# Teaching Methods

This set of modules relate to particular pedagogical techniques or issues that can be used in teaching quantitative skills to students. Some of these modules were developed by workshop participants as a way of building the site and others have been made available through the SERC Pedagogic Service and were compiled by experts in their field.

We welcome your suggestions for topics or resources.

- Back of the Envelope Calculations: These simple exercises help put very large or very small numbers into perspective by analogy with something a student can visualize. Written by Barbara Tewksbury of Hamilton College.
- Kéyah Math: Culturally-Based Learning: The
*Kéyah Math Project*has developed a series of versatile online activities in mathematical geoscience, using the natural and cultural landscapes of the Southwest United States as context and setting. This resource has been developed by a team led by Steven Semken of Arizona State University.

- Measurement and Uncertainty: Students often don't understand what conclusions can or cannot be reached based on the degree of uncertainty of measurements they make. This module tries to help faculty integrate measurements and uncertainty in their instruction. Compiled by Peter Bohacek and Greg Schmidt, Henry Sibley High School.
- Metacognition: Helping students think about their thinking as they engage in problem solving can improve their success. Written by participants at the 2005 workshop

- Models: Models are approximations of nature that can be used to test a particular aspect or set of aspects of a complex system. Authored by Bob MacKay, Clark College.

- Mathematical and Statistical Models: This type of model attempts to quantitatively illustrate pieces of a complex system so that it's behavior can be better understood. Authored by Bob MacKay, Clark College.

- Quantitative Writing: This method engages students with numbers by asking them to analyze and use quantitative data in written reports and arguments. Authored by John C. Bean at Seattle University.
- Teaching with Data: Engaging students with real data sets can provide a context in which they can practice their quantitative skills. Written by Bob MacKay of Clark College.

- Teaching with Data Simulations: Teaching with data simulations means giving students opportunities to simulate data in order to answer a particular research question or solve a statistical problem. Compiled by Danielle Dupuis and Joan Garfield of the University of Minnesota.
- Teaching With Equations: Teaching students to make connections between physical world, words and equations is a fundamental skill for geoscientists. Written by participants at the 2004 workshop.

- Teaching Quantitative Literacy: This module helps to tie particular mathematical concepts together with the geoscience context(s) where it is relevant. Authored by Jennifer Wenner, University of Wisconsin - Oshkosh, and Eric Baer, Highline Community College.

- Teaching Quantitative Reasoning with the News: This teaching method uses newspaper articles as content for the critical analysis of quantitative information. Authored by Stuart Boersma, Central Washington University.
- Teaching with Spreadsheets Across the Curriculum: Teaching with short PowerPoint presentations that guide students to build spreadsheets to solve one or more mathematical problems in the context of their courses. Written by Len Vacher, University of South Florida.
- Understanding Uncertainty: This module looks at different aspects of uncertainty that students often have trouble with, such as significant figures, rounding, and precision versus accuracy. Written by participants at the 2004 Workshop.

## Other References on Quantitative Teaching Methods

This section of the site is devoted to creating a comprehensive set of high quality resources that address methodologies for teaching quantitative skills. We are collecting resources directed specifically at the geosciences, as well as those developed by mathematicians and in other scientific and engineering disciplines that are applicable to teaching in a geoscience context. We welcome your suggestions for resources and your comments on those that we have identified. The quantitative skills email list provides a venue for general discussion of teaching methods.

### Geoscience specific resources

**Mathematics: A Simple Tool for Geologists**(2000, David Waltham, Blackwell Science) This book aimed at students teaches simple mathematics using geological examples to illustrate mathematical ideas.- Quantitative Skills Assessment In Geoscience Courses (more info) (Shah and West) A website at Columbia University with tips for teaching quantitative skills, a guide for assessing quantitative skills, and a survey of the skills in courses.
**Journal of Geoscience Education**, v. 48, no 4. (Macdonald, Srogi and Stracher, 2000 (Eds.) ) and**Mathematical Geology**, v 32., no 2 (2000, Stracher, ed) are devoted to teaching quantitative skills in the geosciences and provide a variety of examples of effective practice.

### Other resources

- The Mathematical Association of America Homepage has a wide range of book reviews including:
**Sourcebook for College Mathematics Teaching**(1990, A. Schoenfled, Mathematics Association of America). An 80 page collection of useful advice based primarily on the work of the MAA Committe on the Teaching of Undergraduate Mathematics- Cooperative Learning in Undergraduate Mathematics: Issues that Matter Strategies that Work ( 2001, Elizabeth C. Rogers, Barbara E. Reynolds, Neil A. Davidson, and Anthony D. Thomas, Editors, Mathematics Association of America). Practical suggestions and strategies both for instructors who are already using cooperative learning in their classes, and for those who are thinking about implementing it.
- Writing in the Teaching and Learning of Mathematics (1998, John Meier and Thomas Rishel, Mathematics Association of America) A discussion of both how tocreate effective writing assignments for mathematics classes, and why instructors ought to consider using such assignment. This book is an argument for engaging students in a dialogue about the mathematics they are trying to learn.

**Overcoming Math Anxiety**(1978, Revised and Expanded 1993, Shelia Tobias,W.W. Norton and Company) An inciteful look at why students can be anxious about mathematics and the role of different learning styles in problem solving.- Small Group Learning in a Technical Course: Procedures, Pitfalls and Payoffs (1994, R.M. Felder and R. Brent, ERIC Document Reproduction Service Report ED 377038) Building on a description of several cooperative learning exercises that have worked well for the authors in engineering courses, this paper suggest ways to maximize the benefits and overcome the challenges of a collaborative learning approach.