This document discusses enhancing calculus concepts through writing assignments. It describes calculus courses at a community college that incorporate group projects or weekly Mathematica labs requiring written reports. For group projects, students chose topics, submitted outlines, and gave presentations. Weekly labs had related questions answered with Mathematica. Student feedback indicated benefits like applying concepts and improved writing. Assessment data showed higher average scores and less failure/withdrawal rates after incorporating writing assignments.

1. Enhance Calculus
Concepts with Writing
Supawan King, Ph.D.
Associate Professor of Math
Session 2.7. AFACCT Conference '12
Harford Community College

2. Presentation Overview
 HCC Calculus I: F2F, Hybrid, Honors
 Expectation
 Course Management
 Group Projects
 Weekly Labs
 Assessments
 Activities
 Grading Criteria (20% of course grade)
 Outcomes
 Student Feedback
AFACCT, Jan 5, 2012 2

3. HCC Calculus I
4 credit hours
5 sessions per semester
F2F
Hybrid
Online
Honors
DWF rate ~ 14-33% (Fa’10 = 22%)
AFACCT, Jan 5, 2012 3

4. Expectation
 Academic Outcomes:
Communication, Critical
Thinking, Computation, and Technology
 Student Learning Objectives: Student will be
able to
 Read, analyze, apply Mathematical principles, and
use appropriate grammatical forms in both oral and
written formats to communicate ideas and concepts.
 Effectively use technology to
collect, analyze, solve, display, and communicate
Mathematical information.
AFACCT, Jan 5, 2012 4

5. Group Projects vs Weekly Labs
Fall 2010 Fall 2011
12 students 13 students
Group Project Weekly Labs with Mathematica
2-3 students per group 2-3 students per group
Submit 2 drafts prior meeting Submit lab report weekly
15-20 minute presentation No presentation
AFACCT, Jan 5, 2012 5

6. Group Projects: Activities
A group of 2-3 students
Choose the topic of interest
Follow the checklist
Consult with the instructor twice before the
presentation
Formal write-up
Presentation
AFACCT, Jan 5, 2012 6

7. Calculus Project Topics
Adapted from David Richeson, Dickinson College, http://www.maa.org/pubs/Calc_articles.html
History Applied Problems based on articles
Biographical sketch of Newton’s Lengthening Shadow: the story of related rates,
life and Newton’s Contribution to by Austin, Barry, and Berman (Math Ag., 2000).
Calculus.
Tangents without calculus, by Aarao (College
Biographical sketch of Leibniz’s Math. Journal, Nov. 2000).
life and Leibniz’s Contribution to
Calculus. The falling ladder paradox, by Paul Scholten and
Andrew Simonson (College Math. Journal, Jan.
Newton and Leibniz calculus 1996).
controversy.
How not to land at Lake Tahoe, by Richard
History of calculus in Egypt, Barshinger (Amer. Math. Monthly, May 1992).
Greece, and India.
The Calculus of Rainbows, by Rachel Hall and
Hyperbolic functions and their Nigel Higson.
history.
Do dogs know calculus?, by Timothy Pennings
Women in calculus. (college Math. Journal, May 2003).
A new wrinkle on an old folding problem, by
AFACCT, Jan 5, 2012 Greg Frederickson (College Math. Journal, 2003). 7

8. Group Projects: Grading Criteria
Group Project
(Topics/Math articles Paper Presentation
provided)
Overview
Well written
Mathematics
All issues addressed
Grading Criteria
(Rubrics) Clarity: Grammar
Clarity
Style and
At least 2 sources
organization
AFACCT, Jan 5, 2012 8

9. AFACCT, Jan 5, 2012 9

10. AFACCT, Jan 5, 2012 10

11. Group Projects: Outcomes
An outline of the write-up was submitted prior the first meeting.
The first/second meetings:
 Shared each member’s responsibility, accomplishment, resources
used, problems the group ran into, and the next step.
 Got feedback suggestions from the instructor (identified
gaps, clarified Mathematical principles, errors.)
Findings: All groups (100%) developed the following skills:
 Ability to apply Math principles and generalizations already learned
to new problems and situations.
 Ability to synthesize and integrate information and ideas.
 Time management skills.
 Writing skills.
AFACCT, Jan 5, 2012 11

12. Group Projects: Outcomes
The end of the semester
Part I: The project presentation
 All groups were well-prepared and organized, delivered topic’s contents
elaborately with confidence.
 The background of the topics explained in an easy way to understand and
the outlines were presented.
 All group connected their topic with topic in Calculus and how it was used in
or applied to their project.
 Some groups incorporated advanced technology i.e. movies, animations, and
simulations, to their presentations.
 There were minor errors on using Mathematical notations and definitions in
one group (out of 5 groups). After being asked to verify, the group explained
correctly and clearly. All classmates were able to understand the contents.
Part II: The final project report
 All reports addressed all the issues in the assigned topic. The papers were
well-written. At least three outside sources were used in each report.
AFACCT, Jan 5, 2012 12

13. Group Projects: Overall Outcomes
 The group projects have reflected the students’
work, concerns, and questions about the course.
 Instructors can check on students’ understanding early in
the process. It provides practice in valuable and transferable
skill.
 With requiring the timeline and meetings with
instructions, the quality of the final report (writing skill) and
in-class presentation (oral skill) are improved, and also
enhances student learning.
 Time management was the main issue preventing team
members to cooperate and discuss as a group;
however, electronic mails were heavily used to communicate
within the group.
AFACCT, Jan 5, 2012 13

14. Student Feedback
"What have students gained the most from doing the project?"
“It helped me visualize where Calculus is used in real life situations like the
presentation about the plane landing in Lake Tahoe.”
“Project gave examples of real-life implementation useful practice.”
“The uses of derivatives outside of Calculus.”
“I have learned a lot about the history of Calculus and where the ideas of
Calculus started and how they related to modern day Calculus”
“I’ve learned more about the Newton vs Leibniz controversy, and how
Calculus’s notion is used.”
“A knowledge of the history of Calculus and a brief idea of what will come in
later classes, i.e., Calc II, III, and Diff Eqn.”
“I have learned the history of people who are involved in the subject and
relation among various equations.”
AFACCT, Jan 5, 2012 14

15. Student Feedback
"What have students gained the least from doing the project?"
“I can’t think of anything bad about it.”
“It was hard cooperating within the group.”
“Time management.”
“Something I lost by doing this project was a lot of
time.”
“Too much on the outskirts of the web, more interested
in the inner core.”
AFACCT, Jan 5, 2012 15

16. Weekly Labs: Activities
 A group of 2-3 students
The class met at the computer lab once a week
to work on Mathematica labs.
Each lab was designed to have related questions
that can be answered with the skills and
knowledge learned in the labs and lectures for
Calculus I contents.
Group members worked on labs together and
submitted only one report electronically before
the next lab session.
AFACCT, Jan 5, 2012 16

17. Weekly Mathematica Lab
Assignments
Lab 00 Getting Started with Mathematica
Lab 01 Introduction: Graphs and Mathematica
Lab 02 New Functions from Old
Lab 03 Limits
Lab 04 The Derivative
Lab 05 Chain Rule and Implicit Differentiation
Lab 06 Related Rates Problems
Lab 07 Velocity, Acceleration, and Rectilinear Motion
Lab 08 Derivative and Graphs
Lab 09 Optimization
Lab 10 Linear Approximation and Newton Method
Lab 11 Antiderivatives
AFACCT, Jan 5, 2012 17

18. Weekly Lab Report Grading Criteria
Collect Students’ feedback from Each Lab:
“Write one or more paragraphs concerning this
laboratory.”
AFACCT, Jan 5, 2012 18

19. The First Lab's Feedback
Lab 01 Introduction: Graphs and Mathematica
“This lab really made me understand how to use
Mathematica. I have not used Mathematica
before, so it was frustrating at first because of my
utter ignorance of the computer commands for the
functions and terminology. As I performed the
problems, it turned to more of a puzzle and rather
enjoyable. I learned much of the coding and got
used to basic function plotting and input formatting.
This was a good lab that really helped me
understand the basics of Mathematica and the work
that I would be doing in here. I look forward to
doing more labs here in Calc 1.”
AFACCT, Jan 5, 2012 19

20. The First Lab's Feedback (Cont'd)
“Neither of us has ever used this program before. So
far it is not a complicated program to use for simple
commands. The classroom assistant certainly
makes it a lot easier.”
“We have not used Mathematica before and it was a
challenge to discover the proper functions
needed to complete the tasks at hand. Other
then that the programmers designed Mathematica
as a user friendly device.”
AFACCT, Jan 5, 2012 20

21. The First Lab's Feedback (Cont'd)
“Neither one of us has used Mathematica before. Both
of us have used the web-based Wolfram Alpha
before, so this program's interface looks somewhat
familiar. We found this lab to be
straightforward, and there were no major obstacles.
The only issue would be getting used to
Mathematica.
Overall, we both liked the interface of this
program a lot and think it will become very
easy to work with once we get used to it.”
AFACCT, Jan 5, 2012 21

22. Evidence of Writing Improvement
Lab 01: “This lab isnt too bad. It is kinda cool what you can do with all the
functions. the lab is kinda confusing but with some practice and guidance ill
get it. I wanna see all the stuff you can do as we get into more complicated
stuff.
I havent used it before, the biggest thing i think is using all the functions and
putting them into the boxes. That was probably the biggest thing everything
else wasnt bad.”
Lab 02: “This lab was ok. Im learning all the commands and feel like im starting
to grasp everything. Its nice to have a program like this so you dont have to do
everything on the calculator and its very visual, which i like.”
Lab 04: “We did a lot of differentiating which will help us as we learn more about
Calculus. Wasnt to sure about hyperbolic functions. Overall a good lab to help
us practice differentiation.”
Lab 11: “This lab was very easy and with … , we knocked it out. The
antiderivative function is very helpful and makes things a lot easier and
faster.”
AFACCT, Jan 5, 2012 22

23. Concept Enhancement
“This lab truly helped me understand the effects of a manipulation on a
function, whether it be stretched, shrunk, rotated, or shifted. The
laboratory continued to challenge our skills at using the program
Mathematica and helped us progress even more in our
knowledge and experience.”
“In this lab we learned even more about how do the graphs work and
also we could see the symmetry, sometimes related to the y-
axis, sometimes to x-axis and sometimes no symmetry.”
“By seeing the actual values in the table around the limit, it gave us a
clear evaluation on the precise y-value limit. Explaining each
individual limit of each problem help us better understand the
material.”
AFACCT, Jan 5, 2012 23

24. Concept Enhancement (Cont'd)
“We didn't know how to differentiate inverse functions or logarithmic
functions when we started this lab. But now we do.”
“This Lab has helped us see how calculus is applied in the word of
physics through velocity and acceleration and position. It
shows us how first and second derivatives can be applied.”
“This lab was a little more challenging than the past labs. It implemented
the concept of implicit differentiation with that of related rates. This
was a very satisfying lab to do as well. I feel like I am learning
much of Mathematica and am able to do a good bit of calculus
work on it. It was difficult trying to stretch the given example to
different kinds of problems. However, once I understood what I was
doing and not just what the example said, it was a lot easier. This
was a good lab.”
AFACCT, Jan 5, 2012 24

25. Some Frustrations
“This lab was not as confusing as others. It
was simple and proved very useful. I had
trouble finding out how to enter the
correct implicit differentiation input
into the cell. Once I learned how to enter
it, the command was easy to remember and
made sense. I wish I would have been
able to do this before the test.”
AFACCT, Jan 5, 2012 25

26. Some Frustrations (Cont'd)
“This lab was confusing at times. For the
first problem, we could not figure out a way
to use Mathematica to find the increasing
and decreasing intervals. Also, under the
absolute extreme values set, we could not
figure out a way to use Mathematica to get
the extrema. It is a very useful lab for
understanding how to interpret the
graphs of derivatives using
Mathematica.”
AFACCT, Jan 5, 2012 26

27. Some Frustrations (Cont'd)
“This lab took an exorbitant amount of
time. Somehow, a few functions got locked
up, and about a half an hour had to be spent
to fix all of the mistakes. If ever we need to
do Newton’s method again, we will use
this to help us. One plus to the length
was getting used to the syntax of
Mathematica.”
AFACCT, Jan 5, 2012 27

28. Student Performance
Student Performance Overall
100
90
82.51 82.21 82.36
80 74.12
71.02
70 67.91
60
% 50
40
30
20
10
0
Fall 2010 Fall 2011 Mean
w/o writing w/ writing
AFACCT, Jan 5, 2012 28

29. Student Performance by Quizzes
and Tests
Student Performance Student Performance
(8 Quizzes) (3 Tests)
100 100
90 84.8 86.7 85.1 85.9 90
81.75 81.55
78.7 77.94 78.71
80 80 75.87
71.85
70 70 65.77
60 60
% 50 % 50
40 40
30 30
20 20
10 10
0 0
Fall 2010 Fall 2011 Mean Fall 2010 Fall 2011 Mean
w/o writing w/ writing w/o writing w/ writing
AFACCT, Jan 5, 2012 29

30. Supawan King, Ph.D.
Associate Professor of Math
sking@harford.edu
(443) 412-2601
STEM Division
Harford Community College