I. Why do intro physics students have so much trouble with math?

The importance of cognitive context: 1

The importance of cognitive context: 2

Failure to see symbols as representing

Some students seem deeply blind to the dimensions -- the measurement structure -- of an equation.

Failure to note associated variations

Failure to be able to parse equations

Failure to coordinatize time and space

Additional difficulty is caused by the number of different kinds of "constants and variables" we use

Student difficulties go deeper than mechanical failures

Many students have a similar response.

V. Impact of incorrect mental models on student’s use of math

Particle Pulses Mental Model of Waves

Applying a wrong mental model: