Office hours: I maintain an open door policy for office hours. I come to the office early each morning and if I am not tied up in a meeting or talking to another student I am available to you.
EMAT 4680: Under our program guidelines, students should enroll concurrently in EMAT 4680 and EMAT 3500. If you are going to follow our undergraduate program and have not already taken EMAT 3500, discuss this situation with me.
Prerequisites for EMAT 4690/6690: MATH 2210 and EMAT 4680/6680. If you do not have these prerequisites, please talk with me.
This follow-up course to EMAT 4680/6680, as outlined on this web site, and is an extension of EMAT 4680/6680 in at least two senses. First, the course aims to develop more depth with the use of various software applications to engage in mathematics investigations, to organize pedagogical demonstrations, and to set up problem explorations. The emphasis here is on mathematical investigations through the presentation of essays. Second, it will emphasize the development of units of material (e.g. sequences of lessons) that might be used with secondary school students.
The students may use application software owned by the Department of Mathematics Education and carry out the course using primarily Macintosh computers. Student owned software and/or Windows computers may also be used. The emphasis is on exploration of various mathematics contexts to learn mathematics, to pose problems and problem extensions, to solve problems, and to communicate mathematical demonstrations.
The following software will be used:
There is no textbook. Course assignments, files, and materials will be given via the network and submitted via the network. Of course, some material will be presented and discussed in class. Communication will be facilitated via e-mail and each student should have an e-mail account.
Your Web Site. IMPORTANT!!!
You will continue to build your own Web Site as begun in the EMAT 4680/6680 course. You can of course read your web page from anywhere with Internet access. Use FTP access if you wish to place material on your web site from off campus. There is a bit of a learning curve . . .
Teams: You are encouraged to work in teams of 2 or 3 people if it facilitates productivity. If you are more productive as a "lone eagle" then work alone. When you work in teams, however, it might be to some advantage to form different teams for different projects.
There will be two kinds of projects: Instructional units and "essays."
An instructional unit will be a set of materials you put together to use with real or hypothetical students. A rule of thumb is to develop material to use for about 10 days of mathematics instruction. Each of you should participate in a team that produces at least one instructional unit. The IU should be placed on the shared files when you are satisfied with it and at the end of the course each of you can copy off to your own disks the IUs from the whole group.
Essays: What is an essay? It is your presentation/write-up of a mathematical investigation. An important criterion is that it communicates something you have done with mathematics and can share with others -- students, fellow teachers, informed citizens, my mother (how is that for a test of whether it communicates?). A model might be a Mathematics Teacher article, but communication does not have to be limited to the printed page and putting your essays on the web site allows use of the hypertext format and the various application tools to add visuals to your presentation.
How many essays are required? That depends. Say three. But, three trivial things will not suffice; one really profound treatise will suffice. If you are going to produce essays on small ideas (not necessarily small essays) then do more than 3. If you get involved in a major work, maybe one is enough. For example, a treatise was produced two years ago showing 25 or more demonstrations and proofs of relationships with arbelos (an arrangement of three related semicircles). Unfortunately we did not keep a computer copy. One participant from this quarter plans to develop a presentation of inversion geometry with Geometer's Sketchpad. These are probably worth a lot more than an Excel page that generates the Pascal triangle.
CLICK HERE for EMAT6690 DOCUMENTATION
Contextual Teaching and Learning (CTL)
I would like either one essay (or more) or an instructional unit to examine the mathematics of some workplace environment. I will try to provide some examples and reaction. The CTL literature is built around the notion that a vital part of our preparation of teachers should attend to the preparation of their students for the workplace (as an alternative to academia). See:
Essentially, the essays and the unit are the summary of your work in the course. Collectively they are a portfolio of your "best work." You can decide what goes into the portfolio and when it is ready. It is assumed that essays that you have finished and submitted can be shared at the end of the quarter so that anyone that wants an electronic copy can take it from the shared folder. Material that is sent to me via e-mail is does not go directly into the shared folder.
Time on computers: You can not expect to accomplish what you should from this course without time on the computers that is in addition to the time we have in class. The usual expectation of 2 hours study outside of class for every hour in class is probably a minimum. Our class will be in Room 111/113 using the PowerPC G3 and G4 computers. Other Macintosh laboratories in Aderhold are available to you and we can help you get some software to run on computers away from the university.
Attendance: You are expected to attend class. If you have to miss for reasons other than illness, see me prior to the absence. If you are ill, your first priority is your health and the health of others. See me afterward and we will work with you.