Math 442 Course Assessment Report and Analysis: Spring 2014
Prepared by Mathematics Department Assessment Committee
Course Description: The second of a three-semester sequence, this course is intended to cover
transcendental functions, methods of integration, parametric equations, and infinite series.
Computer demonstrations will be arranged where appropriate.
General Education Objectives: Use analytical and deductive reasoning to apply the concepts
and methodologies of calculus to questions in mathematics, the physical and biological sciences
and engineering.
Course Objectives/Expected Student Learning Outcomes: Students will develop problem
solving skills and construct mathematical models in the computer laboratory using software such
as MAPLE, DERIVE, CONVERGE, and MATHCAD.
DESCRIPTION OF THE ASSESSMENT PROTOCOL
Course Assessment was done for Math 442 in Spring 2014. The course learning outcomes
assessed were chosen because they are representative of major core objectives in the courses and
imply knowledge of other related concepts and skills. The MA-442 instructors discussed what
learning outcomes of course and college should be addressed in the assessment. Three questions
were chosen and were given to the instructors early in the semester. Instructors placed the
assessment questions where they wished in their final exams and assigned point values to the
questions as they felt was appropriate. A summary of the data and its analysis is given in this
report to serve as the basis for seeing how well the department as a whole is addressing these
learning outcomes and implementing strategies to better address the learning outcomes.
The course learning outcomes and chosen for this assessment and the questions and their
corresponding course learning outcomes and rubrics are listed below. The General Education
and Curricular Learning Outcomes are listed at the end of this document.
Questions:
𝑥𝑥
1- Evaluate the indefinite integral ∫ 𝑥𝑥 2 +1 𝑑𝑑𝑑𝑑.
Course Learning Outcomes
•
•
Use analytical and deductive reasoning to apply the concepts and methodologies of calculus
to questions in mathematics.
Be able to find indefinite integrals of transcendental functions.
General Education Objectives: (1) (3)
(1) Communicate effectively through reading, writing, and speaking.
(3) Reason quantitatively and mathematically as required in their field of interest and everyday
life.
Curricular Objectives (LS1 Liberal Arts and Sciences (Mathematics and Science)
(1)(3a)(3e)
1.
Demonstrate proficiency in factual knowledge and conceptual understanding required for transfer to the
junior year in a baccalaureate program in natural science, mathematics, engineering, or computer science or
any other program in health sciences.
2.
Demonstrate basic knowledge of the humanities and social sciences.
3. Disciplinary learning :
a)
Demonstrate skills in mathematics to the minimum level of basic calculus concepts, including their
applications to science and/ or engineering.
b) Demonstrate proficiency in communication skills, including technical writing and oral presentation.
c)
Apply concepts through use of current technology.
d) Demonstration an understanding of the professional, ethical, and social responsibilities related to the fields
of natural science, mathematics, engineering, and /or computer science.
e)
Demonstrate proficiency in acquiring, processing and analyzing information in all its forms as related to
the field of concentration.
Rubric
•
•
•
•
1(a)
Put an “x” in box 1(a) if a correct substitution is made.
Put an “x” in box 1(b) if the integral resulting from the substitution is correct.
Put an “x” in box 1(c) if the correct antiderivative of the integral resulting from the
substitution is found.
Put an “x” in box 1(d) if the student adds the constant.
1(b)
1(c)
1(d)
2. Determine whether the series converges or diverges. If it converges find the limit.
∞
2n − 1
.
∑
3n
n =1
Course Learning Outcomes
•
Students should be able to determine geometric series converges or diverges.
General Education Objectives: (3)
Curricular Objectives(LS1 Liberal Arts and Sciences (Mathematics and Science) (A)(Ca)
Rubric
•
•
Put an “x” in box 2(a) if the student does not claim that the series is divergent.
Put an “x” in box 2(b) if the student breaks the sum into two smaller pieces
•
•
•
 2  1
  −   or similar.
 3  3
Put an “x” in box 2(c) if the correct formula is used to evaluate the two infinite sums.
Put an “x” in box 2(d) if the student correctly simplifies the individual sums.
Put an “x” in box 2(e) if the student correctly subtracts the individual sums.
n
n
If an answer is incorrect leave the corresponding box blank.
2(a)
3.
2(b)
2(c)
2(d)
2(e)
Find the Taylor series of f ( x) = ln( x) at a = 1 .
Course Learning Outcomes
•
•
Students should be able to calculate the Taylor series expansion of a function at a given
point.
Students should be able to determine the derivatives of transcendental functions.
General Education Objectives: (3)
Curricular Objectives(LS1 Liberal Arts and Sciences (Mathematics and Science) (A)(Ca)
Rubric
•
∞
Put an “x” in box 3(a) if the correct structure of the series is given
∑ c (x − 1)
n =0
•
•
n
n
.
Put an “x” in box 3(b) if the student uses the correct formula for c n (not necessarily
the correct derivative).
Put an “x” in box 3(c) if the correct formula for c n is used and the correct derivative is
given.
•
Put an “x” in box 3(d) if the correct formula for c n is correctly simplified.
•
Put an “x” in box 3(e) if the correct sum is written 1 + ∑ (− 1)n +1
∞
n =1
1
(x − 1)n or a close
n
equivalent is written.
3(a)
4.
3(b)
3(c)
3(d)
3(e)
Find the volume of the solid obtained by rotating the region of plane bounded by the
curves y = x and y = x around the y -axis
Course Learning Outcomes
•
Students should be able to use integration to find the volume of a solid of revolution.
General Education Objectives: (3)
Curricular Objectives(LS1 Liberal Arts and Sciences (Mathematics and Science) (A)(Ca)
Rubric
•
•
•
•
4(a)
Put an “x” in box 4(a) if the correct bounds of the integral are given.
Put an “x” in box 4(b) if the argument of the integral is correct for example
2πx( x − x) or π ( y 2 − y 4 ) .
Put an “x” in box 4(c) if the correct antiderivative given is used and the correct
derivative is given.
Put an “x” in box 4(d) if the student correctly plugs the bounds of the integral into the
antiderivative and subtracts to get the final answer.
4(b)
4(c)
4(d)
Assessment
MA-442
Spring 2014
5 Sections
Number of
Stuents in
Sections
12
10
12
14
17
Total
%
65
65 Students
1a
10
6
12
12
17
1b
10
5
12
12
14
1c
10
5
10
12
13
1d
9
4
10
11
12
2a
12
6
11
13
15
2b
12
4
10
10
14
2c
9
6
10
9
13
2d
3
4
10
9
10
2e
3
4
9
9
6
3a
6
2
10
12
11
3b
6
2
8
14
13
3c
4
1
9
9
9
3d
2
1
7
5
2
3e
2
1
3
3
2
4a
9
7
12
14
13
4b
2
6
8
12
12
4c
8
7
6
12
9
4d
9
7
8
12
9
57
88
53
82
50
77
46
71
57
88
50
77
47
72
36
55
31
48
41
63
43
66
32
49
17
26
11
17
55
85
40
62
42
65
45
79
MA442 Spring 2014
MA 442 Spring 2014
100
90
80
70
60
50
40
30
20
10
0
88
1a
82
1b
88
2a
77
1c
71
1d
77
2b
85
4a
72
2c
55
2d
63
3a
48
2e
66
3b
79
4d
62
4b
49
3c
26
3d
17
3e
65
4c
RESULTS
A summary of the data statistics is provided in the following table and charts.
Fall 2014 Mathematics Department Assessment Results for Math 442
Based on Departmental Final Exams
Total Number of Students
65
Range of Correct Responses (%) for 10 Learning Outcomes
17% − 88%
Mean of Correct Responses (%)
65%
OBSERVATIONS ON THE ANALYSIS OF THE DATA
Student performance was good on Question 1 (using integration by substitution (parts (a) and (b) of
question 1) above 80% of the students answer question 1a and 1b correctly, which demonstrate that most
of the students performed the correct substitution. More than 70% of the students answered correctly part
1c and 1d.
More than 70% of students were able to answer question 2a, b, c correctly, but not as many students were
able to determine the answers to parts 2d( 55%) and 2e ( only 48%).
About half to two-thirds of the students answered 3a,b,c correctly. But only a small number of students
were able to simplify the coefficient in part d, and very few were able to write down the correct sum
(which required part d). Since Taylor series is the last topic in the syllabus, lack of time may have
affected the results.
On average 70% of the students answered question 4 correctly.
The number of points that needed to be checked by the graders for these problems may have been an
excessive burden.
CONCLUSIONS AND PLAN OF ACTION
Overall the results showed that the students good grasp of the subject. However there seems to be some
deficiency in the students’ basic algebra skills. With this in mind, the results for questions 1, 2, 3 and 4
are within expectations. The department should continue its commitment to providing rigorous effective
instruction.
General Education Objectives:
1. communicate effectively through reading, writing, listening and speaking
2. use analytical reasoning to identify issues or problems and evaluate evidence in order to
make informed decisions
3. reason quantitatively and mathematically as required in their fields of interest and in
everyday life
4. use information management and technology skills effectively for academic research and
lifelong learning
5. integrate knowledge and skills in their program of study
6. differentiate and make informed decisions about issues based on multiple value systems
7. work collaboratively in diverse groups directed at accomplishing learning objectives
8. use historical or social sciences perspectives to examine formation of ideas, human
behavior, social institutions, or social processes
9. employ concepts and methods of the natural and physical sciences to make informed
judgments
10. apply aesthetic and intellectual criteria in the evaluation or creation of works in the
humanities or the arts
LIBERAL ARTS & SCIENCES (MATHEMATICS & SCIENCE), A.S. (LS1)
A. Demonstrate proficiency in factual knowledge and conceptual understanding
required for transfer to the junior year in a baccalaureate program in natural
science, mathematics, engineering, or computer science or any other program in
health sciences.
B. Demonstrate basic knowledge of the humanities and social sciences.
C. Disciplinary learning :
a) Demonstrate skills in mathematics to the minimum level of basic calculus
concepts, including their applications to science and/ or engineering.
b) Demonstrate proficiency in communication skills, including technical writing
and oral presentation.
c) Apply concepts through use of current technology.
d) Demonstration an understanding of the professional, ethical, and social
responsibilities related to the fields of natural science, mathematics, engineering,
and /or computer science.
e) Demonstrate proficiency in acquiring, processing and analyzing information in
all its forms as related to the field of concentration.