# Program guide

## Wednesday, July 24

1:00-5:00 p.m. Participants check in, Nourse Hall Lounge5:30 - 7:00 p.m. Reception and Dinner, Alumni Guest House

7:00 - 8:00 p.m. Opening Remarks:Cathy Manduca, Science Education Resource Center, Carleton College

**Quantitative Skills in Multiple Contexts: Learning to Communicate;**Janet Andersen, Dept. of Mathematics, Hope College

**Abstract:** Many students seem to be unable to make connections between content learned in the mathematics classroom and applications encountered in the geoscience classroom. Yet, how many of us are aware of what is being taught in our colleague's classroom and how this connects with our own classroom? I will describe my own journey in learning to communicate with my science colleagues and the tremendous impact this has had on my understanding and my teaching. I will also talk about some of the barriers that often hinder students from making connections between their mathematics courses and their geoscience courses and how we might address these.

## Thursday, July 25

7:30-8:30 a.m. Breakfast, East Dining Hall8:30-9:30 a.m.

**Challenges in Getting Students to Think Deeply about Mathematics**(group activity) Heather Macdonald, Dept. of Geology, College of William and Mary

**Abstract: **Getting students to think deeply about mathematics and about using it effectively as a tool is challenging. For this session, workshop participants will consider the particular challenges they face and share ideas and strategies that have worked in their courses with their students.

**Summary of Discussion**

9:30-10:30 a.m.

**A Geoscience versus a Mathematical Approach to Problem Solving;**Janet Andersen, Hope College

**Abstract:** Understanding is enhanced when we can view a problem through multiple perspectives. For this session, workshop participants will work in mixed groups of mathematicians and geoscientists on a quantitative problem in a geoscience context. The main goal will not be to solve the problem per se, but rather to gain an increased awareness of the differences and similarities of approaches to the problem by a scientist versus a mathematician. We will then discuss how we can use this awareness to enhance the learning of quantitative skills in our classrooms, whether this is a mathematics or a geoscience classroom.

10:30-10:45 a.m. Break

10:45-11:45 a.m.

**A Mathematician's Map of Quantitative Skills**; Sam Patterson , Dept. of Mathematics, Carleton College

**Abstract: ** A list of quantitative tools for geoscience students is presented along with an indication of where in the high school or college curriculum students encounter these topics. Some attempt is made to distinguish between specific mathematical topics, such as understanding derivative as rate of change, and overarching skills, such as using multiple mathematical tools to solve a problem in geology or representing information symbolically. The topics are relatively easy to locate in the mathematics curriculum. The skills, on the other hand, are not consistently included in the curriculum and may be taught, if at all, in non-mathematics courses. Quantitative Skills Checklist (Acrobat (PDF) 50kB Sep20 04). (Also available in Excel Format (Excel 14kB Jan20 04))

The purpose of this session is to frame the scope of the skills we wish to discuss at this workshop and to begin to establish a glossary, if not a common vocabulary, to foster communication between mathematicians and geologists about teaching quantitative skills.

1:00-2:00 p.m.

**A Decade of Changes in Teaching Mathematics: Lessons Learned and Challenges Encountered**; Janet Andersen, Dept. of Mathematics, Hope College and Margie Mason, School of Education, College of William and Mary

**Abstract: **A declining number of mathematics majors, increased number of non-mathematics departments teaching mathematics courses, and large numbers of unsuccessful students in mathematics courses led to unprecedented changes in the undergraduate mathematics curriculum during the last decade. Publications produced by mathematical organizations, sessions and discussions at mathematics meetings, and targeted monies from the National Science Foundation have fueled many of these changes. Collaborative learning, projects, and the use of technology are becoming as standard as the ubiquitous 'word problems' in many mathematics classrooms. In this talk, we will describe how the mathematics classroom has changed, what we have learned about how students learn mathematics, and the challenges encountered along the way. We will also discuss how teaching quantitative skills in a context can benefit both the mathematics and the geoscience students.

2:00-3:00 p.m.

**Teaching Quantitative Skills Using a Cross-Cutting Geoscience Concept**; Mary Savina, Dept. of Geology, Carleton College

**Abstract:**Central to the study of geomorphology, hydrology, sedimentology and other geoscience classes, are the subjects of stream velocity and discharge. In this session, I will discuss (from my viewpoint as a geomorphologist) some of the mathematical/physical concepts and quantitative skills I try to introduce to students as I teach these subjects.

**These subjects and skills include:**

- Conservation of Mass: As applied to free-flowing streams, conservation of mass (and the incompressibility of water) implies that the discharge at point 1 is equal to the discharge at point 2 if there are no sources of inflow or outflow: How can we reconcile this very nice theory with the inability to discern dispersed inflows and outflows in the field?
- The hydraulic geometry: Discharge can be considered an independent variable and a set of equations developed that express the dependence of w, d and v on discharge. The exponent values (b, f, m) tell what proportion of an increase in discharge is due to increases in w, d and v. This is very useful in distinguishing different kinds of stream behavior. These hydraulic geometry equations are useful for both at-a-station comparisons at different discharge states and downstream changes. However, the summary diagram (from Leopold and Maddock, 1953) is at once one of the most helpful syntheses of stream behavior and one of the most confusing to explain to students.
- The Chezy equation for average velocity at a cross section can be derived from first principles of flow and resistance. The Chezy-Manning equation, on the other hand, is empirically derived. Everyone uses the Chezy-Manning equation because it allows us to calculate velocity (and discharge) from channel measurements. How can we reconcile this utility with the ambiguity of Manning's "n," the different forms of the equation in metric and English units, uncertainty about the exponents for hydraulic radius and slope and other issues?

- What are the implications of using the two standard ways of determining an "average" velocity at a single point along a cross-sectionâ€”1) measure the velocity at 6/10 of the depth or 2) add the velocities at 2/10 and 8/10 of the depth and divide by two?
- The curve of velocity with depth (from the surface to the bed of the stream) has a distinctive shape. Theoretically, the stream velocity at the bed should be zero, but it's not physically possible to measure a velocity there. What does this disjunct between field measurements and theory imply for shear stress and average velocity calculations?
- The relationship between stage and discharge (rating curve) is usually not linear. The comparable curve for suspended sediment discharge shows a hysteresis effect at many streams.
- How can field measurements of stream width and depth be used to illustrate the concepts of limit and the idea of integration, even if the shape of the stream bed can't be easily represented?
- Why do so many fluvial geomorphic relationships (say, between drainage area and discharge) tend to be represented best on log-log plots?
- Significant figures and precision/accuracy in reporting discharge and velocity measurements.

3:00 - 3:20 p.m. Break

3:20-4:20 p.m.

**Developing Ideas and Examples: Case Studies of Quantitative Skills in Geoscience Context**- breakout groups; Mary Savina, Dept. of Geology, Carleton College

**Abstract: **In the previous session, we discussed a variety of different ways in which math skills enter into teaching about stream velocity and discharge: constructing and reading graphs, understanding significant figures, reconciling the theoretical with the measurable (stream velocity profiles), using equations, etc. Indeed, many subject in the geosciences depend on mathematics and can be used to incorporate quantitative skills into the curriculum. Our task for this hour is to brainstorm in small groups about other specific topics in the geosciences that invite quantitative reasoning. Our goal is to compile a series of such topics, each with short statements of geological and mathematical contexts and a list or description of the quantitative skills that relate to that subject. Some workshop participants may choose these topics for their group projects at the workshop. In any case, the final compilation will be one of the workshop products that we can take back to our home campuses. These ideas should give other mathematicians and geologists examples of ways in which the two fields intersect.

**Suggested Topics:**

- Ground-water flow (uniform, non-uniform; steady, non-steady)
- Interpreting phase relationships in petrology
- Analyzing multispectral imagery (remote sensing)
- Understanding feedback and equilibrium in earth systems
- Interpreting seismic data to determine properties of multiple layers (inverse problem)
- Understanding clay flocculation and particle settling in a moving fluid
- Determining the hydrologic characteristics of an aquifer, given a selection of well data (drilling logs, static water levels, water chemistry, etc.)

**Instructions:**

- Brainstorm a series of geologic topics on a sheet of poster paper.
- For at least two of the topics, describe the geological and mathematical contexts and the quantitative skills associated with the topic, on separate overheads.
- Be prepared to share your examples orally during the last 20 minutes of the session.

4:20-5:20 p.m.

**Teaching Math-Phobic Students**; Margie Mason, School of Education, College of William and Mary

**Abstract:**Math phobia can paralyze students and prevent them from grasping concepts which otherwise might have been easy for them. This session focuses on what causes math phobia and, more importantly, on practical approaches to controlling it for the student and the teacher.

6:00 p.m. Dinner/Picnic

7:30-9:00 p.m.

**Sharing Best Ideas from home**- Poster session / Sharing materials

**Abstract:**This time provides an opportunity for workshop participants to showcase the projects, products, or activities they are engaged in with the group.

Participants are invited to share:

- Examples of their favorite class activities (either in a geoscience context or in other contexts as an example for what we might develop in the geosciences),
- Descriptions of how math and science departments are working together at their institution
- Information on projects they are working on
- Demonstrations of web-resources that they have developed or find very useful
- Other information or resources of interest to the group

We will provide poster space, internet connections, and tables for handouts to facilitate interaction. To most efficiently use the space available, each participant is encouraged to bring one display that integrates the variety of information they would like to share . If you would like to demonstrate software or websites, please bring your own computer.

## Friday, July 26

7:30-8:30 a.m. Breakfast, East Dining Hall8:30 -10:00 a.m.

**Teaching Mathematical Concepts: Conceptual Steps and Geologic Examples**, Cathy Manduca, Carleton College

**Abstract:**The goal of this session is to develop strategies for teaching fundamental mathematical concepts that occur throughout the geoscience curriculum. Working in teams of mathematicians and geoscientists, we will develop recommendations and examples that will assist in teaching these concepts in both geoscience and math courses. Each team will produce a poster describing

- the mathematical concept they are addressing;
- Critical steps or strategies in teaching this concept;
- an example of how these steps or strategies can be incorporated in a geological context.

- Rate of change
- Linearity
- Optimization
- Logarithms/exponential growth
- Approximation
- Data analysis
- Vectors
- Matrices and eigenvectors
- Algebra (fractions and percentages, variables, solving equations)
- Units and significant digits
- Systems of equations

10:00-10:30 a.m. Poster Session and Break

10:30-11:00 a.m.

**Quantitative Approaches in Geoscience Research: Applications to Upper Division Coursework**(presentations followed by discussion); Heather Macdonald, Department of Geology, College of William and Mary, Albert Hsui, Univ. of Illinois, Champaign-Urbana, Alan Shapiro, Univ. of Oklahoma, and Jennifer Wenner, Univ. of Wisconsin, Oshkosh

**Abstract:**The first 1/2 hour of this session will include three short presentations by geoscientists on their research and its quantitative aspects.

**Virtual Laboratories-Using Technologies to Enhance Quantitative Geoscience Learning**- Albert Hsui, Department of Geology, Iniversity of Illinois at Urbana-Champaign

**Mathematics of Doppler Radar Wind Analysis, Vortex Dynamics and Thermal Convection**- Alan Shapiro, Department of Meteorology, University of Oklahoma

**Geology by Number: Everyday Use of Quantitative Skills (PowerPoint 10.8MB Jan20 04)**- Jennifer Wenner, Geology Department, University of Wisconsin, Oshkosh

The presentations will set the stage for a discussion addressing the following questions:

- What are the critical aspects of successful applications of mathematics to problem solving in the natural world?
- How can we best prepare geoscience students with the quantitative skills they need?

11:00 a.m.-12:00 p.m. Discussion

12:00-1:30 p.m. Lunch; optional birds of a feather lunch sessions

1:30-3:30 p.m.

**Quantitative Skills in the Field**(field trip), Mary Savina, Dept. of Geology, Carleton College

On this short field trip, we will look at several ways that quantitative skills can be incorporated into field studies. The emphasis will be on geomorphology, hydrology and soils. We will start at Mudd Hall, walk east to Evans Hill, then go into the Carleton Arboretum and the West Gym playing fields. Total distance is less than a mile.

3:30-3:45 p.m. Break

3:45-4:15 p.m.

**Establishing project teams and work plans**Heather Macdonald and Cathy Manduca

One of the major outcomes of this workshop will be a "final project" developed by mathematician-geoscientist teams. Our goal is to have a set of products at the close of the workshop that will help faculty in both mathematics and geoscience teach quantitative skills in a geoscience context. We leave the nature of your product open to your imagination.

However, ideas might include:

- a scenario for one or more classroom activities or assignments
- a classroom module ready for classroom testing
- one or more assignments based on a particular data set (see for example QELP)
- a problem or set of problems based on an important cross-cutting theme (building on the Thursday afternoon case study session)
- a series of assignments based on developing a particular quantitative skill (building on the Friday morning session)
- a syllabus integrating quantitative skills in a geoscience context in a math or geoscience course

The goal of this session is to establish the project teams and the titles of their products. We anticipate that some teams will be a mathematician/geoscientist pair coming from one institution, and that other teams will form based on common interests at the workshop.

Each team will present its final product on Saturday at 11:15. At this time you will need to have:

- A written product ready for reproduction (word file, html document, powerpoint file-e-mailed to cmanduca@carleton.edu or turned in via floppy disk). These products will be printed and reproduced during the session and lunch hour for distribution in the 1:00 session and will be posted on the workshop website.
- A one-minute presentation
- Any additional materials for the sharing session after lunch (hand drawn poster describing your main ideas, computer demonstration)

Our working spaces include power and internet connections for your laptop computers as well as access to computers in the geology building and computer lab. You are encouraged to bring any materials from home that you believe will assist in creating your final product. Following the workshop, teams are welcome to continue to work on their product. We will be pleased to update the website with revised drafts or new materials.

4:15-6:00 p.m. Project team work

6:30 p.m. Dinner

7:30 p.m. Work Time

## Saturday, July 27

7:00 - 8:00 a.m. Breakfast, Mudd/Olin Walkway

8:30-11:15 a.m. Project work time

11:15 a.m.-12:00 p.m. One minute talk session, describing our products

All Participants

This session provides an opportunity for each project team to present a one minute overview of their product. This high level overview will allow the workshop participants to capture the breadth of materials that have been developed and to prioritize their plans for discussing products with creators during the remainder of the workshop.

12:00-1:00 p.m. Bag Lunch, pick up at East dining entrance1:00-2:00 p.m.

**Sharing Final Products**(handouts and/or posters.) Pairs split up the hour.

All Participants

This sharing session provides an opportunity to talk individually with project teams about their products. The format will be the same as that for the Thursday night sharing session. We anticipate that each project team will have a final written product which will be available to all participants at this session. In addition, you are welcome to provide additional information on your project using a hand drawn poster, computer demonstration, or in other appropriate ways. During the session, we ask that teams organize themselves in order to both provide someone at the display to answer questions throughout the hour and an opportunity for each team member to visit other displays. Post-it notes will be provided to participants to offer comments and suggestions on the products. If you would like to revise your final product prior to posting on the website, we would ask that you send a revised file by August 15.

2:00-2:30 p.m.**Quantitative Literacy: A National Movement (PowerPoint 34kB Jan20 04)**, Len Vacher, Weber State University, Cathy Manduca, Carleton College

**Abstract:** Quantitative literacy is a national movement to increase the ability of all Americans to use and understand quantitative information. Motivated by the increasing pervasiveness of quantitative information and the need to act upon it in everyday life, educators from all disciplines and levels, as well as businessmen and policy makers are striving to increase quantitative literacy for all. This session will provide information about the philosophical underpinnings of the movement and activities to date.

2:30-3:30 p.m.
**Next Steps: Collaborations between the Mathematics and Geoscience Communities**. Cathy Manduca, SERC, Carleton College and Sam Patterson, Dept. of Mathematics, Carleton College

**Abstract:** What steps would participants like to take to address quantitative literacy for all students, quantitative skills for science and mathematics majors or other issues raised at this workshop as members of our respective professional communities? How do we want to continue collaborations developed during this workshop?

Break into two groups - one focused on quantitative literacy, one on more majors/upperlevel issues

3:30-3:45 p.m. Break

3:45-4:45 p.m.

**Next Steps: Institutional Action Planning what do we do when we go home?**Janet Andersen, Dept. of Mathematics, Hope College and Heather Macdonald, Dept. of Geology, College of William and Mary

Closing Session

4:45 p.m. Workshop Evaluation

7:00 p.m. Dinner

## Sunday, July 28

4:15 a.m. - 3:30 p.m. Participants departing

6:00 - 9:00 a.m. Breakfast, Nourse Main Lounge