Summary of Discussion of "Challenges in Getting Students to Think Deeply about Mathematics"

Participants divided into small groups and spent some time discussing challenges to teaching quantitative skills in both mathematics and geoscience classes. A few minutes at the end were spent summarizing the discussion as a whole.

Overarching challenges (pervasive in our culture)

• People don't want to be good at math
• Math not seen as important/valuable
• Math Phobia -- students are afraid/terrified
• The answer is more important than the process
• "I'm not good at math" attitude -- barrier to learning

Instructor-centered challenges

• Finding the time to come up with creative ways to teach mathematical concepts can be difficult
• Many geoscience faculty are rusty in math; Math faculty may not know geoscience
• Scientists and mathematicians are encouraged to specialize and not be broad (at least historically -- is it still true?)
• Assessments may not support what we know about learning and mathematics
• Students may not have learned the prerequisite material
• Heterogeneity of abilities in the classroom

Student-centered challenges

• Perceived lack of relevance
• Students have difficulty applying abstract mathematical concepts
• Many students lack math intuition or experience
• Students don't expect to learn quantitative skills that are applicable to real world problems, instead learn the abstract in math classes
• Can't move beyond the example problems to get to the conceptual understanding -- solution is not "the answer"
• Unwarranted reverence for numbers -- cannot evaluate whether the numbers are meaningful or useful
• Misuse or lack of tools/skills -- unable to choose appropriate approaches
• Difficulty in visualizing geometry in 3D

Challenges to both the student and the instructor

• Compartmentalization -- connections are not made between courses (both within geology and between math and geology)
• Timing of courses does not lead to practice of skills when learned
• Real world problems are often difficult and take time to address
• Often not enough time to discover or learn math and science throughout education