Student Difficulties with Math in the Context of Physics

Edward F. Redish

University of Maryland

Student Difficulties

PP Presentation

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

Math in the physics context

The importance of cognitive context: 1

The importance of cognitive context: 2

The Modeling Cycle

II. Semiotics

Students have many problems

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

Mathematical Homonyms

Mathematical Homoglyphs

Student difficulties go deeper than mechanical failures

III. Coding meaning:

Interpreting an equation:

Response

Interpretation

IV. Inappropriate Attitudes

Looking for consistency:

Responses

Changing the conditions:

Responses

Many students have a similar response.

V. Impact of incorrect mental models on studentís use of math

Particle Pulses Mental Model of Waves

Applying a wrong mental model:

Responses

Sample response

Common Student Equations

Interpretation

Focusing on the path

No dead reckoning:

Results

Implications

VI. Conclusions

Implications