MarkC: A teacher student at UTS

This is a teaching resource I developed to demonstrate exponential growth. Have a go a solving the problem on the first page before moving onto the solution lilies-in-the-pond3

The following is an explanation of the Lilies in the pond problem

Teacher’s resource: Exponential growth: Lilies in the pond

• Detail of outcome: 2 unit mathematics HSC Course: Series. To give an understanding of important mathematical ideas, such as variable, function, limit etc. and to introduce students to mathematical techniques which are relevant to the real world (Board of Studies NSW, 1982).
• Where the resource will be used: The resource will be introduced after the students are working on their first geometric series problems. The resource requires a computer, an OHP and Microsoft PowerPoint
• Ideas for its use: Display the first page and ask for a volunteer to solve the problem. The idea is to get the students to dive into a mathematical solution without thinking about the problem. Students typically will develop an equation of the form A(t) = k2^x then they will finally get 2^x = 64 which will be solved using logs on their calculator. The context of the problem is lost. A logical problem is analysed as a mathematical problem (Janvier, 1990)
• The equation for the model and with substitution is T_n = ar^n-1 and T_n = 4*2^n-1
• Instructions for others: Most students will go straight into a mathematical solution and the formula are provided to guide them along that path. The solution is that they need to read the question carefully and use modeling and logic to work out that half the area is one day back from day 7, the last day. Most students work forward as well and this is another trap for them to fall in. Slides 2 and 3 show models to use. This resource demonstrates that reading and understanding the context of the problem is important. Also concepts such as sustainability of natural resources can be linked into the topic.

References

Board of Studies NSW. (1982). Mathematics 2/3 unit: Years 11-12: Syllabus. Sydney NSW: Board of Studies NSW.

Janvier, C. (1990). Contextualization and mathematics for all. In T. J. Cooney & C. R. Hirsch (Eds.), Teaching and learning mathematics in the 1990s. Reston VA USA: National Council of Teachers of Mathematics Inc.

I have created the movie demonstrating the use of using graphical calculator on my mobile phone. The following things were used

• Mobile phone with J2ME and Symbian OS. I used my Nokia 6120c mobile with bluetooth connectivity
• Math4Mobile application Graph2Go and Solve2Go
• Nokia PC Suite software to connect PC to mobile
• Mobiola Screen Capture to record the mobile to a video (trial version)
• Windows Movie Maker V6.0 to edit and add narration (with Microsoft Vista OS)
• AntonyPranata.com Screenshot for Symbian OS (freeware), shown below is a screenshot showing the actual quality

Cubic equation (ax³+bx²+cx+d=0)  for x³-x²-5x+2 (where a=1, b=-1, c=-5 and d=2) showing minima, maxima and infexion points.

This can be used to verify and visulise calculations. Paramaters can be changed on the fly to learn effect.