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
|
