Mel S. Sabella
E. F. Redish
Student Understanding of Topics in Calculus
Introduction
Functions and Variables
Limits and Continuity
Derivatives
Table 1. Student understanding of differentiation.
Description | Mean Scores (0-4) | Error Classification |
gradient of tangent to curve by differentiation | 3.76 | Structural and Executive |
substitution and increases from equations | 3.68 | Structural and Executive |
significance of rates of change from differentiation | 3.62 | Structural and Executive |
carrying out differentiation | 3.50 | Executive |
limits of geometric sequences | 2.78 | Structural |
infinite geometric sequences | 2.56 | Structural |
stationary points on a graph | 2.54 | Structural and Arbitrary |
rate of change from straight line graph | 2.02 | Structural |
average rate of change from curve | 1.92 | Structural and Executive |
use of the -symbolism | 1.40 | Structural |
rate, average rate, and instantaneous rate | 1.18 | Structural |
differentiation as a limit | 1.14 | Structural |
Integral
Table 2. Student understanding of integration.
Description | Mean Scores (0-4) | Error Classification |
simplification of sum of areas of rectangles | 3.52 | Executive |
heights of rectangles under graphs | 3.42 | Structural and Executive |
carrying out integration | 3.40 | Structural, Arbitrary and Executive |
sequence of approximations to area under graph | 3.22 | Executive |
limits of sequences of numbers | 3.06 | Structural and Executive |
limits from general terms | 2.90 | Structural and Executive |
complications in area calculations | 2.78 | Structural, Arbitrary and Executive |
limit from sequence of fractions + from general term | 2.48 | Structural |
limit of sequence equals area under graph | 1.00 | Structural |
volume of revolution | 0.88 | Structural |
integral of sum equals sum of integrals | 0.60 | Structural |
Use of Technology
References
University of Maryland | Physics Department | PERG UMD | Project Links |
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Please address questions and comments to Mel Sabella.
email: msabella@delphi.umd.edu