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?)?

How do we coordinate and not have gaps?

• 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

How do we manage time?

• 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.