Matt Williams thank you for your presentation on Educational Technology.
You have opened our eyes to many possibilities to make learning math more enjoyable,presentable,and relateable to the real world.
It will take some time to review all the wonderful sites that you demonstrated in your presentation, and to find where we can utilize these tools to make math learning more engaging for our students.
Thank you for giving us your expert opinion on some of the sites with your rating of them.
Thank you for showing us the hardware you use and letting us take a closer look than most seminars would allow.
Sunday, November 29, 2009
Doing, assessing and designing a Math Project
Doing, assessing and designing a Math ProjectMina Nozar, Laura Cang and Ralph Baker
Math Projects purpose is to tie the real world to that of the mathematical view with an example or project that can be recognized and found in the real world. The self symmetry of Fractals can be seen all over in nature. The project will require visualization to recognize these building blocks as well as the process by which growth and mathematical iteration simulates growth or change. The IRPs do not specifically mention Fractals but I think this could be a good project.
The Pre-calculus 11, IRP
9. Analyze arithmetic sequences and series to solve problems. [CN, PS, R, T]
9.1 Identify the assumption(s) made when defining an arithmetic sequence or series.
9.2
Provide and justify an example of an arithmetic sequence.9.3 Derive a rule for determining the general term of an arithmetic sequence.
9.4 Describe the relationship between arithmetic sequences and linear functions.
9.5 Determine t1, d, n or tn in a problem that involves an arithmetic sequence.
9.6 Derive a rule for determining the sum of n terms of an arithmetic series.
9.7 Determine t1, d, n or Sn in a problem that involves an arithmetic series.
Spiral and Romanesco broccoli
9.8 Solve a problem that involves an arithmetic sequence or series.
Fractals are not specifically mentioned but could be worked into sequences and series with a twist to uses of math in nature as building blocks.
10. Analyze geometric sequences and series to solve problems. [PS, R, T]
10.1 Identify assumptions made when identifying a geometric sequence or series.
10.2 Provide and justify an example of a geometric sequence.
10.3 Derive a rule for determining the general term of a geometric sequence.
10.4 Determine t1, r, n or tn in a problem that involves a geometric sequence.
10.5 Derive a rule for determining the sum of n terms of a geometric series.
10.6 Determine t1, r, n or Sn in a problem that involves a geometric series.
10.7 Generalize, using inductive reasoning, a rule for determining the sum of an infinite geometric series.
10.8 Explain why a geometric series is convergent or divergent.
10.9 Solve a problem that involves a geometric sequence or series.
Doing and Assessing a Math Project - Fractals by Mina, Ralph & Laura
Part A:
Putting ourselves in the position of Math 11 students, a project we might be able to prepare would involve researched information on Mandelbrot sets and Julia Sets.
We would highlight that although each set can be expanded to create something highly complex, it is built on reiterative equations that are relatively simple. Students should be able to identify the basic building block of such a complex pattern.
Maybe as a group we will show a small clip of how beautiful the creation of mandelbrot sets can be. As the colours move across the screen, we could let our class know that the equation is z=z2+c and when z->0 the point is coloured black. If z-> infinity, the point is coloured. The colours are chosen arbitrarily but each colour represents a different rate of change.
Part B:
A project we, as teachers, could assign to our Math 11 students could be outlined as follows -
a.) Find an instance of fractalization in your life
b.) Discern what the single building block would be
c.) Draw or model the building block
d.) Describe the instructions (transformations/translations) required to build the full fractal form
ie. what is the iterative process entail?
*if we can think of one more project possibility with even more rigorous mathematics, I think that would be good*
Part C:
To assess this project, we have created the following Rubric
| Description | 0 | 1 | 2 | 3 |
| Choice of fractal with description and where you found it | | | | |
| Identify the single building block | | | | |
| Drawing or model of single block | | | | |
| Description of the iteration | | | | |
| Model/Drawing with minimum 2 interations | | | | |
I was thinking that this might be a good start. Obviously, the rubric is just a very rudimentary example. Let me know what your opinions are and we can flesh the rubric out and set some valuations to the numerical mark.
Resources:
http://www.ccd.rpi.edu/Eglash/csdt/african/African_Fractals/applications1.htmlhref="file:///C:%5CUsers%5CAMPRO6%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml">
Photo credits:
Applications 2: Spiral leaf -- David R. Parks (drparks@stanford.edu)
href="file:///C:%5CUsers%5CAMPRO6%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml">Fractal Geometry
www.cosmiclight.com/imagegalleries/fractals.htm
www.bcps.org/offices/lis/models/fractals/index.html
href="file:///C:%5CUsers%5CAMPRO6%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml">
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