Sep 12, 2015
MA 119 Curriculum Committee
Mathematics and Computer Science
MA 119 College Algebra Spring 2015
Assessment Report and Analysis
Introduction
This account contains the assessment report and analysis for the MA 119 College Algebra course. The
assessment considers 54 sections which is about half of the course sections being taught by the department
during the Spring 2015 semester. There are 1, 139 students participated in this assessment. This report
augments to the previously conducted assessment during the Fall semester of 2014.
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 members of the MA-119 Curriculum Committee – Zeynep Akcay, Lucien Makalanda, Andrew Bulawa,
Sylvia Svitak, Andrew Russell, Venessa Singhroy, Daniel Garbin and Robert Holt – would like to express
much appreciation to 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
The course consists of 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 first 4 question on the final exam numbered
1 through 4.
1. Solve for x:
log3 (2x − 5) = 2 .
Learning outcomes: Apply the relationship between logarithmic and exponential functions to solve logarithmic equations; recognize that the solution requires solving a linear equation; determine, and solve the
required linear equations.
Check boxes 1a through 1c respectively if the student has:
a) written the equation either as 2x−5 = 32 ; alternate equations are log3 (2x−5) = log3 (32 ) or 3log3 (2x−5) =
32
b) arrived at the linear equation 2x − 5 = 9
c) solved correctly the equation in part b)
2. Write the domain of the function using interval notation
√
f (x) = 28 − 4x .
Learning outcomes: Recognize that a domain of a function defines what values for the input are permissible;
recognize and apply inequalities to determine a domain; solve the required inequalities correctly; write the
domain in interval notation.
Check boxes 2a through 2d respectively if the student has:
2
a) identified that the radicand must be non-negative, i.e. 28 − 4x ≥ 0
b) arrived at one of the two inequalities 28 ≥ 4x or −4x ≥ −28
c) solved correctly, i.e. x ≤ 7
d) provided the solution using interval notation.
3. Simplify completely
1
2
− 2
x x .
4
1− 2
x
Learning outcomes: Recognize rational expressions as ratios of algebraic expressions, which may be simplified to ratios of polynomials; simplify rational expressions by appropriate techniques.
Check boxes 3a through 3d respectively if the student has:
a) found the least common multiple of all the fractions, i.e. LCM = x2 ; alternatively, combined the
x−2
x2 − 4
fractions at the top and bottom as
and
resp.
x2
x2
b) scaled up (amplified) the fraction by LCM; alternatively, arrived at
c) arrived at
x−2
x2
·
x2
x2 − 4
x−2
x2 − 4
d) simplified to
1
.
x+2
4. Solve for x and check
√
5x − 9 + 1 = x .
Learning outcomes: Recognize radical expressions in equations; apply the techniques required to solve
equations that involve radical expressions.
Check boxes 4a through 4e respectively if the student has:
a) arrived at 5x − 9 = (x − 1)2
b) obtained correct binomial expansion (x − 1)2 = x2 − 2x + 1
c) arrived at the quadratic equation x2 − 7x + 10 = 0
d) obtained x = 2, 5 as solutions
e) checked the solutions and identified that both are correct.
3
Data Analysis
Overall, students performed better on the first two questions. This is most likely due to the fact that
questions 3 and 4 require better grasp on the algebraic machine and involve more steps. Students continue
to have difficulties with fractions and word problems. Students are generally more comfortable with
questions that are broken down into 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 detail and make recommendations to the
department.
Question 1 was answered correctly by 3 out of 5 students. Once students know the definition of the
logarithm, students are able to solve the resulting linear equation.
About half answered question 2 correctly. However, the final answer had to be expressed in two different
ways (inequality and interval notation.) When orientation or direction is understood, then the two forms
of answering are synonymous. Only 1/3 of students provided both forms.
Question 3 requires algebraic manipulation (simplification of fractions where the parts themselves are
fractions.) About 2/3 of students commenced on the right path. However, it is disappointing to see that
only 1/4 of the students were able to solve it all the way through. Question 4 is also algebraic, involving
a radical equation. Here again, 2/3 started correctly, 1/3 found the solution, yet only 1/4 checked the
validity of the solutions.
Worth noting is the fact that all these assessed questions, while different in level of difficulty and complexity,
carry the same grade weight. The same applies to the uniform exam in whole. It may be somewhat
debatable, that question 4 ought to be worth twice as much as question 1. If questions were weighted at
their true values, it would align the grades on the final more with the data from the assessment.
We hypothesizes the following: A possible reduction in course topics and strong emphasis of in-depth coverage of the topics, together with applications of mathematics to the quotidian life, will have an impact in the
way students experience mathematics. This may contribute towards our goal of promoting understanding in
mathematics as well as increasing the passing rate, and motivating professors towards introducing students
to the actual world of mathematics. Metaphysical issues such as what mathematics is, why mathematics
should be studied, and that mathematics should not be a dry subject, but more an art on the one hand
and philosophy and pattern recognition (or lack of) on the other.
4
Math 119 -- Spring 2015 -- Assessment Data Sheet
Total
number of
students
in a section
Section
Section count:
Student count:
54
1139
Obtained Obtained Solved
Radicand Obtained Obtained Wrote
equation equation part b
28-4x
either
x <= 7 correct
2
2x-5 = 3 2x-5 = 9 correctly >= 0
28>=4x
interval
or an
or
equiv.
equiv.
equation
Found LCM
x2 or
combined
top and
bottom
fractions
Scaled
Arrived SimplifiedObtained
fractions at fractionto
5x-9 =
2
by LCM
x-2
1
(x-1)
or
x2-4
x-2
correct
alt.
Expanded Arrived
the
at
binomial correct
correctly quad.
equation
Found
x=2,5
as
solutions
Checked
solutions
and
stated
both are
correct
1a
3a
3b
4b
4d
4e
1b
1c
2a
2b
2c
2d
3c
3d
4a
4c
1
22
12
11
9
14
14
6
4
12
9
6
4
17
8
4
2
1
2
17
11
11
11
14
14
13
10
10
8
8
7
11
10
7
5
4
3
16
8
11
11
11
11
10
6
9
9
6
3
9
9
9
5
4
4
24
14
14
14
9
8
7
3
17
13
12
9
13
12
11
11
3
5
18
3
6
6
7
7
4
3
13
13
5
4
6
5
4
4
4
6
22
17
17
17
16
17
14
7
20
17
15
4
12
9
9
6
6
7
26
14
11
11
19
13
13
10
19
16
12
8
17
15
12
10
12
8
22
13
13
15
4
4
4
4
8
7
7
4
10
8
6
6
7
9
27
7
4
2
13
7
7
4
13
4
0
0
12
10
8
7
7
10
21
15
14
13
12
11
8
8
17
15
15
15
18
14
13
11
5
11
11
4
4
4
5
7
5
4
6
5
4
3
5
5
5
5
4
12
27
13
13
12
11
10
8
7
20
10
8
3
16
12
12
11
8
13
20
10
10
10
15
16
16
13
9
6
6
6
13
11
11
10
7
14
26
13
11
11
7
7
4
2
20
14
7
6
13
8
8
8
7
15
25
7
7
6
5
5
5
4
19
7
7
4
6
4
3
2
1
16
18
11
12
12
11
11
8
9
11
9
9
9
13
11
7
6
5
17
22
9
7
7
13
12
9
7
18
6
6
3
5
3
2
2
2
18
20
15
14
16
10
11
10
6
15
12
10
8
8
8
6
10
2
19
27
23
22
22
24
23
17
12
20
18
17
15
19
17
17
16
15
20
24
15
14
13
16
16
11
11
13
9
9
7
12
10
10
10
9
21
17
9
9
9
9
8
13
3
10
9
9
5
13
11
10
10
8
22
21
13
13
13
11
16
15
6
18
7
6
3
13
11
11
8
9
23
24
20
20
21
12
12
9
4
13
11
9
7
9
6
6
5
4
24
13
4
4
4
5
6
4
1
2
1
1
1
9
7
6
6
3
25
16
7
7
6
4
3
3
2
4
2
2
2
4
4
4
4
3
26
21
12
11
11
10
10
10
1
15
10
9
7
12
12
11
11
5
27
26
22
19
19
24
22
21
18
21
11
11
7
11
9
9
7
5
28
24
21
21
21
24
23
23
19
19
12
12
8
16
15
13
11
8
29
14
11
10
10
7
6
5
3
9
9
9
7
7
5
3
3
3
30
17
12
11
10
12
11
10
7
11
8
8
7
12
11
8
7
4
31
25
15
15
14
14
12
10
7
16
14
10
6
13
11
8
5
4
32
23
16
17
17
7
5
5
6
14
11
10
4
12
7
5
5
5
33
23
6
5
4
16
16
16
13
15
4
4
1
12
8
8
6
6
34
21
19
19
19
17
18
15
19
18
12
12
12
17
17
15
14
13
35
24
10
10
10
5
5
4
3
16
9
8
5
10
9
8
8
7
36
20
15
13
11
18
16
16
8
18
17
4
3
13
13
7
5
4
37
24
14
13
13
20
20
7
7
19
15
13
9
15
11
10
8
4
38
21
15
15
15
13
13
13
12
11
11
11
10
16
14
10
10
3
39
20
10
10
9
9
8
7
2
8
5
3
3
11
7
6
6
4
40
23
22
22
21
14
15
16
13
16
12
9
8
14
8
8
7
5
41
19
11
11
11
4
4
4
0
14
11
10
3
8
6
6
5
4
42
19
16
16
14
13
13
11
8
8
8
7
5
9
9
6
6
5
43
20
16
14
12
14
11
10
5
11
10
10
8
10
10
10
10
3
44
23
14
14
12
16
9
6
5
10
10
9
8
13
13
12
12
10
45
18
11
11
11
3
3
3
2
10
9
8
4
8
7
6
5
4
46
26
14
14
14
10
10
8
5
19
15
15
6
15
13
10
9
5
47
16
11
11
11
10
8
7
6
12
10
10
3
9
7
7
6
5
48
20
11
11
11
10
9
9
8
9
6
6
3
15
14
10
9
3
49
15
4
4
4
7
7
5
2
4
2
2
1
5
4
3
3
3
50
21
6
6
6
6
6
5
4
8
8
7
5
10
8
8
9
5
51
23
9
9
8
13
11
10
5
9
4
4
1
4
4
3
3
3
52
25
24
24
24
19
18
15
11
20
17
13
7
13
12
12
12
6
53
22
20
20
20
15
13
12
8
20
12
12
7
14
11
11
11
6
54
20
14
14
14
6
6
5
5
13
10
8
5
9
6
6
6
3
Total
1139
688
669
651
633
597
511
362
729
529
450
303
616
509
440
399
285
Percentage Pass
60%
59%
57%
56%
52%
45%
32%
64%
46%
40%
27%
54%
45%
39%
35%
25%