Quantitative skills issues

Initial Publication Date: October 12, 2006

Issues in teaching quantitative skills to introductory geoscience classes

from the participants of the 2006 Infusing Quantitative Skills into Intro Geoscience workshop

Scaling models of how to infuse the quantitative skills in geoscience education

The group came up with two "end-member" models, challenges and how to overcome these challenges.

Model 1—The institution has a General Education course requirement classified as Quantitative Natural Science.

For example at the University of Missouri it is called the "Math Reasoning Proficiency course". In this case the Geology Departments should develop large courses that teach introductory geosciences infused with math and quantitative reasoning.

As a result a larger population will be exposed to quantitative skills and the geosciences will establish themselves among the other sciences as quantitative. The challenge is that not all faculty within the department agree to put the effort into designing quantitative courses.

Model 2 The institution does not have a General Education course requirement classified as Quantitative Natural Science.

Challenges:

Convince other colleagues of the importance of quant skills infusion
Convince the institution of the importance of having the quantitative requirement

If geology is the only science some students take, how can we do to stop the "leaky pipe"?

Solutions:

Change the way you teach by being explicit about the math that is behind the concepts, usually taught in a qualitative way. The students actually need to be taken out of their comfort zone in order to learn, but not too far. This can be defined as a subtle infusion of quantitative skills, without major changes to a course, as opposed to radical infusion.

Many institutions belong to the first group (Model 1) but we do not know what is the percentage and current trend. Jen Wenner and Mona Sirbescu will try to work together and talk to Len and contact the NNN to see if it is possible to have a survey to answer this question.

Using Google Earth to teach Geosciences quantitatively

See Peter Selkin's pagethat came out of the workshop.

Ogle Earth is a great website (blog)
One quantitative exercise is to use information on the picture to determine the date when the picture was taken. Google Earth doesn't time-stamp their pictures. There is someone who did this from a web-cam, but more interesting would be to use shadows.
Peter Selkin will put together all the materials, activities, that we have for SERC.
Overlaying topo maps - GPS Visualizer overlays for Google Earth allows you to put a USGS Topo onto the Google Earth 3-d topography . There may be a way to go from TOPO! (jpeg or tiff) overlay to Google Earth. Arc (GIS) to KML file is possible.
Peter showed a plate tectonic boundary and then overlaid earthquakes to show earthquakes along the transform fault zones. Peter also showed volcanoes.
ideas- compare old topo maps of glaciers and rivers and compare to Google Earth view and calculate the rate of change.
Teaching vertical exaggeration with Google Earth- would it work? (You can change the vertical exaggeration on Google Earth
Look at The Cutting Edge website for more ideas such as Volcanic Landforms and Magma Composition that use Google Earth.
GE Graph: Graph for Google Earth allow you to put graphs onto Google Earth
Reminder- if you send a link, make sure to add annotation so people know what it is
As an alternative to Google earth for seismic and eruption data, try Seismic Eruption
Google Earth is available on Mac, PC or Linux.
Some cities have 3-D buildings - see New York City.

Quantitative Literacy/Quantitative Reasoning

The definition of quantitative literacy is like greywacke - it's ambiguous. quantitative literacy and quantitative reasoning and numeracy are synonymous; numeracy is a British term that's probably been around a lot longer.

Lynn Steen's book, Quantitative Literacy and Democracy, is available online at the MAA site but not through Amazon.com. Steen uses the term QL.

The math skills described by Steen would seem to develop a quantitatively literate society, whereas those skills listed on the SERC quantitative skills website appear to benefit geology majors, but not the public as a whole; most students in our introductory classes do not continue on to pursue a degree in geology.

Gave some ideas about membership to NNN - the National Numeracy Network:

Reduced fees to $25
Monthly email from NNN to members regarding a large scale social issue
Reduced membership fees to faculty whose institutions join the NNN

GIS

Rob Benson (participant) has been ESRI Instructor for years.
No need for a GIS degree - it has gotten integrated - he is trying to get GIS components into each course.
GIS has gotten easier to use,
2 ½ week course learning to use GIS and apply it.
Example: census data and query data shifts
CA is great at providing GIS data.
Northwestern University "My World" contains good geology modules, separate from their Environmental package.
Free GIS is available—no saving or manipulating
What is the future for GIS? Answer: a very marketable skill, cartography is high growth position
About half of the EOS job listings mention GIS, not to mention the many applications in other fields.
GIS is not the same as ESRI, but they almost have a monopoly
Mastering Arc GIS, Meribeth Price 2006- has a good set of data
UC Santa Barbara Geography department may be willing to share data
GIS may be too easy to "plug and chug" bringing the process of triple integral interpolation. Shouldn't blindly apply the results to the physical world, since it can create interpretations that are mathematically accurate, but not realistic.
Does GIS increase QL? Consensus that it does.
Aida is using 3 GIS activities now and sees students more motivated than when they did the same with maps. She says that they can move further toward quantitative literacy using GIS than with maps
GIS takes the drudgery out of plotting, which give more time to do more computational work.
Good transfer of GIS skills to other areas.
Aida wants to give her school tech department assurances that GIS is applicable to other areas- talk to University geography depts., bureau of labor statistics, local geologic survey, local water boards, (but she found that local community colleges were not supporting it)
Spreadsheet -> PDF-> arcview easy form of access
Rob showed pocket pc that attaches to GPS for field work
Check out https://cdt.ca.gov/services/gis/ the California Geographic Information Systems (GIS) web portal.

Breadth vs. Depth

This group explored the question of depth vs. breadth for geoscience courses. They identified some key topics:

Plate tectonics
Earth as a system
Climate change
Deep time
Energy resources
Rock cycle
Water cycle

Math Anxiety questions and tips

Students don't panic in the grocery store or when they play electronic games, so why do they panic in class?
The issue may not be anxiety or inability, but the motivation to use math appropriately. Fear, inability, and inexperience may lead to anxiety. We must provide opportunities to become less anxious using math.
What do kids do for entertainment? There are a lot of role playing games that require calculations and rates. They do keep track of a lot of information. What strategies do the kids use in the games? Why aren't they anxious?
College math testing may play a role in supporting math anxiety if students place poorly.
One view: Math skills may not be bad, but they just can't apply the skills. Another view: Students are so anxious about formal math.
How do we test to find out if students shut down when they see algebra yet they are quantitatively literate?
Is it the symbolism and algebraic substitution that cause problems?
Repetition of a mathematical skill throughout the semester may reduce the stress as the semester continues.
Students may not see the connections; especially when there are multiple issues that students don't understand.
Do students with an anxiety toward math have a barrier to learning?
Teach heuristics (a method) as a means to reduce anxiety.
Need to help build student confidence: repetition (with continuous improvement in success rate) and scaffolding.
What is the relationship between confidence and anxiety?

To help overcome the lack of confidence and math anxiety, include:

scaffolding, repeated success, heuristics, hand holding
The classroom dynamics are also important: fun, exciting and engaging

Teaching Math as a language

Tips, suggestions, and difficulties with teaching students to "read" math and communicate that math is an effective shorthand as well as addressing the problem that students don't know how to read equations like you would read a sentence.

Teachers should model how you get from words to equations and equations to words.
Student should be encouraged to take their time to "read" a long equation.
A precise English description leads to a mathematical equation.
Think working with students in terms of inequalities; statement -> proportionality -> equation.
The tyranny of the symbol can be restrictive to students.
Trying to connect to something that is in the student's culture might help them to see how "cool" it is to express a physical process in an equation.
An analogy was offered of different speeds a long days driving paths with different seismic speeds through the earth.
Students get confused about the meeting of an equals sign,"=". In their personal life often "=" means "is the same as"; in an equation, the two sides of the equation are not the same object, causing confusion.