Arapahoe Community College
Mathematics Assessment in the
First Two Years
Dr. Erica Johnson – Department
Chair
Jeffrey Berg
David Heddens
I. Abstract
During the last two years, the Arapahoe Community College Mathematics
Department participated in a college-wide effort to expand assessment
activities to the program and discipline level. A report at http://www.arapahoe.edu/custom/SAmathematics.html
details accomplishments during the first year. This report details
second-year accomplishments that focused on analyses of data from College
Algebra entrance and common final exams.
Appendix A
| Contents |
|
| Table1 |
Learning Outcomes Addressed by Departmental Courses |
| Table 2 |
Colorado Community College System Core Transfer
Program Student Learning Outcomes for College Algebra |
| Table 3 |
College Algebra Common Final (Calculator Based
Calculus Readiness) Question Learning Outcomes |
| Table 4 |
College Algebra Uniform Final Fall 2002 Grading
Curve |
| Table 5 |
College Algebra Uniform Final Spring 2003 Grading
Curve |
| Table 6 |
College Algebra Common Final Spring 2003 Rank Order
of Student Performance on Questions |
| Table 7 |
Distributions of Final Exam Correct Answer Rates,
AY 2001 |
| Table 8 |
Distributions of Final Exam Correct Answer Rates,
AY 2002 |
| Table 9 |
Distributions of Final Exam Correct Answer Rates,
Spring 02 and Spring 03 |
| Table 10 |
Tests of Each Question for Significantly Different
Correct Response Rates, Spring 2002 Form 1H and Spring 2003 Form
1D |
| Table 11 |
Linkage Across Calculus Readiness (1H) and Calculator-Based
Calculus Readiness (1D) Versions of the Common Final |
| Table 12 |
Student Enrollment in College Algebra 2002-2003
Academic Year |
| Table 13 |
Student Entrance Exam/Common Final Exam Completion
Status |
| Table 14 |
Entrance Exam Competency Measurement Distributions |
| Table 15 |
Final Exam Competency Measurement Distributions |
| Table 16 |
Contingency Table Cross-Classifying Students by
Their Entrance and Final Competency Measures, Fall 2002. |
| Table 17 |
Contingency Table Cross-Classifying Students by
Their Entrance and Final Competency Measures, Spring 2003. |
| Table 18 |
Student Learning Outcome Strengths and Weaknesses
College Algebra Common Final Spring 2003 |
| Table 19 |
Calculus I Common Project Scoring Rubric |
| Table 20 |
Assessment Methods Used to Measure Student Learning
Outcomes |
Table1
Learning Outcomes Addressed by Departmental Courses
| |
|
|
|
|
|
|
|
| |
Students
will acquire the ability to read, write, listen to, and speak
mathematics
|
Students will demonstrate a mastery
of competencies identified by the competency-based syllabi for
specific courses.
|
Students
will use appropriate technology to enhance their mathematical
thinking and understanding and to solve mathematical problems
and judge the reasonableness of their results.
|
Students will engage in substantial
mathematical problem solving.
|
Students will acquire the ability
to use multiple approaches-numerical, graphical, symbolic, and
verbal-to solve mathematical problems.
|
|
Fund
of Math
|
x
|
x
|
|
x
|
|
|
Pre-Algebra
|
x
|
x
|
|
x
|
|
|
Intro
Algebra
|
x
|
x
|
|
x
|
x
|
|
Math
Support
|
|
x
|
|
|
|
|
Survey
of Algebra
|
x
|
x
|
x
|
x
|
x
|
|
Tech
Lab for Algebra
|
|
x
|
x
|
|
|
|
Applied
Math I
|
x
|
x
|
|
x
|
x
|
|
Applied
Math II
|
x
|
x
|
|
x
|
x
|
|
Math
for Pre-Secondary Teachers I
|
x
|
x
|
|
x
|
x
|
|
Math
for Liberal Arts
|
x
|
x
|
x
|
x
|
x
|
|
College
Algebra
|
x
|
x
|
x
|
x
|
x
|
|
Trigonometry
|
x
|
x
|
x
|
x
|
x
|
|
Finite
Math
|
x
|
x
|
x
|
x
|
x
|
|
Survey
of Calculus
|
x
|
x
|
x
|
x
|
x
|
|
Statistics
|
x
|
x
|
x
|
x
|
x
|
|
Statistics
Lab
|
|
x
|
x
|
x
|
x
|
|
Calculus
I
|
x
|
x
|
x
|
x
|
x
|
|
Calculus
II
|
x
|
x
|
x
|
x
|
x
|
|
Calculus
III
|
x
|
x
|
x
|
x
|
x
|
|
Math
for Pre-Secondary Teachers II
|
x
|
x
|
|
x
|
x
|
|
Linear
Algebra
|
x
|
x
|
x
|
x
|
x
|
|
Differential
Equations
|
x
|
x
|
x
|
x
|
x
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Table 2
Colorado Community College System Core Transfer Program
Student Learning Outcomes for College Algebra
http://www.cterc.cccoes.edu/cccns/index.html
A.
Be
familiar with set notations, subsets of the real numbers and properties
of real numbers.
B.
Perform
algebraic manipulations including working with exponents, radicals,
polynomial operations, factoring and algebraic fractions.
C.
Present
methods for solving first and second degree equations and inequalities
and related topics.
D.
Solve
the following types of equations: linear, quadratic, equations involving
radicals, equations in quadratic form and equations involving absolute
value.
E.
Work
with formulas including formula evaluation and solving a formula for
any of the variables.
F.
Read
and analyze problems in the form of word problem applications and obtain
solutions using equations.
G.
Solve
first degree inequalities, higher degree inequalities and inequalities
involving absolute value.
H.
Recognize
and graph linear functions, rational functions, absolute value functions,
and graph inequalities in two variables.
I.
Work
with function notation and demonstrate knowledge of the meaning “function”.
J.
Demonstrate
an understanding of function composition, one-to-one functions and inverse
functions.
K.
Examine,
evaluate and graph exponential functions.
L.
Examine,
evaluate and graph logarithmic functions.
M.
Work
problems and solve equations containing exponential and logarithmic
functions.
N.
Explore
a variety of techniques used to solve linear and non-linear systems
of equations.
O.
Use
at least two of the following techniques to solve linear and non-linear
systems of the equations: substitution, addition, Gaussian elimination,
Cramer’s rule.
P.
Have
some familiarity with matrices and operations involving matrices.
Q.
Graph
systems of inequalities.
R.
Graph
conic sections including circles, parabolas, ellipses and hyperbolas.
S.
Identify
the conic section represented by a given second degree equation.
T.
Introduce
various topics related to sequences and series.
U.
Work
with series notation and sequence formulas, and counting principles.
V.
Apply
the Binomial Theorem.
W.
Demonstrate
an understanding of proof by mathematical induction.
X.
Present
topics in theory equations.
Y.
Perform
synthetic division.
Z.
Use
the Remainder Theorem and the Factor Theorem to factor and evaluate
polynomials.
AA.
Solve
polynomial equations using the Rational Root Theorem and/or approximation
techniques.
BB.
Write
and speak clearly and logically in presentations and essays.
CC.
Demonstrate
the ability to select and apply contemporary forms of technology to
solve problems or compile information.
Table
3: College Algebra Common Final (Calculator Based Calculus Readiness)
Question Learning Outcomes
|
Question
|
State Core Transfer Program Learning Outcome
|
MAA Placement Test Competency
|
|
1
|
O.
Use at least two of the following techniques to solve linear and
non-linear systems of equations: substitution, addition, Gaussian
elimination, Cramer’s rule.
|
Graphs of Functions, Equations and Factoring
|
|
2
|
F. Read and analyze problems in the form of word problem
applications and obtain solutions using equations.
|
Word Problems, Modeling, Numerical Awareness, Exponential
Functions
|
|
3
|
I.
Work with function notation and demonstrate knowledge of the meaning
“function”.
|
Graphs of Functions, Inequalities, Absolute Value
|
|
4
|
E. Work with formulas including formula evaluation and solving
a formula for any of the variables.
|
Geometry and Measurement, Word Problems, Modeling
|
|
5
|
J. Demonstrate an understanding of function composition,
one-to-one functions, and inverse functions.
|
Exponents and Logarithms
|
|
6
|
H.
Recognize and graph linear functions, rational functions, absolute
value functions, and graph inequalities in two variables.
|
Graphs of Functions, Concept Formulation
|
|
7
|
H.
Recognize and graph linear functions, rational functions, absolute
value functions, and graph inequalities in two variables.
|
Graphs of Functions
|
|
8
|
M.
Work problems and solve equations containing exponential and logarithmic
functions.
|
Exponents and Logarithms
|
|
9
|
E. Work with formulas including formula evaluation and solving
a formula for any of the variables.
|
Geometry and Measurement
|
|
10
|
U. Work with series notation and sequence formulas, and
counting principles.
|
Concept Formulation, Numerical Awareness, Exponents
and Logarithms
|
|
11
|
K. Examine, evaluate, and graph exponential functions.
|
Graphs of Functions, Exponential Functions
|
|
12
|
B.
Perform algebraic manipulations including working with exponents,
radicals, polynomial operations, factoring, and algebraic fractions.
|
Equations and Factoring
|
|
13
|
I.
Work with function notation and demonstrate knowledge of the meaning
“function”.
|
Geometry and Measurement, Graphs of Functions
|
|
14
|
B.
Perform algebraic manipulations including working with exponents,
radicals, polynomial operations, factoring, and algebraic fractions.
|
Equations and Factoring
|
|
15
|
I.
Work with function notation and demonstrate knowledge of the meaning
“function”.
|
Function Notation
|
|
16
|
H.
Recognize and graph linear functions, rational functions, absolute
value functions, and graph inequalities in two variables.
|
Graphs of Functions
|
|
17
|
G. Solve first degree inequalities, higher degree inequalities,
and inequalities involving absolute value.
|
Inequalities, Absolute Value
|
|
18
|
F. Read and analyze problems in the form of word problem
applications and obtain solutions using equations.
|
Geometry and Measurement, Word Problems, Modeling
|
|
19
|
H.
Recognize and graph linear functions, rational functions, absolute
value functions, and graph inequalities in two variables.
|
Word Problems, Modeling, Concept Formulation
|
|
20
|
F. Read and analyze problems in the form of word problem
applications and obtain solutions using equations.
|
Geometry and Measurement, Word Problems, Modeling
|
Table 4:
College Algebra Uniform Final Fall 2002 Grading Curve
|
Exam Score (out of 20)
|
Curved percentage
|
|
20
|
|
|
19
|
98
|
|
18
|
96
|
|
17
|
93
|
|
16
|
90
|
|
15
|
88
|
|
14
|
86
|
|
13
|
83
|
|
12
|
80
|
|
11
|
78
|
|
10
|
75
|
|
9
|
72
|
|
8
|
68
|
|
7
|
65
|
|
6
|
62
|
|
5
|
60
|
|
4
|
Instructor discretion
|
|
3
|
|
|
2
|
Instructor discretion
|
|
1
|
|
|
0
|
|
Table 5:
College Algebra Uniform Final Spring 2003 Grading Curve
|
Exam Score (out of 20)
|
Curved percentage
|
|
20
|
|
|
19
|
100
|
|
18
|
98
|
|
17
|
96
|
|
16
|
94
|
|
15
|
92
|
|
14
|
90
|
|
13
|
88
|
|
12
|
85
|
|
11
|
82
|
|
10
|
80
|
|
9
|
77
|
|
8
|
73
|
|
7
|
70
|
|
6
|
67
|
|
5
|
63
|
|
4
|
60
|
|
3
|
56
|
|
2
|
53
|
|
1
|
50
|
|
0
|
instructor discretion
|
Table 6:
College Algebra Common Final Spring 2003 Rank Order of Student Performance
on Questions
|
Question
|
%
Correct
|
State
Core Transfer Program Learning Outcome
|
|
19
|
88.33%
|
H
|
|
11
|
79.44%
|
K
|
|
15
|
79.44%
|
I
|
|
3
|
74.44%
|
I
|
|
17
|
72.22%
|
G
|
|
9
|
70.00%
|
E
|
|
18
|
69.44%
|
F
|
|
16
|
67.22%
|
H
|
|
4
|
63.89%
|
E
|
|
7
|
63.33%
|
H
|
|
12
|
63.33%
|
B
|
|
14
|
62.78%
|
B
|
|
5
|
57.78%
|
J
|
|
6
|
51.67%
|
H
|
|
10
|
48.33%
|
U
|
|
20
|
43.89%
|
F
|
|
13
|
42.78%
|
I
|
|
1
|
41.11%
|
O
|
|
8
|
41.11%
|
M
|
|
2
|
36.11%
|
F
|
Table 7
Distributions of Final Exam Correct Answer Rates, AY 2001
| |
exams
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
|
Fall
01
|
214
|
132
|
140
|
138
|
179
|
74
|
129
|
199
|
131
|
199
|
105
|
193
|
144
|
142
|
201
|
116
|
101
|
86
|
133
|
138
|
177
|
|
proportion
|
|
0.6
|
0.7
|
0.6
|
0.8
|
0.3
|
0.6
|
0.9
|
0.6
|
0.9
|
0.5
|
0.9
|
0.7
|
0.7
|
0.9
|
0.5
|
0.5
|
0.4
|
0.6
|
0.6
|
0.8
|
|
Spring
02
|
159
|
100
|
104
|
90
|
121
|
72
|
121
|
154
|
92
|
145
|
91
|
146
|
107
|
110
|
152
|
91
|
70
|
55
|
110
|
103
|
137
|
|
proportion
|
|
0.6
|
0.7
|
0.6
|
0.8
|
0.5
|
0.8
|
1
|
0.6
|
0.9
|
0.6
|
0.9
|
0.7
|
0.7
|
1
|
0.6
|
0.4
|
0.3
|
0.7
|
0.6
|
0.9
|
Table 8
Distributions of Final Exam Correct Answer Rates, AY 2002
| |
exams
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
|
Fall
02
|
158
|
49
|
36
|
109
|
111
|
84
|
65
|
94
|
58
|
113
|
68
|
121
|
78
|
48
|
78
|
121
|
89
|
93
|
103
|
128
|
60
|
|
proportion
|
|
0.3
|
0.2
|
0.7
|
0.7
|
0.5
|
0.4
|
0.6
|
0.4
|
0.7
|
0.4
|
0.8
|
0.5
|
0.3
|
0.5
|
0.8
|
0.6
|
0.6
|
0.7
|
0.8
|
0.4
|
|
Spring
03
|
180
|
74
|
65
|
134
|
115
|
104
|
93
|
114
|
74
|
126
|
87
|
143
|
114
|
77
|
113
|
143
|
121
|
130
|
125
|
159
|
79
|
|
proportion
|
|
0.4
|
0.4
|
0.7
|
0.6
|
0.6
|
0.5
|
0.6
|
0.4
|
0.7
|
0.5
|
0.8
|
0.6
|
0.4
|
0.6
|
0.8
|
0.7
|
0.7
|
0.7
|
0.9
|
0.4
|
Table 9
Distributions of Final Exam Correct Answer Rates, Spring 02 and Spring
03
|
Form 1H
|
exams
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
|
S02
|
159
|
100
|
104
|
90
|
121
|
72
|
121
|
154
|
92
|
145
|
91
|
146
|
107
|
110
|
152
|
91
|
70
|
55
|
110
|
103
|
137
|
|
proportion
|
|
0.6
|
0.7
|
0.6
|
0.8
|
0.5
|
0.8
|
1
|
0.6
|
0.9
|
0.6
|
0.9
|
0.7
|
0.7
|
1
|
0.6
|
0.4
|
0.3
|
0.7
|
0.6
|
0.9
|
|
Form 1D
|
exams
|
4
|
3
|
2
|
1
|
6
|
|
7
|
8
|
11
|
12
|
|
9
|
15
|
16
|
13
|
14
|
20
|
17
|
18
|
19
|
|
S03
|
180
|
115
|
134
|
65
|
74
|
93
|
|
114
|
74
|
143
|
114
|
|
126
|
143
|
121
|
77
|
113
|
79
|
130
|
125
|
159
|
|
proportion
|
|
0.6
|
0.7
|
0.4
|
0.4
|
0.5
|
|
0.6
|
0.4
|
0.8
|
0.6
|
|
0.7
|
0.8
|
0.7
|
0.4
|
0.6
|
0.4
|
0.7
|
0.7
|
0.9
|
Table 10
Tests of Each Question for Significantly Different Correct Response
Rates, Spring 2002 Form 1H and Spring 2003 Form 1D
|
Form 1H
|
exams
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
|
Form 1D
|
exams
|
4
|
3
|
2
|
1
|
6
|
|
7
|
8
|
11
|
12
|
|
9
|
15
|
16
|
13
|
14
|
20
|
17
|
18
|
19
|
| |
z
|
0.1
|
1.2
|
-4
|
-6
|
1.2
|
|
-4
|
-3
|
-1
|
0.9
|
|
0.4
|
1.3
|
-3
|
-3
|
3.3
|
2.2
|
0.4
|
0.6
|
0.2
|
| |
p-val
|
0.9
|
0.2
|
0*
|
0*
|
0.2
|
|
0*
|
0*
|
0.2
|
0.4
|
|
0.7
|
0.2
|
0*
|
0**
|
0*
|
0.03
|
0.7
|
0.5
|
0.8
|
* p-value was less than 0.002
** pvalue was less than 0.01
Table 11 Linkage Across Calculus Readiness
(1H) and Calculator-Based Calculus Readiness (1D) Versions of the Common
Final
|
Question
1H
|
Question
1D
|
Student Learning Outcome
|
|
1
|
4
|
E.
Work with formulas including formula evaluation and solving a
formula for any of the variables.
|
|
2
|
3
|
I.
Work with function notation and demonstrate knowledge of the meaning
“function”.</p>
|
|
3
|
2
|
M. Work problems and solve equations containing exponential
and logarithmic functions.
|
|
4
|
1
|
O.
Use at least two of the following techniques to solve linear and
non-linear systems of equations: substitution, addition, Gaussian
elimination, Cramer’s rule.
|
|
5
|
6
|
H.
Recognize and graph linear functions, rational functions, absolute
value functions, and graph inequalities in two variables.
|
|
6
|
None
|
B.
Perform algebraic manipulations including working with exponents,
radicals, polynomial operations, factoring, and algebraic fractions.
|
|
7
|
7
|
H.
Recognize and graph linear functions, rational functions, absolute
value functions, and graph inequalities in two variables. (category
D is possible)
|
|
8
|
8
|
M.
Work problems and solve equations containing exponential and logarithmic
functions.
|
|
9
|
11
|
K. Examine, evaluate, and graph exponential functions.
|
|
10
|
12
|
B.
Perform algebraic manipulations including working with exponents,
radicals, polynomial operations, factoring, and algebraic fractions.
|
|
11
|
None
|
B. Perform algebraic manipulations including working with
exponents, radicals, polynomial operations, factoring, and algebraic
fractions.
|
|
12
|
9
|
E. Work with formulas including formula evaluation and solving
a formula for any of the variables.
|
|
13
|
15
|
I.
Work with function notation and demonstrate knowledge of the meaning
“function”.
|
|
14
|
16
|
H.
Recognize and graph linear functions, rational functions, absolute
value functions, and graph inequalities in two variables.
|
|
15
|
13
|
I.
Work with function notation and demonstrate knowledge of the meaning
“function”.
|
|
16
|
14
|
B.
Perform algebraic manipulations including working with exponents,
radicals, polynomial operations, factoring, and algebraic fractions.
|
|
17
|
20
|
F. Read and analyze problems in the form of word problem
applications and obtain solutions using equations.
|
|
18
|
17
|
G. Solve first degree inequalities, higher degree inequalities,
and inequalities involving absolute value.
|
|
19
|
18
|
F. Read and analyze problems in the form of word problem
applications and obtain solutions using equations.
|
|
20
|
19
|
H.
Recognize and graph linear functions, rational functions, absolute
value functions, and graph inequalities in two variables.
|
Table
12 Student Enrollment in College Algebra 2002-2003 Academic Year
|
Section Fall 02
|
Student Count
|
Section Spr 03
|
Student Count
|
|
L01
|
28
|
L01
|
29
|
|
L02
|
30
|
L02
|
28
|
|
L03
|
25
|
L03
|
29
|
|
L04
|
34
|
L04
|
24
|
|
L05
|
32
|
L05
|
12
|
|
L06
|
38
|
L06
|
31
|
|
L07
|
30
|
L07
|
31
|
|
L08
|
26
|
L08
|
17
|
|
L48
|
22
|
L09
|
20
|
|
L85
|
14
|
L10
|
20
|
|
TOTAL
|
279
|
L66
|
26
|
| |
|
TOTAL
|
267
|
Table
13 Student Entrance Exam/Common Final Exam Completion Status
|
Entrance Exam Completed
|
Final Exam Completed
|
Student Count Fall ‘02
|
Student Count Spring ‘03
|
|
Yes
|
Yes
|
119
|
168
|
|
Yes
|
No
|
121
|
87
|
|
No
|
Yes
|
39
|
12
|
|
No
|
No
|
0
|
0
|
| |
TOTAL
|
279
|
267
|
Table
14 Entrance Exam Competency Measurement Distributions
|
Correct Responses on Entrance Exam
|
Proportion Correct on Entrance Exam
|
Student Count Fall ‘02
|
Student Count Spring ‘03
|
|
0
|
0
|
8
|
18
|
|
1
|
0.5
|
41
|
64
|
|
2
|
1
|
70
|
86
|
| |
TOTAL
|
119
|
168
|
Table
15 Final Exam Competency Measurement Distributions
|
Correct Responses on Final Exam
|
Proportion Correct on Final Exam
|
Student Count Fall ‘02
|
Student Count Spring ‘03
|
|
0
|
0
|
19
|
31
|
|
1
|
0.333
|
28
|
61
|
|
2
|
0.666
|
39
|
45
|
|
3
|
1
|
33
|
31
|
| |
TOTAL
|
119
|
168
|
Table
16 Contingency Table Cross-Classifying Students by Their Entrance and
Final Competency Measures, Fall 2002.
|
Fall ‘02
|
Correct
Responses on Final Exam
|
|
|
0
|
1
|
2
|
3
|
|
Correct
Responses on Entrance Exam
|
0
|
3
|
2
|
3
|
0
|
8
|
|
1
|
6
|
13
|
13
|
9
|
41
|
|
2
|
10
|
13
|
23
|
24
|
70
|
| |
19
|
28
|
39
|
33
|
119
|
Table
17 Contingency Table Cross-Classifying Students by Their Entrance and
Final Competency Measures, Spring 2003.
|
Spring ‘03
|
Correct
Responses on Final Exam
|
|
|
0
|
1
|
2
|
3
|
|
Correct
Responses on Entrance Exam
|
0
|
6
|
8
|
4
|
0
|
18
|
|
1
|
16
|
21
|
16
|
11
|
64
|
|
2
|
9
|
32
|
25
|
20
|
86
|
| |
31
|
61
|
45
|
31
|
168
|
Table
18 Student Learning Outcome Strengths and Weaknesses
College Algebra Common Final Spring 2003
Table
19 Calculus I Common Project Scoring Rubric
| |
10 points
|
9 points
|
7 points
|
5 points
|
0 points
|
|
Problem Statement
|
The student(s) provide an accurate statement of the problem in
the introduction of the written presentation. All components
of the problem are presented correctly.
|
The student(s) provide a mostly accurate statement of the problem
in the introduction of the written presentation. Some minor components
of the problem are missing or incorrect.
|
The student(s) provide a fairly complete statement of the problem
in the introduction of the written presentation. Major components
of the problem are missing or incorrect.
|
The student(s) provide a vague statement of the problem in the
introduction of the written presentation. Major components of
the problem are missing and the statement may include extraneous
components.
|
The student(s) provide no introduction addressing the statement
of the problem in the written presentation.
|
| |
20 points
|
17 points
|
15 points
|
10 points
|
0 points
|
|
Problem Solution
|
The student(s) correctly and completely apply appropriate mathematical
principles and algorithms to obtain solution. All conditions
of the problem are satisfied and strong supporting arguments are
exhibited. Efficient, focused, and rigorous.
|
The student(s) correctly and completely apply appropriate mathematical
principles and algorithms to obtain solution. All essential conditions
of the problem are satisfied but some minor conditions are overlooked.
Sufficient supporting arguments are exhibited. Minor problems
with efficiency, focus, and rigor do not detract from solution
presentation.
|
The student(s) apply appropriate mathematical principles and
algorithms to obtain a nearly complete and correct solution.
Some essential conditions of the problem are overlooked and/or
few supporting arguments are exhibited. Lack of efficiency, focus,
and/or rigor detracts from solution presentation.
|
The student(s) apply some appropriate and/or unrelated mathematical
principles and algorithms to obtain an incomplete and incorrect
solution. Several essential conditions of the problem are overlooked
and supporting arguments are virtually nonexistent. Inefficient,
unfocused, and superficial.
|
The student(s) present no solution.
|
| |
15 points
|
13 points
|
11 points
|
7 points
|
0 points
|
|
Mathematical Notation
|
The student(s) consistently use correct mathematical notation
and terminology.
|
The student(s) use correct mathematical notation and terminology
except in a few cases. Incorrect notation and/or terminology
do not substantially detract from the presentation of the solution.
|
The student(s) use correct mathematical notation most of the
time. Incorrect notation and/or terminology slightly detract
from the presentation of the solution.
|
The student(s) consistently use incorrect mathematical notation
and terminology that significantly detracts from the presentation
of the solution.
|
The student(s) use no mathematical notation or terminology.
|
| |
10 points
|
9 points
|
7 points
|
5 points
|
0 points
|
|
Graphs
|
The student(s) clearly indicate axis labels and scale on all
graphs. All graphs are accurate and use an appropriate scale
to show important aspects of presented curves. All curves and
important points are clearly labeled
|
The student(s) clearly indicate axis labels and scale on all
graphs. The student(s) present a few graphs with minor flaws.
Scale on graphs appropriate to show important aspects of presented
curves on all but possibly a few graphs.
|
The student(s) do not include labels and scale on graphs; however,
curves are correctly graphed if scale is inferred OR student(s)
include labels and scale on graphs; however, some curves are incorrectly
graphed.
|
The student(s) do not include labels and scale on graphs and
most curves are correctly graphed if scale is inferred OR most
curves are incorrectly graphed.
|
The student(s) do not include any supporting graphs.
|
|
15 points
|
12 points
|
10 points
|
7 points
|
0 points
|
|
Presentation
|
The overall appearance of the presentation
is neat and the paper is easy to read. All pertinent information
can be readily found. The student(s) communicate effectively
and clearly to target audience and include all appropriate graphs
and diagrams.
|
The overall appearance of the presentation is neat and the paper
is readable. All pertinent information is in the same area or
is appropriately referred to if in a different area, but arrangement
could be improved. The student(s) communicate effectively and
clearly to target audience; however, a few supporting graphs and
diagrams may be missing.
|
The presentation is hard to read and/or pertinent information
is hard to find. The student(s) communicate to target audience
but the presentation contains gaps in the flow and several supporting
graphs and diagrams may be missing.
|
The presentation is hard to read and pertinent information is
hard to find. The student(s) minimally communicate to target
audience. The presentation contains major gaps in flow and few
if any supporting graphs and diagrams.
|
The presentation is illegible, incoherent, and contains no pertinent
information or supporting graphs or diagrams.
|
| |
10 points
|
9 points
|
7 points
|
5 points
|
0 points
|
|
Creativity
|
The presentation is sophisticated and elegant and includes several
insightful interpretations, extensions, and generalizations.
|
The presentation is thorough and appealing and includes some
insightful interpretations, extensions, and generalizations.
|
The presentation is sound but includes few insightful interpretations,
extensions, and generalizations.
|
The presentation marginally extends mathematical concepts and
algorithms to obtain the problem solution but includes essentially
no interpretations, extensions, or generalizations.
|
The presentation exhibits no creativity.
|
| |
10 points
|
9 points
|
7 points
|
5 points
|
0 points
|
|
Conclusion/Reflection
|
The student(s) provide an accurate summary and a complete reflection
of mathematical concepts and algorithms exercised.
|
The student(s) provide a mostly accurate summary but minor aspects
of the project are missing. Reflection of mathematical concepts
and algorithms exercised is nearly complete but some minor points
are neglected.
|
The student(s) provide a reasonable summary but key aspects of
the project are missing. Reflection omits key mathematical concepts
and algorithms exercised.
|
The student(s) provide a minimal summary and little reflection
of mathematical concepts and algorithms exercised.
|
The student(s) provide no summary or reflection.
|
| |
10 points
|
9 points
|
7 points
|
5 points
|
0 points
|
|
English
|
The student(s) include appropriate and sufficient narrative to
provide structure to the presentation using complete sentences,
correct spelling, correct grammar, and correct punctuation.
|
The student(s) include appropriate narrative using complete sentences
that may include some minor spelling, grammar, and/or punctuation
errors. Narrative may fall slightly short of providing adequate
structure to the presentation.
|
The student(s) include narrative using a few incomplete sentences
and/or committing significant spelling, grammar, and/or punctuation
errors. Narrative may fall somewhat short of providing adequate
structure to the presentation.
|
The student(s) include narrative using very few complete sentences
and committing significant spelling, grammar, and punctuation
errors. Narrative falls significantly short of providing adequate
structure to the presentation.
|
The student(s) include no narrative to provide structure to the
presentation.
|
Table
20 Assessment Methods Used to Measure Student Learning Outcomes
|
Outcome/Tool
|
Project
or Portfolio
|
Standardized
Exam
|
Pre-test/
Post-test
|
Faculty
Survey
|
Student
Survey
|
|
Students
will acquire the ability to read, write, listen to, and speak
mathematics
|
CP2003
|
|
|
|
|
|
Students
will demonstrate a mastery of competencies identified by the competency-based
syllabi for specific courses.
|
CP2003
|
CF2001
|
PP2002
|
|
|
|
Students
will use appropriate technology to enhance their mathematical
thinking and understanding and to solve mathematical problems
and judge the reasonableness of their results.
|
CP2003
|
CF2001
|
|
|
|
|
Students
will engage in substantial mathematical problem solving.
|
CP2003
|
|
|
|
|
|
Students
will acquire the ability to use multiple approaches-numerical,
graphical, symbolic, and verbal-to solve mathematical problems.
|
CP2003
|
|
|
|
|
CF2001 - College Algebra common final data collection and analysis
began in 2001-2002 academic year
PP2002 - College Algebra entrance exam/common final data collection
and analysis began in 2002-2003 academic year
CP2003 - Calculus I common projects with scoring rubric beginning
in 2003-2004 academic year
|
