Dec 23, 2014
Daniel Garbin
Mathematics and Computer Science
MA 119 College Algebra Fall 2014
Assessment Report and Analysis
Introduction
This account contains the assessment report and analysis for the MA 119 College Algebra course. The
assessment considers 39 sections out of 95 currently offered, representing about 41% of the course sections being taught by the department during the Fall 2014 semester. There are 796 students that have
participated in this assessment.
The assessment is done based on the students’ performance on the final exam. Given that the final exam
is uniform and cumulative, it is inferred that the assessment should be representative of the population of
students taking College Algebra at Queensborough Community College CUNY and that the course may
be addressed based on the findings of the assessment.
Acknowledgments
The principal investigator would like to acknowledge the great help received from the members of the
MA-119 Curriculum Committee, in particular Zeynep Akcay, Lucien Makalanda, Andrew Bulawa, Sylvia
Svitak, Andrew Russell, Venessa Singhroy, and Robert Holt. Additionally, the PI would like to express the
help of the MA-119 final exam committee Changiz Alizadeh, Kwai Chiu, Danielle Cifone, Robert Donley,
and Lixu Li, and the secretaries of the Mathematics and Computer Science department, Carol Schilling
and Arlene Rodriguez, for help with the logistics of the assessment. Lastly, we express our gratitude to
the various faculty members that have participated in the assessment and gone the extra mile in gathering
data.
Course description
A basic presentation of the fundamental concepts of college algebra, systems of linear equations, inequalities, linear, quadratic, exponential and logarithmic functions. During the recitation hour, students review
properties of signed numbers, graphing of linear equations, basic geometric concepts, solution of linear
equations, factoring algebraic expressions and its applications to rational expressions. A graphing calculator will be required. The course is required/recommended towards the following: A.A. degree in Liberal
Arts and Sciences, A.S. degree in Visual and Performing Arts, A.S. Degree Programs in Liberal Arts
and Sciences (Science and Mathematics), Engineering Science, Health Sciences, Environmental Health,
Criminal Justice.
Student learning outcomes and general education objectives
Following the departmental course syllabus, the general education objectives listed therein are as follows
• use analytical reasoning skills to identify issues or problems and evaluate evidence in order to make
informed decisions;
• reason quantitatively and mathematically as required in their fields of interest and in everyday life;
• integrate knowledge and skills in their program of study;
1
• use information management and technology skills effectively for academic research and lifelong
learning.
As far as the student learning outcomes, the class promotes the following goals:
• understand the important concepts and theories of algebraic, geometric, exponential, and logarithmic
functions;
• apply such concepts to solve problems in mathematics, engineering and other disciplines.
Description of assignment
While there may be several ways as far as student assignments, it is the final exam that can be viewed
as a unifier among them and consequently one of the better ways for assessing learning. The final exam
is cumulative, consisting of almost all topics covered by the course. The final exam is also uniform and
written up by several faculty members of the department. Additionally, the department policy is that
“the final exam must count at least 30% of the grade and the student must score a minimum of 55 on the
uniform final exam to pass the course.”
In order to measure students’ performance, we examine the students’ solutions to 4 carefully chosen questions on the final exam. The questions chosen are broad enough so that on the one hand, they encompass
several concepts covered in the course, while on the other hand, they help us understand and measure
the degree to which students have fulfilled the above learning outcomes and general education objectives.
Below you can find a description and assessment rubric for the last 4 question on the final exam numbered
16 through 19.
16. Find an equation of the line that is perpendicular to the line . . . and passes through the point . . . .
Learning outcomes: Understand the concept of linear functions together with geometric concepts such as
lines and perpendicularity. Such concepts are ubiquitous.
Rubric: Check boxes 16a through 16c respectively if the student has:
a) found the slope of the given line
b) found the slope of the perpendicular line, based on part a) answer
c) found correct equation (in any form) of the perpendicular line, based on part b).
17. Determine the amount of money you will
!nthave after . . . years if you deposit . . . at . . . annual interest
r
compounded quarterly, using A = P 1 +
. Round to the nearest cent (in dollars and cents.)
n
Learning outcomes: Understand the concept of exponential functions; Apply such concept to solve a
problem in real life (finance). The question also requires that students understand various concepts from
finances and proper use of technology such as calculator.
Rubric: Check boxes 17a through 17c respectively if the student has:
a) plugged in the correct value for the interest rate
2
b) used the correct value of the number of compounding periods per year
c) computed the amount correctly.
18. A rectangular garden whose length is . . . feet longer than its width has an area of . . . square feet.
Find the dimensions of the garden, rounded to the nearest tenth of a foot.
Learning outcomes: Understand the concept of quadratic functions and equations together with geometric
concepts such as lines and perpendicularity. Apply such concepts to solve a problem in a real life situation
(interior design/carpentry.)
Rubric: Check boxes 18a through 18d respectively if the student has:
a) written correct equation for the area
b) derived the quadratic equation
c) solved the equation correctly
d) found the dimensions.
19. For the function y = x2 + bx + c ,
a) Determine the coordinates of the x-intercepts (if any).
b) Determine the coordinates of the y-intercept.
c) Determine the equation of the axis of symmetry.
d) Determine the coordinates of the vertex.
e) Graph the function, and label and indicate an appropriate scale on the axes.
Learning outcomes: Understand the concept of quadratic functions together with geometric concepts such
as turning points, symmetry, and graphing parabolas. Apply such concept to solve questions from say
physics (if coefficients are changed, the function describes the motion or height of a vertically thrown
object.)
Rubric: Check boxes 19a through 19e respectively if the student has:
a) found the x-intercepts.
b) found the y-intercept
c) found the axis of symmetry
d) found the vertex
e) graphed the function.
3
Results
The following tables summarize the number and percentage of correct answers based on the aforementioned
rubric items. For the complete data table, please see the appendix. We will recall here that 796 students
have participated in this assessment.
Rubric item
Correct answer count
Correct answer percentage
Rubric item
Correct answer count
Correct answer percentage
18a
457
57%
16a
516
65%
18b
361
45%
16b
312
39%
18c
205
26%
16c
259
33%
18d
174
22%
17a
531
67%
19a
552
69%
17b
492
62%
19b
556
70%
17c
367
46%
19c
428
54%
19d
426
54%
19e
461
58%
Data Analysis
The results in this assessment demonstrate the students’ usual pluses and minuses. Students continue to
have difficulties with fractions and word problems. Students are generally more comfortable with questions
that are broken down over several parts; difficulties occur when students have to connect several concepts in
order to solve a problem. The department continues to make every effort in providing rigorous instruction
based on conceptual understanding rather than procedural problem solving. The MA-119 committee will
continue to evaluate the results in even greater details and make recommendation to the department.
The student performance in question 16 is weak as only about a third are able to answer the question
correctly. One would expect a better performance since this question deals with perpendicular lines and
such are ubiquitous. The issue here seems to be poor arithmetic skills as solving the question correctly
requires knowledge of fractions.
Question number 17 deals with computing the amount of money in an account based on initial deposit,
annual rate, and compounding periods per year. About two thirds of students are able to convert the
annual rate from percentage to decimal and a little less than this understand the concept of number of
compounds per year. Nonetheless, short of half of students are able to compute the amount, using the
calculator. While students tend to use a calculator more than needed, when it comes to slightly more
sophisticated calculator computations students have greater difficulties.
The weakest performance is in 18, a question that deals with a word problem involving several concepts
such as area of a rectangle, relation between quantities, and quadratic equations. Here only a quarter
provide a complete solution. This may be indicative of lack of vue d’ensemble. It is not speculative to
suggest that if this question were scaffolded over several parts (much like in question 19), the students
performance would improve.
In question 19 the students have to combine algebra, arithmetic, and geometry concepts to ultimately graph
a quadratic equation (a parabola). Here the situation improves as little over two thirds handle the algebra
and arithmetic portion, little over half find the vertex of the parabola, and about three fifths provide the
graph. Albeit that the vertex is needed to graph the parabola, more students graph the parabola without
necessarily solving correctly for the vertex. This indicates that students use the calculator to graph the
function.
4
Math 119 -- Fall 2014 -- Assessment Data Sheet
Total
number of
students
in a section
Section
Section count:
Student count:
39
796
Found
Found
Found
Plugged
Found
Found
Wrote
Derived
Solved
Found
Found
Found
Found
Found
Graphed
slope
slope
eqn
correct
correct
correct
correct
the
eqn.
both
x-ints
y-int
axis
coords.
the
of given
perp
of perp
rate
number
amount
eqn.
quad.
correct.
dimens.
of
of
func.
line
line
line
comp.
for area
eqn.
symm.
vertex
based
based
periods
on 16a
on 16b
per year
18a
18b
19c
19d
16a
16b
16c
17a
17b
17c
18c
18d
19a
19b
19e
1
23
16
4
2
4
13
3
21
11
4
3
20
18
17
15
17
2
24
17
8
8
7
8
3
9
6
4
6
15
17
8
11
15
3
19
17
5
7
13
8
8
11
8
4
5
13
13
10
8
12
4
23
16
11
8
12
10
9
17
15
4
4
13
9
7
14
12
5
18
7
10
10
13
9
8
11
8
7
9
15
17
10
12
10
6
21
5
2
0
14
13
5
7
6
2
0
10
9
7
4
12
7
21
13
8
13
13
16
9
9
9
8
7
14
12
9
10
7
8
25
20
11
6
20
20
15
14
17
9
6
16
20
14
19
18
9
24
17
6
6
12
14
9
6
6
2
2
20
17
13
11
16
10
13
11
4
3
13
9
8
8
8
4
2
9
10
7
7
7
11
21
15
13
12
18
18
13
19
17
2
5
16
15
14
8
9
12
22
15
9
10
21
20
21
21
21
17
14
20
19
20
14
19
13
22
18
11
9
19
18
16
19
15
10
7
16
17
12
13
13
14
22
13
8
5
11
8
3
6
3
2
0
12
14
4
10
11
15
17
12
8
3
12
11
9
9
5
4
2
14
10
12
9
4
16
25
16
6
5
18
19
14
15
9
10
7
21
15
16
15
13
17
19
7
5
3
10
10
7
10
5
2
1
8
14
6
8
8
18
14
8
7
9
6
9
3
5
3
0
0
7
10
3
6
11
19
21
10
4
8
11
11
6
7
4
2
2
16
11
7
8
14
20
20
18
12
4
15
9
9
7
6
1
2
8
11
9
12
14
21
26
16
10
7
15
9
6
17
13
7
6
18
17
9
13
15
22
19
12
10
10
13
13
13
9
8
8
6
15
15
13
11
11
23
23
11
10
9
10
10
9
14
11
9
8
17
11
12
11
11
24
24
13
4
1
17
19
10
7
5
2
4
21
19
14
18
16
25
16
11
5
3
12
10
9
7
4
0
4
9
11
10
11
11
26
19
16
13
13
16
16
16
11
10
9
9
17
18
16
12
12
27
10
4
3
3
4
6
4
3
2
1
0
6
6
4
6
5
28
11
4
4
3
3
6
4
2
2
2
1
4
4
5
4
4
29
19
15
12
9
17
16
11
17
14
6
6
16
16
14
13
12
30
21
16
10
13
19
15
16
15
13
7
5
16
16
13
12
14
31
23
8
3
1
15
15
10
15
13
4
4
8
15
10
10
12
32
22
20
6
3
15
5
4
15
9
4
3
22
17
13
14
16
33
22
17
12
7
18
16
12
17
14
10
7
16
18
16
10
8
34
23
14
9
7
10
4
1
12
6
2
0
8
11
8
5
10
35
17
10
9
8
15
15
10
14
14
7
7
13
13
8
11
14
36
22
17
10
4
21
20
18
16
15
11
8
19
20
16
15
15
37
25
15
11
5
21
24
15
15
10
6
4
21
22
16
12
13
38
21
15
11
17
20
15
17
12
10
7
4
16
18
16
16
15
39
19
11
8
5
8
5
4
8
6
5
4
7
11
10
8
5
796
516
312
259
531
492
367
457
361
205
174
552
556
428
426
461
65%
39%
33%
67%
62%
46%
57%
45%
26%
22%
69%
70%
54%
54%
58%
Totals
Percentage Pass