Math 441 Course Assessment Report and Analysis: Fall 2015
Prepared by Mathematics Department Assessment Committee
Course Description:
This course is the first semester of differential and integral calculus. Topics emphasized include
functions and graphs; derivative of algebraic and trigonometric functions with applications; indefinite
and definite integrals with applications; the fundamental theorem of integral calculus; conic sections.
Students will develop problem solving skills and construct mathematical models in the computer
laboratory using software such as MAPLE, DERIVE, CONVERGE, and MATHCAD. MA-441
covers many important topics, with emphasis on developing problem-solving skills as well as on
concepts and theorems.
General Education Objectives for the course: Use quantitative skills and mathematical reasoning to
solve problems with the aid of the tools and techniques learned in calculus; reason quantitatively and
mathematically as required in their fields of interest and in everyday life; integrate knowledge and
skills in their program of study; use information management and technology skills effectively for
academic research and lifelong learning.
Course Objectives/ Expected Student Learning Outcomes for the course: Understand the important
concepts and theorems of the elementary calculus of algebraic and trigonometric functions, and apply
them to solve problems in mathematics, engineering, physics and other disciplines; interpret and
appreciate, both qualitatively and quantitatively, the areas in which rates of change and total change
apply; analyze functions, draw conclusions, and communicate results to others orally and in scientific
writing using computer algebra systems; use modern computer technologies in mathematical
investigations.
DESCRIPTION OF THE ASSESSMENT PROTOCOL
Course Assessment was done for Math 441 in Fall 2015. The course learning outcome assessed,
rated rates, was chosen because student performance was weakest in that area in the Course
Assessment of MA 441 that was performed in Fall 2014. It should be noted that student
performance on the topic of related rates was determined to be acceptable in the 2014
assessment. The present assessment was to measure the effectiveness of a new strategy.
Five videos were made by members of the Mathematics and Computer Science Department.
Each video corresponded to a solution of a typical related rates problem. Links to the videos
were sent out to the instructors via email to be passed on to the students in late November. The
assessment question for related rates was given to the instructors around the same time in the
semester. Instructors placed the assessment question 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 strategy of posting
videos for the students to watch effected performance on related rates.
The question, course learning outcome, and rubric for the Fall 2014 assessment and the Fall 2015
assessment, respectively, are listed below. The General Education and Curricular Learning
Outcomes are listed at the end of this document.
Question from the Fall 2014 assessment: Oil from a damaged well in the ocean spreads in a
circular pattern. If area of the oil spill is increasing at a constant rate of 2 square miles per hour,
how quickly is the radius of the oil spill increasing when the radius is 3 miles? Be sure to
include units in your final answer.
Course Learning Outcomes

Understand the important concepts and theorems of the elementary calculus of algebraic and
trigonometric functions and apply them to solve problems in mathematics, engineering
physics and other disciplines, interpret and appreciate, both qualitatively and quantitatively,
the areas in which rates of change and total change apply; analyze functions, draw
conclusions

Be able to solve problems involving related rates.
General Education Objectives: (1) (3)
Curricular Objectives(LS1 Liberal Arts and Sciences (Mathematics and Science)
(1)(3a)(3b)(3e)
Rubric

Put an “x” in box 3(a) if the correct equation relating the area and radius of a circle is
given 𝐴 = 𝜋𝑟 2 .

Put an “x” in box 3(b) if the student correctly finds the derivative of both sides of the
their proposed equation relating area and radius with respect to time.
𝑑𝐴
𝑑𝐴
𝑑𝑡
𝑑𝑟
= 2𝜋𝑟 𝑑𝑡

Put an “x” in box 3(c) if the student replaces

Put an “x” in box 3(d) if the student replaces 𝑟 by the appropriate value which is 3.
𝑑𝑡
by the appropriate value which is 2.

𝑑𝑟
Put an “x” in box 3(e) if the student correctly solves for 𝑑𝑡 based on their proposed
equation.

3(a)
Put an “x” in 3(f) if the student gives the correct units in their final answer.
3(b)
3(c)
3(d)
3(e)
3(f)
Question for Fall 2015 assessment: Each side of a square is increasing at a constant rate of 8
centimeters per second. At what rate is the area of the square increasing when the area of the
square is 16 square centimeters? Include units with your answer.
Course Learning Outcomes

Understand the important concepts and theorems of the elementary calculus of algebraic and
trigonometric functions and apply them to solve problems in mathematics, engineering
physics and other disciplines, interpret and appreciate, both qualitatively and quantitatively,
the areas in which rates of change and total change apply; analyze functions, draw
conclusions

Be able to solve problems involving related rates.
General Education Objectives: (1) (3)
Curricular Objectives(LS1 Liberal Arts and Sciences (Mathematics and Science)
(1)(3a)(3b)(3e)
Rubric

Put an “x” in box 3(a) if the correct equation relating the area and side length of a
square is given 𝐴 = 𝑥 2 .

Put an “x” in box 3(b) if the student correctly finds the derivative of both sides of
their proposed equation relating area and side length with respect to time.
3(a)
𝑑𝑥
𝑑𝐴
𝑑𝑡
𝑑𝑥
= 2𝑥 𝑑𝑡

Put an “x” in box 3(c) if the student replaces

Put an “x” in box 3(d) if the student replaces 𝑥 by the appropriate value which is 4.

Put an “x” in 3(e) if the student gives the correct units in their final answer.
3(b)
3(c)
3(d)
𝑑𝑡
by the appropriate value which is 8.
3(e)
RESULTS
A summary of the data statistics is provided in the following charts.
MA441 Fall2014 (232 students)
1
0.9
0.8
0.70
0.7
0.65
0.6
0.57
0.6
0.53
0.47
0.5
0.4
0.3
0.2
0.1
0
1a
1b
1c
1d
1e
1f
Series 1
MA441 Fall2015 (260 students)
1
0.9
0.8
0.7
0.62
0.6
0.48
0.5
0.51
0.48
0.4
0.4
0.3
0.2
0.1
0
1a
1b
1c
Series 1
1d
1e
OBSERVATIONS ON THE ANALYSIS OF THE DATA
Before starting one thing should be noted. The Fall 2014 question is slightly harder because the
𝑑𝑟
𝑑𝐴
student must solve for 𝑑𝑡 (bullet 3e in the rubric), whereas the quantity 𝑑𝑡 does not need to be
separated from the other terms in the Fall 2015 question. For this reason, column (1e) of the Fall
2014 assessment should disregarded. Indeed, column (1e) in chart for the Fall 2015 assessment
should be compared to column (1f) in the chart for the Fall 2014 assessment.
Student performance was worse or at least not better in every category.
CONCLUSIONS AND PLAN OF ACTION
The charts would seem to show that there the videos where ineffective in the implementation
used here. However, there were two factors that may have skewed the results in a way that
would make the videos seem less effective than they really are.
 In the Fall 2014 assessment the instructors knew the assessment question from the
beginning of the semester and in the Fall 2015 assessment the instructors did not know
the assessment question until about three weeks before the final exam (long after related
rates would have been covered in almost every class).
 The videos were made available late in the semester (after related rates would have been
covered in most classes). They might have been more effective if they were available at
the time students were learning the material.
It may be worthwhile to make the videos available again and run another assessment that takes
the two factors above into account. Also a question of a difficulty equal to that of the Fall 2015
assessment should be used.
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
Curricular Objectives(LS1 Liberal Arts and Sciences (Mathematics and Science)
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.