Assessing the Mathematics Major with
a Bottom-Up Approach
Sarah V. Cook
Washburn University
Appendix B
Calculus I Results
The table below gives the results of students who took both the Calculus I
pre and post-test in Fall 2003 (n=37).
|
Problem
|
Pre-Test Mean
|
Post-Test
Mean
Alg/Trig skills
|
Post-Test
Mean
Calculus skills
|
|
Line/tangent
|
3.65
|
3.32
|
2.89
|
|
Inequality/increasing
|
2.76
|
3.51
|
3.43
|
|
Equation/extrema
(rational exponents)
|
2.73
|
3.32
|
2.49
|
|
Rationalize/limit
|
2.38
|
3.49
|
3.46
|
|
Complex fraction/limit
|
1.86
|
2.59
|
2.49
|
|
Simplify/integrate
(divide)
|
1.92
|
3.11
|
2.49
|
|
Trig Equation
/critical numbers
|
2.54
|
2.84
|
2.16
|
|
Ladder/ Rate of Change
|
3.76
|
3.62
|
3.11
|
The following table give the results of students who took both the Calculus
I pre and post test in Fall 2003 and passed Calculus I in Fall 2003 with a grade
of D or better (n= 32).
|
Problem
|
Pre-Test Mean
|
Post-Test
Mean
Alg/Trig skils
|
Post-Test
Mean
Calculus skills
|
|
Line/tangent
|
3.69
|
3.50
|
3.09
|
|
Inequality/increasing
|
2.91
|
3.78
|
3.69
|
|
Equation/extrema
(rational exponents)
|
2.84
|
3.50
|
2.78
|
|
Rationalize/limit
|
2.22
|
3.91
|
3.88
|
|
Complex fraction/limit
|
2.06
|
2.84
|
2.72
|
|
Simplify/integrate
(divide)
|
2.13
|
3.41
|
2.75
|
|
Trig Equation
/critical numbers
|
2.56
|
2.94
|
2.44
|
|
Ladder/ Rate of Change
|
3.72
|
3.84
|
3.25
|
Calculus II Results
The table below gives the results of students who took both the Calculus II
pre and post-test in Fall 2003 (n=12). All of these students passed the course.
|
Problem
|
Pre-Test Mean
|
Post-Test
Mean
Calc I skills
|
Post-Test
Mean
Calc II skills
|
|
Product/chain rule
|
3.67
|
3.58
|
3.67
|
|
Nested chain rules
|
3
|
---
|
---
|
|
Definite integral/u-sub
|
2.33
|
---
|
---
|
|
Critical numbers (Trig)
|
2.17
|
1.42
|
2.5
|
|
Intersection points
|
4.00
|
4.00
|
4.00
|
|
Integrate after dividing
|
1.58
|
---
|
---
|
|
Inverse trig integration
|
1.92
|
3.17
|
2.67
|
|
Ladder/ Rate of Change
|
1.00
|
---
|
---
|
Calculus III Results
The table below gives the results of students who took both the Calculus III
pre and post-test in Fall 2003 (n=12). All of these students passed the course.
|
Problem
|
Pre-Test Mean
|
Post-Test
Mean
Calc II skills
|
Post-Test
Mean
Calc III skills
|
|
Integration by parts
|
3.75
|
3.58
|
3.08
|
|
u-sub integration
|
3.42
|
---
|
---
|
|
Partial Fractions
|
2.25
|
---
|
---
|
|
Area between graphs
|
3.08
|
3.67
|
2.67
|
|
L’Hopitals
|
3.17
|
---
|
---
|
|
Equation of a plane
|
2.25
|
3.17
|
3.08
|
|
Parametric Equations
|
2.50
|
---
|
---
|
Combined results from Fall 2003 and
Spring 2004
The following table gives mean scores on the Calculus I post test and corresponding
questions on the Calculus II pre-test for those who took Calculus I in Fall
2003 and are taking Calculus II in Spring 2004 (n=17).
|
Problem on
Calculus II pre-test
|
Calc I
post-test mean
|
Calc II
pre-test mean
|
|
Product/chain rule
|
2.82
|
3.82
|
|
Nested chain rules
|
3.12
|
3.65
|
|
Definite integral/u-sub
|
3.29
|
3.11
|
|
Critical numbers (Trig)
|
2.41
|
3.18
|
|
Intersection points
|
|
3.76
|
|
Integrate after dividing
|
3.24
|
2.71
|
|
Inverse trig integration
|
3.00
|
1.82
|
|
Ladder/ Rate of Change
|
3.71
|
1.59
|
The following table gives mean scores on the Calculus II post-test and corresponding
questions on the Calculus III pre-test for those who took Calculus II in Fall
2003 and are taking Calculus III in Spring 2004 (n=6).
NOTE: There was an error made in Spring 2004 and the wrong version
of the Calculus III pre-test was given. Because of this, the questions
regarding L’Hopital’s rule and graphing a curve from its parametric
equations were not given on the pre-test.
|
Problem on
Calculus III pre-test
|
Calc II
post-test mean
|
Calc III
pre-test mean
|
|
Integration by parts
|
3.00
|
2.83
|
|
u-sub integration
|
2.83
|
0.83
|
|
Partial Fractions
|
2.83
|
2.50
|
|
Area between graphs
|
4.00
|
3.00
|
|
L’Hopitals
|
2.83
|
|
|
Equation of a plane
|
2.50
|
1.67
|
|
Parametric Equations
|
3.67
|
|
| 