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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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