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HHMI Assessment Mathematical Competence

Page history last edited by erickuo 7 years, 8 months ago

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 




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