# July 26th Morning Discussion Notes

How can we best prepare geoscience students with the quantitative skills they need?

- What are the roles of math (skills?) and geology (application?)?

- Repetition and pervasive use throughout curriculum
- Use rich math vocabulary
- Make more math requirements?
- Focus on relevant skills in topic - not all at once; level playing field
- Variety of real world skills with exercises as delivered
- Increase complexity gradually and discuss what is gained on same problem

- Too many courses
- Too many prerequisites
- Too much to do in class

Work with math to determine what skills are needed in course and where they are in math to set appropriate prerequisites.

Math-science student partnerships

Integrated textbooks - Primarily math text with disciplinary supplements

Shackled by course structure - think radically about this

- Lab
- Modules
- Tutorials

Don't call it math

Much of what we are doing is applying math to physics

Goals

- Quantitative skills as tool for thinking critically for all students
- Turn to quantitative approaches as a reflex
- Curricular approaches at first year level for critical thinking, including quantitative approaches.

Application for teaching

- Set realistic expectations given length of course (limit topics)
- Think about curriculum

For students:

- Enable just in time learning of math techniques
- Model strategies for gaining math expertise on the fly
- Collaboration
- Tutorial
- Text
- Point out when intuition grows
- Help students developing intuition by making our thinking explicit including problem solving strategies and translation to techniques
- Repetition leads to internalization
- Set realistic expectations on time [notes trail off copy]
- Make clear that there are important quantitative models that are necessary/useful in understanding cause and process making predictions

What are critical aspects of successful applications of mathematics to problem-solving in the real world?

- Understand physical situation
- Visualize physical systems quantitatively
- Grounded in understanding of physical laws
- valid simplifying assumptions

How to go from physical world to equation-representation and back - do this early and often

- Visualization
- Language

Develop mathematical intuition

Make simplifying assumptions clear and decision making explicit

Make clear differences between analytical and numerical solutions and strengths of each

Application of successful application:

- Quantify Simplifying assumptions
- General
- Specific
- Scale analysis of order of magnitude reasoning
- Prediction is an important aspect of quantitative analysis.