Margaret Sinclair - Onsite Participant
Francis Libermann C. H. S, Toronto, Ontario, Canada
Margaret Sinclair was a participant in the Geometry Forum's 1995 Summer Institute, where you can read her introduction and see her first home page.
For the last few years Margaret has been working on using spreadsheets with her classes, and she has three "units" that she thinks would make good additions to the Forum:
- Linear transformations
This unit uses a spreadsheet to set up the multiplication of a transformation matrix and column vectors to produce reflections, rotations, and dilatations in a graph. It looks at the relation between the area of a transformed figure and the determinant of the transformation matrix, the orientation of the figure and the sign of the determinant, and the shape of the object and the dot product of the basis vectors of the transformation. It is suitable for Canada's grade 13's (last year of high school, first year college.) It was developed by a friend and Margaret has used it successfully for four years (and made alterations to it) so it's student approved. She uses ASEASYAS, but other spreadsheets would also work.
- Algebraic problem solving with grade 9's
This unit introduces algebraic problem solving using spreadsheet columns as the variables. It emphasizes thinking about a problem and using numbers first to "play around" with the ideas before writing formulas, but when the formulas are written it doesn't limit students to one letter. They can write A+B+C = 32 and solve the problem by simple substitution.
- An introduction to functions using EXCEL (grade 11 level)
This unit was sent to Margaret by a friend who knows she's interested in using spreadsheets. She hasn't used the unit but says it looks fabulous and would transfer to the online environment very well.
Margaret has also done some assignments using Sketchpad that she thinks might give teachers some focus for a geometry unit. She writes,
Most Sketchpad books give very detailed info on how to do constructions and they pose good questions, but I find that I don't have the time required and the material doesn't always fit my curriculum. I want to telescope many ideas into a few lab periods, get the most out of those sessions, then head back to class and work on proof. In most cases I'm dealing with kids who've never used a geometry program so an introduction needs to be built in.
For the last few years Margaret has taught an OAC Algebra and Geometry course (similar to Advanced Placement in the U.S.). It includes vector geometry, linear transformations, complex number theory and three dimensional Cartesian graphing. For the independent study associated with the course (worth about 10%), students usually do essays or reports on topics. They use Spreadsheets, Sketchpad, Maple, or a TI-83 to investigate a topic (the Koch snowflake, Sierpinski triangle, Napoleon's theorem, Polar graphing, the Glad proof, etc.). They must produce a 2-minute display of their work for the class and hand in a short outline of the mathematics behind the display. Margaret writes that
last year the "show and tell" [display] session even brought non-math people in from the corridor. The students learned quite a bit about using their chosen program (which was the whole point!) and the displays were great. This idea for an independent study could be put on the Forum so teachers could use it in their classes, but I think it could also be run as an online "show and tell." Since attachments are easier to send these days, maybe we could have a contest where the best demonstrations are put online, with their accompanying math explanations.
Margaret says many parents ask what can be done when their kids are falling behind in math - especially in grade 11. She thinks there could be online practice of some sort to fill in the gaps where students are missing chunks of knowledge, and would be interested in exploring such a possibility.
This past year, as Margaret has continued her doctoral work in Computer Applications and Mathematics, she has been taking some courses online in Computer Mediated Communication and online course design. She hopes to use the knowledge she has gained to get involved in developing Web resources.
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