MTE 494 / 598 – Fall 2008
Technology and
Mathematical Visualization
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Numbers 82384 / 87168
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Instructor: |
Dr. Michael Oehrtman |
Office Hours: |
TTh: 12:00-1:30pm |
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Class Time: |
Tuesday and Thursday, 3:00-4:15pm |
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Location: |
PSA 303 |
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Class Website: |
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Course
Description: The course
Technology and Mathematical
Visualization teaches students to use several technological devices and
software packages for exploring mathematics, starting from introductory
skills
and leading to advanced techniques. Particular emphasis is placed on
visualization of mathematical structures and relationships. Lessons and
assignments develop proficiency in using technology in service of two
main
goals:
- exploring mathematical questions related to secondary content from an advanced undergraduate perspective and
- designing effective pedagogical tools for teaching secondary mathematics content.
The interplay of these two goals is intended to clarify foundational concepts in the secondary mathematics curriculum and explore how technology can give insight into those ideas.
Devices and software packages covered during this
course may vary according to class interest. Technology typically
covered includes but is not limited to:
Geometer’s Sketchpad: A dynamic geometric construction and visualization package. Students learn to use this software to illustrate and explore geometric properties and connections between geometry, algebra and calculus and to create dynamic models of real-world objects and relationships.
Fathom: A dynamic data and modeling software package. Students learn to generate powerful visualizations of data, statistical representations and tests, analytic function models, simulations of probabilistic models, and collection and analysis of real-time data with sensors. All representations of data and models are interactive through an intuitive graphic interface and linked so that changes made in one representation are instantly and dynamically represented in the others.
Excel: A popular and widely available spreadsheet package. This program offers powerful data processing and basic graphic visualization of data with files in a standard shareable format. Students learn to construct “What-If” analyses based on key parameters and to implement difference equation models of complex dynamical systems.
TI Navigator: A wireless connectivity system for graphing calculators. Students learn to use this device to enable collaboration on modeling activities and participatory simulations of dynamic events. Results captured from each individual student are combined and displayed for the entire class to make products of student thinking public in a non-threatening atmosphere.
VPython: An object-oriented programming language with a real-time 3D graphics module. Students learn to write programs in this environment to create visualizations of geometric objects and to model motion and other dynamic events.
Maple, MATLAB, Mathematica: Computer Algebra Systems (CAS) can perform powerful symbolic and numerical computations and generate a variety of visual output formats.
In general, extensive tutorials and help systems are available for all of these devices and software packages. I will expect you to become proficient in supporting your own learning. Rather than show you how to do everything in a step-by-step fashion, I will instead focus on helping get you started on each technology, introducing you to basic functionality, troubleshooting usage difficulties, introducing useful tips, and most importantly, guiding our exploration into using these technologies in mathematics instruction. I am almost always available by email, so if you get stuck on anything, please feel free to email me with your questions.
Homework: Weekly assignments will focus on exercises to develop proficiency with the various technologies covered in class, readings about research and theory of technology in mathematics instruction, conceptual analyses of foundational concepts in the secondary mathematics curriculum, and in-depth explorations of mathematical problems and structures using technology. All assignments must be generated in Word or TEX with proper mathematical typesetting, figures, tables and graphs.
Projects: You will complete four projects throughout the course of the semester. Details of each project will be discussed in class. For each project, you must propose the details to me in writing and receive approval at least two weeks before the due date.
- Instructional Design Team
Project: You will partner with one or two other classmates to
develop a technology-mediated lesson for some secondary mathematics
topic.
- In-Depth Mathematical Analysis:
You will use technology to explore some secondary mathematics content
and discover new insights about the underlying structures.
- Instructional Design Individual Project: You will work on your own to develop a technology-mediated lesson for some secondary mathematics topic.
- New Software/Device
Presentation: You will demonstrate the features, basic
mechanics, and instructional potential of some technology not
previously covered in class.
Midterm and Final: The midterm and final will assess understanding of the theory and practice of implementing technology in instruction, proficiency using specified technology, and mathematical content. The final will be comprehensive.
Graduate Credit: If you are taking this course for graduate credit (MTE 598, SLN 87168), you will not take the midterm and final. Additionally in place of Projects 2 and 3, you will complete an individual research project on the implementation of a technology-mediated instructional design. You will need to speak with me about ideas for your project and submit a 1-2 page proposal no later than September 16. Upon approval, you will complete the project during the course of the semester. The project should involve implementation, evaluation, and refinement of activities you develop based on the theoretical and practical foundations of this course. A final report should include an abstract, an introduction, a review of relevant research literature, a conceptual analysis of the mathematical content covered, a description of the instructional activities, report and analysis of the results, a description of modifications to the activities based on the outcomes of your analysis, conclusions, and references. You will work independently but should consult me regularly throughout the semester to make sure you are progressing appropriately and for feedback. The final paper is due on December 9, however, I strongly recommend that you submit a draft before Thanksgiving so that you may incorporate my feedback into a final version.
| Undergraduate level grades will be determined as follows: | |||||
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400 |
Homework Assignments |
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A+ |
970 and above |
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400 |
Projects |
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A |
930 - 969 |
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100 | Midterm I |
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A- |
900 - 929 |
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100 |
Final (December 11, 12:10-2:00pm) |
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B+ |
870 - 899 |
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B |
830 - 869 |
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1000 | Total |
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B- |
800 - 829 |
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C+ |
770 - 799 |
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| Graduate level grades will be determined as follows: |
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C |
700 - 769 |
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D |
600 - 699 |
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Projects 1 & 4 |
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E |
below 600 |
| 400 | Research Paper | ||||
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| 1000 | Total | ||||
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credit will be assigned letter grades only (no plus/minus). |
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Academic Dishonesty: In the
“Student Academic Integrity Policy” manual, ASU defines “’Plagiarism”
[as] using another's words, ideas, materials or work without properly
acknowledging and documenting the source. Students are responsible for
knowing the rules governing the use of another's work or materials and
for acknowledging and documenting the source appropriately.” You
can find this definition at:
http://www.asu.edu/studentaffairs/studentlife/judicial/academic_integrity.htm#definitions
Academic dishonesty, including inappropriate collaboration, will not be
tolerated. There are severe sanctions for cheating, plagiarizing and
any other form of dishonesty.