Enhance Calculus Concepts with

Writing

Supawan King, Ph.D.Associate Professor of Math

Session 2.7. AFACCT Conference '12

Harford Community College

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Presentation Overview

HCC Calculus I: F2F, Hybrid, HonorsExpectationCourse Management

Group ProjectsWeekly Labs

AssessmentsActivitiesGrading Criteria (20% of course grade)Outcomes

Student Feedback AFACCT, Jan 5, 2012

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HCC Calculus I

4 credit hours

5 sessions per semesterF2FHybridOnlineHonors

DWF rate ~ 14-33% (Fa’10 = 22%)

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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.

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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

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A group of 2-3 studentsChoose the topic of interestFollow the checklistConsult with the instructor twice before the

presentationFormal write-upPresentation

Group Projects: Activities

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Calculus Project TopicsAdapted from David Richeson, Dickinson College, http://www.maa.org/pubs/Calc_articles.html

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History Applied Problems based on articles

Biographical sketch of Newton’s life and Newton’s Contribution to Calculus.

Biographical sketch of Leibniz’s life and Leibniz’s Contribution to Calculus.

Newton and Leibniz calculus controversy.

History of calculus in Egypt, Greece, and India.

Hyperbolic functions and their history.

Women in calculus.

Lengthening Shadow: the story of related rates, by Austin, Barry, and Berman (Math Ag., 2000).

Tangents without calculus, by Aarao (College Math. Journal, Nov. 2000).

The falling ladder paradox, by Paul Scholten and Andrew Simonson (College Math. Journal, Jan. 1996).

How not to land at Lake Tahoe, by Richard Barshinger (Amer. Math. Monthly, May 1992).

The Calculus of Rainbows, by Rachel Hall and Nigel Higson.

Do dogs know calculus?, by Timothy Pennings (college Math. Journal, May 2003).

A new wrinkle on an old folding problem, by Greg Frederickson (College Math. Journal, 2003).

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Group Projects: Grading Criteria

Group Project(Topics/Math

articles provided)Paper Presentation

Grading Criteria(Rubrics)

Well written

All issues addressed

Clarity

At least 2 sources

Overview

Mathematics

Clarity: Grammar

Style and organization

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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.

Group Projects: Outcomes

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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.

Group Projects: OutcomesThe end of the semester

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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.

Group Projects: Overall Outcomes

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“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.”

Student Feedback"What have students gained the most from doing the project?"

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“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.”

Student Feedback"What have students gained the least from doing the project?"

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A group of 2-3 studentsThe 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.

Weekly Labs: Activities

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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

Weekly Mathematica Lab Assignments

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Collect Students’ feedback from Each Lab:

“Write one or more paragraphs concerning this laboratory.”

Weekly Lab Report Grading Criteria

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“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.”

The First Lab's FeedbackLab 01 Introduction: Graphs and Mathematica

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“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.”

The First Lab's Feedback (Cont'd)

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“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.”

The First Lab's Feedback (Cont'd)

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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.”

Evidence of Writing Improvement

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“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.”

Concept Enhancement

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“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.”

Concept Enhancement (Cont'd)

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“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.”

Some Frustrations

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“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.”

Some Frustrations (Cont'd)

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“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.”

Some Frustrations (Cont'd)

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Student Performance

Fall 2010 Fall 2011 Mean0

10

20

30

40

50

60

70

80

90

100

67.91

74.1271.015

82.51 82.21 82.36

Student Performance Overall

w/o writing w/ writing

%

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Student Performance by Quizzes and Tests

Fall 2010 Fall 2011 Mean0

10

20

30

40

50

60

70

80

90

100

84.878.7

81.7586.7 85.1 85.9

Student Performance(8 Quizzes)

w/o writing w/ writing

%

Fall 2010 Fall 2011 Mean0

10

20

30

40

50

60

70

80

90

100

65.7666666666667

77.9471.8533333333332

75.866666666666781.55

78.7083333333333

Student Performance(3 Tests)

w/o writing w/ writing

%

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Supawan King, Ph.D.Associate Professor of Math

sking@harford.edu(443) 412-2601

STEM DivisionHarford Community College