UTPA STEM/CBI Courses/Calculus/Calculus I

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The following cycles are currently in classroom testing:

  • Legacy Cycles
    • lead designer: Will Watkins
  • Graphing
    • lead designer: Will Watkins
  • Derivative Algorithm
    • lead designer: Will Watkins
  • Differentiation and Derivatives
    • lead designer: Tsay
  • WFFs, Algebraic Expressions, and Derivatives
    • lead designer: Will Watkins
  • Limits
    • lead designer: Huaien Li
  • Why Derivatives Work
    • lead designer: Will Watkins
  • Kidnapper's Headquarters
    • lead designer: Will Watkins
  • Car Trip
    • lead designer: Will Watkins

Partially funded by U.S. Department of Education Grant #ED-grants-051308-002. University of Texas-Pan American, Edinburg, TX

Dr. Will Watkins is using these cycles in a current Calculus I course.


Summer 2009


LC CBI Calculus Course Design Team

partially funded by U.S. Department of Education Grant #ED-grants-051308-002

Team Members:

  • Dumitru Caruntu (Mechanical Engineering/UTPA)
  • Huaien Li (Mathematics/STC)
  • Jenq-Jong Tsay (Mathematics/UTPA)
  • Will Watkins (Mathematics/UTPA)

Abstract A CBI module is defined (by the Calculus LC CBI Course Design Team) to be complete once it is fully developed as a webpage. This report discusses the mechanisms, processes and rational used by the Team to produce complete CBI modules. Finally a list shows the current status of each module being developed. Appendices contain supporting documentation.

Introduction The Calculus LC CBI Course Design Team (CBI Calculus Team) is one of five design teams partially funded by U.S. Department of Education Grant #ED-grants-051308-002. The grant provided a number of full day workshops teaching the teams Challenge Based Instruction (CBI) concepts and beginning the design process. After completing the workshops, the CBI Calculus Team meet every Tuesday and Thursday beginning in May and then throughout June and July. Emails, an online forum, BlackBoard, WebWork, Google Docs, and a webpage server are used to enhance communication between CBI Calculus Team members.

Early on it was clear that the CBI Calculus Team has a spectrum of ideas regarding what could and should be accomplished by a CBI module. The team members bring various perspectives to the table. The team includes an engineer, a specialist in mathematics education, and one mathematician from STC and another from UTPA. All members of the team have experience teaching calculus.

The Team began by identifying the objectives and concepts to be met in the Calculus I course. Syllabi from UTPA, STC and other institutions were reviewed. The textbooks used at STC and UTPA are both made available to members of the Team. The objectives for the course are divided into four major concept areas and each member has accepted the challenge of creating modules for one of the concepts areas. Although an individual member is responsible for each concept area, Team members feel free to contribute ideas and module development in any of the areas. Drafts of modules are distributed through emails, posted online, and printed copies are reviewed at the Tuesday/Thursday meetings. Modules that have been formulated as webpages are available on a server for the Team members review. At the sametime the modules are being reviewed, the Team is formulating strategies for evaluating them (see appendices for evaluation documents).

Team Collaboration The following mechanisms are used to facilitate collaboration amongst Team members.

Tuesday/Thursday meetings. These regularly scheduled face-to-face meetings provide the basis of our collaboration. Each of us feel a responsibility to report progress at the meeting, we give encouragement and critiques about the progress, and future directions evolve through the discussion. We agreed early on to bring printed reports to the meetings. Most recent versions of these reports are attached as appendices to this report. Online Forum. In our earliest meetings we considered using an online forum as a place to post our progress and carry out our discussions. A sub-forum entitled “CBI (Challenge Based Instruction)” was created in the existing http://math.utpa.edu/forum. At first, the forum was open to anyone on the World Wide Web. Seven discussion topics were posted and then was abandoned by the Team. Although the forum did not catch the interest of the CBI Calculus Team, it did attract significant world wide interest. Logs from the forum show that one of the topics was viewed 66,299 times, and the topic viewed least often had 27,875 hits. Within the topic posts were 5 PDF files, one of which was downloaded 12,251 times. The PDF file downloaded the least number of times was downloaded 5,920 times. The math forum has since been password protected. (See the Appendices for the PDF files posted to the Forum.) The CBI Calculus Team worked best with printed reports brought to the Tuesday/Thursday meetings. BlackBoard. BlackBoard became the depository for our draft documents. All four team members are familiar with BlackBoard and have used it at one time or another. We asked the Center for Distance Learning to create and empty BlackBoard shell and grant each of us designer priviledges. We then created a folder for each of us where we have deposited drafts. Email. Team members regularly email each other. Reports are made available through emails prior to the Tuesday/Thursday meetings. Email is also used to discussing conflicts in meeting times. Discussions are seldom done through emal. Google Docs. The Team maintains two documents on Google Docs. One is a spreadsheet indicating the progress being made on individual modules. The other is a list of resources including contact information for people on campus (who can help us make videos, who is our BlackBoard IT person, etc.) and webpages of interest (Blackboard, WebWork, Google Docs, VaNTH*ERC, etc.). WebPage Server. The Mathematics Department has provided a folder where Team members can sftp the webpage version of their modules. A list of available modules can be seen at http://www.math.utpa.edu/cbi/watkins/index.html (anything else we should put here?)

Progress on Modules When our Team began we shared a spectrum of ideas regarding what a CBI module is and what objectives and expectations are appropriate. On one extreme:

Definition One “A CBI module begins with a problem that is beyond the reach of the students. As they progress through the module new concept and skills are taught in such a way that the student sees how they can be used to solve the problem.” (An example is Micky’s acceleration concept draft.)

On the other extreme

Definition Two “A CBI module begins with challenges that are accessible to the student. By completing the module the student obtains experience that is referenced and used as a basis for developing and defining key concepts in future modules and lectures.” (An example is Will’s graphing concept draft.)

Drafts of new modules appear to fit at different points on the spectrum. While we write the modules, we are developing and rewriting our rubrics for defining and evaluating. Our understanding of module continues to mature as the modules are developed, and hence the our definition and process of evaluation is also maturing.

Our process for developing a module begins when a Team member prepares a concept draft including suggestions for each of the six CBI components (Challenges, Develop Ideas, Multiple Perspectives, Research and Revise, Test your Mettle, and Go Public). That written concept draft is discussed by the Team and the individual member begins to “flesh out” the ideas, often rewriting the concept draft a number of times (current concept drafts are in the Appendices). At some point, development of the module is turned over to webpage design. At that point are rewrites are done in the webpage—meaning the final webpage may differ from the concept draft.

List of Appendices[edit]

Appendix A: Reports Posted on Forum

  • The Study of Speed: Inquiry into the Nature of Motion (12,251 downloads)
  • UTPA Mathematics Department Colloquium Report (5,920 downloads)
  • STEM Learning Community for Prepared Freshmen (5,924 downloads)
  • Evaluating Mathematics Courses in the Core (6,938 downloads)
  • Computers in the Tutoring Labs (6,935 downloads)

Appendix B: Google Documents

  • CBI Resources
  • CBI Calculus Project Development

Appendix C: Most Recent Concept Drafts

  • Challenge Based Instruction for Limits and Continuity, Huaien Li, July 1, 2009
  • Challenge Based Instruction Calculus I (Objectives), Dumitru Caruntu, June 8-23, 2009
  • Rules for Finding Derivatives of Elementary Functions, Will Watkins, June 22, 2009
  • CBI Discussion of Limits, Will Watkins, June 17, 2009
  • Math 1401 Graphing Module, Will Watkins, (undated)
  • CBI, The Slingshot, Will Watkins, April 2, 2009
  • CBI, The Car Trip, Will Watkins, June 16, 2009
  • Calculus Knowledge Base, Will Watkins, (undated)
  • VaNTH-ERC Workshop, Objectives, Will Watkins, March 6, 2009
  • CBI, Calculus I Objectives, Dumitru Caruntu, June 8-23
  • CBI, Car Racing Module, Dumitru Caruntu, June 23-30, 2009
  • CBI, Area fit Module, Dumitru Caruntu, July 1-7
  • CBI, Inertial Navigation Module, Dumitru Caruntu, July 7-15, 2009
  • CBI, Beam Bend Module, Dumitru Caruntu, July 15-23

Appendix D: Rubrics for Evaluating Modules

  • CBI Star-Legacy Module Checklist, June 22, 2009
  • CBI Module Evaluations, Will Watkins (undated)

Appendix E: Webpages