On the Cutting Edge - Professional Development for Geoscience Faculty
Teaching Quantitative Skills in a Geoscience Context
Carleton College, Northfield, MN -- July 2002
Quantitative Skills > Community > Workshop 2002 > July 26 AM Poster Session Notes

7-26 AM Posters

Rate of Change

Strategies that Work:

Examples in a Geoscience context:

  1. Determine average plate motion by measuring distance between two Hawaiian islands of known age. Determine average for several pairs of islands and discuss whether plate motion is a constant rate.
  2. Determine the rate of retreat of St. Anthony Falls based on location in historical record and location today on topographic maps. Assuming retreat began at the confluence of the Minnesota and Mississippi Rivers and that the glacier was present at this location, and a constant rate of retreat, calculate when the glacier began to retreat from the Minneapolis area.</span>

  3. Illustrate half-lives and exponential decay by giving each student a coin. All flip coins, if a student has "heads" they are not "decayed" and can flip again. Count students with "heads," flip again, and repeat. Data can be plotted, etc.

Remote Sensing Examples

Matrices and Eigen vectors:

Question: Why? Is it worth the math?
Strategy that works: Principle components (also teaches covariance)
  • See diagram on poster
Challenge: Getting math poor/phobic/atrophied students to appreciate it

Systems of equations:

Strategy that works: Endmember analysis/classification
  • (Spectral unmixing)
  • See diagram/example on poster
Challenges: undersolving and oversolving
Simultaneous equations

Vectors

Jordan, Hutchings, Hutchings

Focus: Using vectors for navigation and mapping

Strategies that work:

  1. Don't be abstract - Go outdoors and take measurements of distance between real objects and establish direction
  2. Use a magnetic compass (quality will determine accuracy and precision) and your pace or tape measure.
  3. Use protractor and scale to draw a representation of real situation. (Add points to map as a function of precision - users)
  4. Triangulate, triangulate, triangulate OR trilaterate, trilaterate, trilaterate volcano, your house (or any other spatially distributed feature)

Graphical Literacy

Moe M., Carol D., Janet A., Cathy S.

Strategies that work:

  1. Decide
FINISH

Approximation

Kohn, Kroeger, Macdonald, Shell-Gellasch

Reasonableness

Purpose Implementation

Evaluation and refinement

Example: Approximate rainfall within a drainage basin.

Evaluation: consider "outliers"

Data Analysis/ Intro. Statistics

Carolyn Dobler, Chris Gellash, Patty Crews, Marvin Bennett and Rick Ford

Critical steps/strategies in teaching this concept:

  1. What is the problem / research question?
  2. Which data will be useful in answering the question?
    • Issues related to data collection:
      • Sampling strategies / constraints
      • Sample size
      • Representative samples
      • Samples over time (time series)
      • Data quality - accuracy and precision;
      • Quality assurance and control
      • Nature of the phenomena being studied (geoscience context)
  3. Data description
    • Averages, mean, mode, median, variance, etc.
    • Weighted mean - important in many geoscience contexts
    • Correlations / regression
    • Graphs
  4. Drawing conclusions from our data (statistical inference)
    • Estimation, hypothesis testing, prediction

Units and Significant Digits

Check errors in work using significant digits

Motivate significant digits from error analysis

Convert units

Dimensional analysis

Strategies that work

Example in a geoscience context:

  1. (a) Use dimensional analysis to obtain the drag law for a spherical particle dropped through a viscous fluid (water or magma)
    (b) Conduct physical experiments to determine the viscosity coefficient
  2. Repeat the hydraulic example using order of magnitude reasoning:
    Q= Av: A is order 1, v is order 1, so Q must be order 1
    i.e. Q cannot be greater than 10 or less than 1

Optimization in Geology

Co, Bruce, Will

Math

Definition:
Min/max functions, typically misfits between data and a model
Issues:
Constraints
Global vs. local minima
Difficulties:
"Word Problem"
No such thing as perfect data

Geology

Definition:
Finding the best earth model to explain a given set of data
Issues:
Realism of results
Sufficiency of model
Difficulties:
Lack of perfect answer
Equivalence of solutions

Strategies that work:

Concrete examples
Diagrams, photos, road cuts, graphic solutions
Guidance and comfort

Example: Overdetermined 3-pt. Problem

Examples [to what?]

Problem: Are containments leaking from an underground storage tank?

Data:
Nature of phenomenon - soil and water
Variables to measure: hydrocarbon, lead
Data collection issues:
  • Sampling strategy:
  • Sample size - number and placement of wells
  • Sample design - multi-stage to determine ground water flow direction
    • Place additional wells in down gradient direction
    • Background sample
Data quality:
Data collection - field collection protocol
  • Chain of custody
Certified lab quality
Data description:
Plot data on map
Inspect for variability
  • Compare concentrations with background value to define presence of a plume
Draw contours
Data Conclusions:
If values are unusal, are they significant?
If values are not unusual, how confident are you that the site is clean?

Graphical Literacy

Strategies that work:

  1. Decide upon what type of graphs you want students to work with:
    (bar and scatterplot vs. [absolute?] lines - drawn on poster
  2. Be clear about how students should work with graphs
    • simply read information
    • find slopes and calculate percent change
    • fit a line to a "bunch of points" (i.e. data)
    • interpret and predict (requires use of symbols)
    • differentiate between different types of graphs and define behavior of system (is it linear or exponential? Power function made linear on log graph)
    • understand scatter and error

Examples in Geoscience:

Exponential:
Number of aftershocks / time
Population Growth</br> Energy consumption
Atmospheric carbon dioxide concentrations
Draw down in well
Land subsidence
Radiometric decay
Linear:
Travel-time of seismic waves (approximately)
Topographic slope (gradient)
Water-table slope
Miscellaneous: Bowen's reaction series
Sea-level curves
Climatic data/variation
Pressure-temperature curves

Helping Students Visualize Better in 3-D

Vince Schielack, Jim Sochacki, Denyse Lemaire

Our Goals:

Problem:

See diagram depicting earth with tropics, arctic circles, equator marked

3D Visualization of Earth

(Coordinates of Rotation)

Strategies: (Diagrams included for each step on original)

  1. Axis of Earth
  2. Meridian and coordinates on surface of Earth
  3. If a point moves in miles along the equator, how far would another point at a degrees of latitude move at the same time?
    • x / r = sin (90-a)

      x = r cos (a)

      Degrees Latitude: x/r Proportion => 90:0, 80:0.1736, 70:0.3420, 60:0.5, 50:0.6428, 40:0.7660, 30:0.8660, 20:0.9397, 10:0.9848, 0:1.0


Cycles of changes

Specific topics: e.g. tides, cycles of sea-level change

Strategies: (use tide as example)


Exercise II: Let's Predict Tides (with 6 components)

Examples in a geoscience context: Oceanography (intro)

Sedimentary Geology (sedimentary processes)