The honors program is not for every student, but it is for those who are seeking an enriched academic experience.
Gen Ed Goal:1. Read with comprehension and communicate analytically, critically and/or creatively in speech and writing.2.Analyze information objectively and apply knowledge and technology across a variety of disciplines.3. Interpret and apply scientific data, gathered in a variety of methods, by employing the scientific method and organize and express observations and results in a clear and concise manner.4.Apply reasoning, creativity, estimation, and/or computational skills to solve complex problems.5. Define information needs, access information efficiently and effectively, evaluate GenEd-Math Goals: a) Define, represent, and solve Mathematical problems using methods and principles of Mathematics.b) Use appropriate grammatical forms in both oral and written formats to communicate ideas and concepts.c) Effectively use technology to collect, analyze, solve, display, and communicate Mathematical information.
Fall 2010: ProjectPrior meetings, each team submitted the draft of team report and presentation to the instructor. Reports and presentations must be updated right after the meeting based on instructor’s feedback and suggestions. To complete the group project, students can use any resources i.e. textbooks, books from the library, journal articles, the internet, etc. Each group was required to use at least two sources in addition to the handouts given in the class. Presentation:Overview (5 points): - What is the context of the problem? - Was the background of the topics explained? - What assumptions are you making?Mathematics (10 points): - How is calculus used in your project? - Are the methods of this course which help answer the question exlained? - Is outline of the development of the necessary Mathematical theory presented?Clarity (5 points): -Are all new terminology and notation defined?Style and organization (10 points): - Is the talk polished? Does it look like each group member has practiced it? Is the talk well organized and well planned? - Did all members participate in the presentation?Paper:There is no page limit. The write-up will include more information than the presentation.The paper should be written in complete sentences, with correct grammar and punctuation. It should read like a research paper, not like a homework assignment. It is very important to cite any outside sources and to include a bibliography. The paper will be graded on the following criteria:Do you address all of the issues in the assignment?Can the paper stand on its own? That is, can the paper be understood by someone who did not see the presentation?Is the paper well written (including punctuation and grammar)?Did you use at least two outside sources? (The course textbook does not count toward this minimum.)
2010: f2f = 20,Hons = 122011: f2f = 21, Hons = 13
Transcript
1. Enhance CalculusConcepts with Writing Supawan King, Ph.D. Associate Professor of Math Session 2.7. AFACCT Conference 12Harford Community College
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 presentationAFACCT, Jan 5, 2012 5
6. Group Projects: ActivitiesA group of 2-3 students Choose the topic of interest Follow the checklist Consult with the instructor twice before the presentation Formal write-up PresentationAFACCT, Jan 5, 2012 6
7. Calculus Project TopicsAdapted from David Richeson, Dickinson College, http://www.maa.org/pubs/Calc_articles.html History Applied Problems based on articlesBiographical 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 (CollegeBiographical sketch of Leibniz’s Math. Journal, Nov. 2000).life and Leibniz’s Contribution toCalculus. 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 RichardHistory of calculus in Egypt, Barshinger (Amer. Math. Monthly, May 1992).Greece, and India. The Calculus of Rainbows, by Rachel Hall andHyperbolic functions and their Nigel Higson.history. Do dogs know calculus?, by Timothy PenningsWomen in calculus. (college Math. Journal, May 2003). A new wrinkle on an old folding problem, byAFACCT, 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 organizationAFACCT, Jan 5, 2012 8
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11. Group Projects: OutcomesAn 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: OutcomesThe end of the semesterPart 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 LabAssignmentsLab 00 Getting Started with MathematicaLab 01 Introduction: Graphs and MathematicaLab 02 New Functions from OldLab 03 LimitsLab 04 The DerivativeLab 05 Chain Rule and Implicit DifferentiationLab 06 Related Rates ProblemsLab 07 Velocity, Acceleration, and Rectilinear MotionLab 08 Derivative and GraphsLab 09 OptimizationLab 10 Linear Approximation and Newton MethodLab 11 AntiderivativesAFACCT, Jan 5, 2012 17
18. Weekly Lab Report Grading CriteriaCollect Students’ feedback from Each Lab:“Write one or more paragraphs concerning this laboratory.”AFACCT, Jan 5, 2012 18
19. The First Labs FeedbackLab 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 Labs Feedback (Contd)“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 Labs Feedback (Contd)“Neither one of us has used Mathematica before. Both of us have used the web-based Wolfram Alpha before, so this programs 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 ImprovementLab 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 (Contd)“We didnt 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 (Contd)“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 (Contd)“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/ writingAFACCT, 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 DivisionHarford Community College
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