting to build a parachute on the way down.

### Research Skills in Theoretical Ecology

• Goal:

• Introduce interdisciplinary research in mathematics/biology to talented students at an early stage in their careers.

“Early” means “between high school and college.”

### Constraints

• The course must be self-contained.

• We cannot assume knowledge of calculus, statistics, or any specific biology topic.

• We cannot assume laboratory experience.

• The course must be integrated at different levels.

• Math and biology

• Theory and experiment

• Research design, conduct, and dissemination

### Objectives

• Hard objectives: objectives that can be demonstrated with behavioral outcomes

• Soft objectives: objectives that are emergent properties of a broad whole

• The soft objectives are often more important for service courses. Don’t neglect them just because they can’t be measured.

### Soft Objectives

• Experience the challenge and excitement of research.

• Appreciate the synergy between theory and experiment and between biology and mathematics.

• Developskills that will be useful in theoretical ecology research.

• Understand the theory developed through the experiments and analysis.

### Hard Objectives

• Collectlaboratory data on real research questions using sophisticated techniques.

• Analyzedata using statistical methods.

• Construct mathematical models and use them to makepredictions.

• Prepare a poster to communicate research results.

• Design a research study.

### Outcomes

• Students will work together to conduct experiments and record data.

• Students will do homework and quizzes on mathematical content.

• Students will build a mathematical model and use it to make predictions.

• Students will prepare a poster summarizing their research.

• Students will prepare a research proposal abstract to indicate possible future work.

### Course Content

• Discrete linear stage-structured model:

xt+1 = Mxt,wherexis a vector giving the populations of the different stages and Mis a matrix of parameters