Background
Both these courses are independent learning courses offered through the Independent Learning Centre, TVOntario. The OAC Calculus course was originally a print-based course. As such, the validity, expectations and student feedback were all in place before the medium of the Web was introduced. The Grade 9 Applied course was designed for the Web. Since these two approaches proved to be radically different I will address each of them separately.

OAC Calculus MCA0A-X

As creative director of this project, I would like to address the pedagogical issues behind the transformation of this course. The course was redesigned using knowledge building techniques, and principles of visual thinking made possible through the use of software such as LiveMath, Flash, Shockwave and Coursebuilder.

Mathematical Visualization
Mathematical visualization is not just math appreciation through pictures. It must be linked to the numerical and symbolic aspects of mathematics to give depth and meaning to understanding, to serve as a reliable guide to problem solving and to inspire creative discoveries.
In other words, not only is it important to see mathematics in a realistic context, the visual solution, but it is equally important that the tools of the culture also be defined and understood. This has been achieved by using a graphical solution that requires the students to translate the visual into mathematical language. The third and final approach is from a calculus prospective, connecting the concrete to the abstract.

Knowledge Building
The process, moving from the concrete to the abstract and the simple to the complex is a fluid process which I have coined as Architechnics. The term applies to the thought process used by Architects. Firstly we have a problem, for the Architect it is a space that is to be filled. For a mathematician, it is a mathematics problem or theorem. The Architect then takes her ideas and translates them into a blue print, a musician into notes, an artist onto a canvas and a mathematician into an equation of mathematics symbols. From this step the architect; musician and artist move on to produce an artifact. The mathematician rarely uses artifacts. With the power of technology today it is now possible to create mathematical virtual artifacts with infinite manipulatives. This Calculus course was designed to complete this fluid process, taking abstract concepts and creating concrete interactive manipulatives. The samples were chosen to illustrate this process.

Assessment
The course consists of 4 units with each unit containing 5 lessons. At the end of each unit the students submit their work using an e journal and Equation Editor. The final test is paper based and written at designated areas around the province.

Contacts
The students have a variety of methods to attain help. The Independent Learning Centre has a phone help line. The course also has a built in WebBoard, which is a moderated threaded discussion. Here the students are encouraged to 'discuss' problems amongst themselves. In addition, there was a synchronized session using TutorsEdge software. Each student received a headset and microphone in order to participate in a virtual classroom.

Grade 9 Applied Mathematics MFM1P-X

The new curriculum with new rubrics, new expectations and new evaluation based on activity learning had its own challenges. Then to add a new medium, Internet delivery made me rethink how to design such a course. With all the requirements of this course, I believe that creating the print-based version first would have helped remove some of the obstacles. However, activity learning with many simulations was easier to achieve using appropriate technology such as Flash, Coursebuilder, LiveMath, Geometer's Sketchpad and Spreadsheets.

Activity Based
Mathematics is not a spectator sport. Students develop deep understanding of mathematical ideas by engaging in and with mathematics. Reading solutions rather than doing mathematics is analogous to showing students swimming strokes and expecting them to win a swim meet. Through this course, students used many simulations to collect data, make hypothesis and draw their own conclusions. There were built-in error factors to better simulate real experimental data. Algebraic concepts were introduced in context rather than through pages of drill.

Problem Solving Framework
Just as one needs to practice swimming or playing piano, students learn problem solving through practice.
If one is to practice problem solving then it is necessary to devise a framework or plan. Firstly, the students must understand the problem, through visualization. Then, in order to devise a plan, connections must be made between the unknowns and the data. This is accomplished by connecting the graphical to the visual. Technology has given these students the opportunity to work in a more concrete and stimulus-rich environment.

Contact
Once again, the students have a variety of methods to attain help. The Independent Learning Centre has a phone help line as well as TVO's "Ask a Teacher". The course also has a built in WebBoard.

This course will be launched on April 1, 2003.

Submitted by:
Sarah Inkpen
sinkpen@tvo.org
Education Officer
Independent Learning Centre
E learning Division
TVOntario