Teach the Earth > Quantitative Skills > Community > Workshop 2002 > July 26 Morning Discussion Notes

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.



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