MA442 MAPLE Assessment Report and Analysis: Fall 2015
Prepared by Dr. Carolyn King
Course Description: MA-442 is 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.
Student Learning Outcomes and General Education Outcomes:
This assessment will focus on the following student learning outcomes:
1)
2)
3)
4)
Students will be able to use MAPLE to define functions. (S1)
Students will be able to use MAPLE to plot functions. (S2)
Students will be able to use MAPLE to write and evaluate an integral (S3)
Students will be able to use MAPLE, via the Tools function, to plot 3-D graphs. (S4)
The above student learning outcomes pertain to General Education Objectives: (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; and (4) use information management and technology skills effectively for
academic research and lifelong learning.
Description of the Assessment
Four instructors met and discussed what learning outcomes should be addressed in this
assessment. It was determined that one of the best features of MAPLE is its computational power.
Integrals that are extremely difficult to evaluate by hand can be done very quickly with MAPLE.
The focus was on arc length and the area of a surface of revolution since the calculations of these
involve integrals that are usually very difficult and tedious to compute.
Assessment Protocol
1) Created a MAPLE lab that taught how to find the arc length and the area of a surface of
revolution.
2) Gave the lab in the 4 sections of MA-442 and the instructors helped the students complete
the lab.
3) Gave a short quiz later in the semester that required the students to find the arc length and
the area of a surface of revolution. Basically a short MAPLE lab to be completed without
help from the instructor.
4) Each instructor collected this MAPLE lab from their students and completed the scoring
rubric to assess students’ proficiency in using MAPLE to solve these problems.
KING, CAROLYN
1
Student Assessment Assignment
Lab: Arc Length and Area of Surface of Revolution (Assessment)
Dear Student,
Thank you for participating in this MAPLE assessment!! It will help CUNY understand how MAPLE
can positively affect student performance in Calculus. Please do the best that you can and complete this
lab without help from others!!
Student Name:
1. Graph the curve
for
and find its length.
2. Graph the curve, and find the area of the surface of revolution when
is rotated about
the x-axis. Then, also use the Surface of Revolution tutor to check your answer and plot the surface for
the curve.
KING, CAROLYN
2
Description of Rubric
Sample Assessment Question 1:
Use MAPLE to plot the graph and find the length of the curve
𝑥3
1
𝑦=
+
,
1≤𝑥≤2
3
4𝑥
•
Put a “1” in box 1(a) if the function has been correctly defined. (S1)
•
Put a “1” in box 1(b) if the function has been correctly graphed. (S2)
•
Put a “1” in box 1(c) if an integral is written (May Not be correct) (S3)
•
Put a “1” in box 1(d) if the correct value of the arc length is given.
1(a)
1(b)
1(c)
1(d)
Sample Assessment Question 2:
Use MAPLE to find the exact area of the surface obtained by rotating the curve
𝑦 = 𝑥3 0 ≤ 𝑥 ≤ 2
around the x-axis. Plot the function and also use the Surface of Rotation tutor to graph the surface
and check your answer.
•
Put a “1” in box 2(a) if the function has been correctly defined. (S1)
•
Put a “1” in box 2(b) if the function has been correctly graphed. (S2)
•
Put a “1” in box 2(c) if an integral is written (IT MAY NOT BE Correct) (S3)
•
Put a “1” in box 2(d) if the correct value of the surface area is given.
•
Put a “1” in box 2(e) if the area of the surface has been correctly graphed. (S4)
2(a)
2(b)
2(c)
2(d)
2(e)
KING, CAROLYN
3
Results
Four sections of MA442 participated in the MAPLE Assessment. Sixty students (60) completed the
assessment, which is almost all of the students who are registered in these 4 sections of the
course. (Examples of two MAPLE Assessments are provided in the appendix under a separate pdf
file)
Once the scoring rubric has been collected from the 4 sections of MA442, the number of students
who completed each part correctly was computed. The total points that could be given for the
MAPLE Assessment was 9. A score of 6 out of 9 or approximately 67% was considered
satisfactory. The majority of the students, 54 out of 60 or 90% of the students had a satisfactory
score in the MAPLE Assessment.
MA442 MAPLE Assessment
Frequency Distribution
Aggregaate (4 sections)
Fall, 2015
45
40
35
30
25
20
15
10
5
0
42
Frequency
8
6
Below .65
2
2
0.66
0.77
0
0.89
1
Breakdown by 4 sections, total 60 students.
Scoring Rubric
Number of
Students in
Section
14
20
14
12
1(a)
1(b)
1( c)
1(d)
2(a)
2(b)
2( c )
2(d)
2( e)
11
20
14
12
13
20
14
12
11
19
12
12
10
18
12
12
10
20
13
12
11
20
11
12
11
19
13
12
8
15
12
12
11
19
11
12
Frequency
Percentage
57
59
54
52
0.95 0.98 0.90 0.87
55
54
55
47
53
0.92 0.90 0.92 0.78 0.88
KING, CAROLYN
4
Observations and Analysis of the Rubric
MA442 MAPLE Assessment
Fall 2015
1.20
Percent Correct
1.00
0.95
0.98
0.90
0.87
0.92
0.90
0.92
0.88
0.78
0.80
0.60
0.40
0.20
0.00
1(a)
1(b)
1( c)
1(d)
2(a)
2(b)
2( c )
2(d)
2( e)
Assessment Questions
Rubric items 1(a) and 2(a) assessed whether a student could define a function using MAPLE. The
majority of students, 95% and 92% respectively, correctly defined a function.
Rubric items 1(b) and 2(b) assessed whether a student could plot a function using MAPLE. The
majority of students, 98% and 90% respectively, correctly plotted a function.
Rubric items 1(c) and 2(c) assessed whether a student could define and evaluate an integral using
MAPLE. The majority of students, 90% and 92% respectively, correctly defined and evaluated the
integrals.
Rubric item 1(d) assessed whether the student correctly found the arc length of the curve. Eightyseven percent were correct. This item really measures whether the student understood the
calculus.
Rubric item 2(d) assessed whether the student correctly found the area of the surface of
revolution. Only 78% of the students were able to find the correct answer. Again this item really
measures whether the students understood the calculus.
Rubric item 2(e) assessed whether the student was able to use the TOOLS menu in MAPLE.
Correctly using this menu will produce a 3-D image of the surface of revolution and will also show
the correct answer. Eighty-eight percent (88%) of the students correctly completed this item
KING, CAROLYN
5
Conclusions and Plan or Action
The majority of the students, 90%, demonstrated proficiency in using some of the basic functions
of MAPLE. The students were able to use MAPLE to define functions, plot functions, and define and
evaluate integrals.
The students had difficulties writing the correct integrals to compute both the arc length and area
of a surface of revolution. This demonstrates that they need more help with understanding the
calculus. Both of these topics involve visual representations that are often hard for students to
image or draw. MAPLE is not only useful for its computational power, but it’s graphing
capabilities, in both 2-D and 3-D, could be great tools in assisting with the visual representations
of areas of surface of revolutions and volumes of solids created by revolving regions about lines.
This is the first MAPLE assessment that has been done in a calculus course in recent years. This
investigator recommends duplicating this assessment in Spring 2016 and Fall 2016 semesters to
generate more data. There were only 5 sections of MA442 during this Fall 2015 semester. The
assessment should also be expanded to include volumes of solids, which is a topic that the
students in MA442 find very difficult.
As the instructions came together to discuss what MAPLE skills students would benefit from the
most, the conversation also led to ideas for how MAPLE could be better integrated into the
coursework. Some basic MAPLE skills were assessed, but there are many other MAPLE functions
that would be helpful to students studying calculus.
This investigator also recommends conducting MAPLE assessments for the first course in the
calculus sequence, MA441 as well as the third course in the calculus sequence MA-443.
KING, CAROLYN
6
Raw data
Scoring Rubric
Student
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
1(a)
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1(b)
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1( c)
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1(d)
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2(a)
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2(b)
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2( c )
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2(d)
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2( e)
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
SCORE
0.4
1.0
1.0
0.3
0.2
0.7
1.0
1.0
0.1
0.9
1.0
1.0
1.0
1.0
1.0
0.9
1.0
1.0
1.0
0.8
0.9
1.0
1.0
0.9
0.9
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.6
1.0
0.3
1.0
KING, CAROLYN
7
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Frequen
cy
Total
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
57
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
59
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
54
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
52
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
55
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
54
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
55
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
47
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
53
1.0
0.9
0.9
0.7
0.8
1.0
1.0
1.0
1.0
0.9
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
54
3
1
6
8
5
6
5
13
7
6
Percent
age
0.95
0.98
0.90
0.87
0.92 0.90
0.92
0.78
0.88
0.90
Corr
ect
Inco
rrec
t
KING, CAROLYN
8