Data Collection Main Page

Assessing Mathematical Competence

see also Quantitative Skills and Reasoning on Assessing Competencies page

What is mathematical competence (in this course)?

Below is a tentative list of things we might mean. First order of business it to see what we already do and how it maps to or helps us expand/modify a list like this.

Making sense of equations

•  mapping between the symbols and the world
•  attending to dimensions and units

Building mathematical models

• creating equations that describe natural/physical situations
• understanding assumptions/limitations
• choosing appropriate parameters/units

Manipulating equations and interpreting solutions

• rearranging equations to gain insight
• interpreting solutions
• exploring sensitivities and limits

Working with and coordinating multiple mathematical representations

• coordinating among different representations
• understanding, interpreting and choosing among representational forms

Quantification and Estimation

• knowing when quantification can yield insights
• appropriate use of estimation

More Data in:

PHYS 131:132 HW - Math Competencies.xlsx

What competencies are students most asked to show in Phys 131/132 (fall 2012 - spring 2013)?

• Generating equations from canonical ideas in physics that describe specific natural/physical situations:
  (Problems where the answer can't be found by directly applying a known equation.  A conceptual understanding of the situation is needed to figure out how to manipulate or generate equations.)
• The Cat and the Antelope
• The Tortoise and the Hare
• Testing the motion detector
• Diffusion and Slime Molds
• What if the Greenland Ice Sheet Melts?
• Fish Buoyancy
• Polymers and Entropy
• Free Expansion
•  Connecting graphs to physical situations/concepts
• Graph for a cart on a tilted airtrack - with spring
• Hitting a Bowling Ball
• Carts and Graphs
• Bound States
• Going to a Deeper Well
• The Train, the hill, and the bumper
• Thermal to Chemical Energy Transfer
• The Penny and the Jelly Donut
• The Bulldog on the skateboard
• Tracking Round a Circuit
• SHO Energies
• Numerical Estimation in Scientific Contexts
• Sensing Molecular Signals
• How big is a protein molecule?
• Moving through a Cell
• Blood and Breath
• Propelling a Paramecium
• What if the Greenland Ice Sheet Melts?
• Muscle Contraction
• The Penny and the Jelly Donut
• Population Growth: I
• Counting Charges
• Packing DNA
• Atorvastatin Calcium
• Interfering Atoms 
• Dimensional Analysis (2 categories: either "attending to dimensions" in making sense of equations or "choosing appropriate dimensions" in building mathematical models)
• Counting Cubes
• Propelling a Paramecium
• Diffusion and Viscosity
• Enthalpy calculation for a simple molecule
• Boltzmann -- chemist or physicist?
• Capacitance dimensions
• Investigating dependencies with equations (2 categories: either "using equations to investigate dependencies/proportionality" or "exploring sensitivities and limits" in manipulation equations and interpreting solutions)
• Heat Generation Big and Small
• The Cat and the Antelope
• Forces between charges
• Analyzing Dipoles
• Random vs Coherent Motion
• Polymers and Entropy
• Random or not, here I come
• Free Expansion
• Both Ions Moving