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
Don't call it math
Much of what we are doing is applying math to physics
- 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
- Enable just in time learning of math techniques
- Model strategies for gaining math expertise on the fly
- 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
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
- Scale analysis of order of magnitude reasoning
- Prediction is an important aspect of quantitative analysis.