Here’s a draft syllabus for March’s online course.
This is the first draft and will not be the official one. Participants will get the official one shortly before the course begins.
In the meantime, have a look and let me know what you’re wondering about.
It’s going to be a good old time.
The Mathematics in School Curriculum: Functions
Pilot spring 2012
The goals of this course are to broaden participants’ knowledge of (a) curricular approaches to function relevant to the middle school, and (b) the ideas behind the formal mathematical idea of function.
An important assumption behind the content of this course is that item (b) above encompasses both formal/logical components and psychological components pertaining to how both sophisticated and naïve learners think about these ideas.
This course takes place entirely online with no requirements for synchronous participation. Regular, daily participation will be essential but time of day for this participation is at participants’ discretion and convenience. See Principles of the course below.
All materials will be provided as downloads or links through Canvas.
Principles of the course
- Full participation will mean agreeing to spend about an hour a day for the duration of the course. The “hour” is an average and is at your convenience. Course activities will include working through mathematics tasks, reading articles, seeking resources and participating in asynchronous online discussions.
- But full participation is not just about seat time. It is about committing to learning, and to supporting the learning of your classmates.
- We are here to learn; this will require critical examination of what we think we already know. We cannot be possessive of old ideas—we need to be ready to expand them, to let go of them when necessary, and to welcome new ones.
- We should seek to appear curious, not smart.
- We all bring expertise; we should seek to share ours, and to take advantage of that of others.
- This is not a pedagogy course. We will examine mathematics and curriculum quite closely, but implications for teaching are not the direct product of our activity. Conceptual insight is. Instructional implications will follow. These may require long term fermentation before ripening.
- We should base our arguments and claims on evidence.
- We should ask honest questions, and lots of them.
- Discussions are not ever closed. Continue to contribute to old discussions as we move forward; it would be lovely to have each discussion be a record of our developing thinking.
Approximately one hour per day for the duration of the course is expected. The “hour” is an average and is at a participant’s convenience.
This course is ungraded and not for college or graduate credit.
All participants adhering to the principles of the coruse above and completing all assignments will be issued a certificate for clock hours towards relicensure. Participants requiring additional documentation of their participation should email the instructor with necessary details.
Summary of activities
Introductory activities: Reading principles of the course, introducing ourselves and exploring the online platform.
Discussion: What is a function? Participants will discuss their own understanding of functions, the ways that they and their students think about functions, and the relevance of these ideas to middle school curriculum.
Tasks: Participants will work a number of paper-and-pencil mathematics tasks involving function ideas. These tasks either come directly from elementary and middle school curricula, or are adapted from them. Sources include Everyday Mathematics, Connected Mathematics and Mathalicious.
Reading: Vinner, S. (1992). The function concept as a prototype for problems in mathematics learning. In E. Dubinsky & G. Harel (Eds.) The concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America.
Discussion: Participants will work to integrate the ideas from the initial discussion with those in the tasks and the reading by considering the question, What images do you carry around pertaining to function? together with the implications of these images.
Task: Participants consider functions graphed in polar coordinates. They begin with a game from Connected Mathematics to develop polar coordinates, and move to simple (i.e. constant and linear) functions.
Create: Participants create a product for public sharing. This may take any number of forms, including (but not limited to):
- a blog post reflecting on experiences as a learner and/or implications for instruction,
- a lesson plan (for any audience),
- an interpretive dance,
- a work of visual art,
The exact form of the product is not important. The important thing is that it adhere to the spirit of the assignment, which encompasses these two criteria: (1) it should be made public (i.e. shared beyond the course participants), and (2) it should incorporate one or more ideas of the course pertaining to function.
To complete the course, the product—or a link to, or a photograph or other description of the product—must be submitted through Canvas.