If you haven’t heard of Modeling and you teach math or science, you should check it out. It’s an awesome curriculum and allows teachers to focus on planning for their students rather than inventing effective lesson plans. http://modeling.asu.edu/ To access the full curriculum, one has to attend a workshop.

## Modeling

## The Hot Tub

Found at: http://math.rice.edu/~lanius/Algebra/hottub.html

The technologies used in this lesson are a word processor, a blog, a microphone, and sound editing software (such as Audacity).

### Objectives of the technologies:

- Word processor – Students will use a word processor to compose a brief (less than one page) story following the idea given in the “Another Story…” section of the lesson plan.
- Blog – Students will publish their stories on a class or public blog. This follows the meme of “explain this picture mathematically”. They will publish both their printed and their reading of the story. (This motivates a conversation on the pros and cons of different representations of the story.)
- Microphone – The microphone will be used to capture each student telling their story in front of the class.
- Sound editing software – The students will use Audacity to prepare their story for inclusion on their blog as a podcast.

### Software and Hardware requirements:

- computer with enough storage space for a hour or so of uncompressed audio
- web browser
- sound editing software
- microphone
- Internet/Intranet access to the blog

### Skills required:

- Teacher – The teacher must be able to troubleshoot audio problems and levels with the student to record the student’s presentation, should be familiar with sound editing, and should know how to upload audio to a blog.
- Students – Students should be familiar with a word processor and know how to use their class/individual blog account.

### Reflections on the technology:

The comprehensiveness of the storytelling might be overkill, but it does illustrate an edit cycle of preparing a word processing document *for* something, rather than an end in itself. The underlying assumption here is that students will enjoy hearing the stories that their peers concoct. The process of creating a story emphasizes thinking deeply about how mathematics is connected to life. To shorten the process, an alternative to formal presentations is to set up a sound booth station in a closet or a corner, but then one cannot ensure that other students will hear the stories.

## Multiplying binomials with F.O.I.L.

Found at: http://www.lessonplanspage.com/MathMultiplyingBinomialsWithFOIL812.htm

The technologies used in this lesson are a Wiki, a graphics program (such as Inkscape), and the World Wide Web.

### Objectives of the technologies:

- Wiki – The Wiki will be used to present and share the group’s solution to a way to multiply binomials in the expanded discovery phase of the lesson; it should explain in detail to an audience including their classmates how to perform their method. At the end of the creation phase, students will use the Wiki to compare their solutions. Each student will individually choose a method and add to that Wiki page an example of how to use it.
- Graphics program – Inkscape or another program will be used to create illustrations for the Wiki.
- World Wide Web – After completing their project, students will use the World Wide Web to explore other solutions to the project and compare other student’s solutions to existing solutions.

### Software and Hardware requirements:

- A class-wide Wiki should be selected—one that can handle mathematics is preferable.
- A graphics program
- Internet access and web browser

### Skills required:

- Teacher – The teacher must be facile with the software and hardware above, including how to export images for use on the wiki and how to represent mathematics on the wiki.
- Students – Familiarity with searching and conducting research is essential, as is knowing how to evaluate Internet sources. Familiarity with graphics software is helpful.

### Reflections on the technology:

The students will eventually use the Web to evaluate methods for multiplying binomials, but they will first struggle on their own to find their own representations. The culminations of the struggle is their group page on a class Wiki, a tangible form of effort spent. The hardest part for students will probably be not using computers in the discovery phase, as they will simply want to look up *an* answer and consider it the right answer. Hopefully, the emphasis on comparing their solution to the solutions of other groups in the class and those found on the Internet will require them to think critically and realize that there is no one right answer. Some students might not want or need to use the graphics program, but those students who think visually should have some outlet for their creativity. An alternative for those students who like to draw is using a scanner to digitize a paper drawing.

## Kirby Urner

O’Reilly features one of my math pedagogy heroes, Kirby Urner, in an article “Teaching Math with Python“. Yeah, the article is way old and the links out of date, but you can see what Kirby is up to at Oregon Curriculum Network (OCN), his own project.

## Focusing power of an ellipse

One of my favorite applications of conic sections, this picture shows how quantum fields also reflect off of the ellipse.

To learn more about this feat, check out IBM’s Almaden Labs page.

## software facilities for teaching mathematics, part 2

I thought I’d follow up on my post about using a “Deal or No Deal”-type game to teach math. If I were starting off with beginners to Python, I probably wouldn’t use so much functional syntax, but I thought I better show some code.

# "Deal or no deal"-isomorphic game import math values = [0.01, 1, 5, 10, 25, 50, 75, 100, 200, 300, 400, 500, 750, 1000, 5000, 10000, 25000, 50000, 75000, 100000, 200000, 300000, 400000, 500000, 750000, 1000000] class Possibilities(object): def __init__(self, possibilities=values): self.possibilities=possibilities def E(self, fcn): return sum(list(map(fcn, self.possibilities)))/len(self.possibilities) def mean(self): return self.E(lambda x: x) def standard_deviation(self): return math.sqrt(self.E(lambda x: x*x)-self.mean()**2) def population_deviation(self): n=len(self.possibilities) return self.standard_deviation()*math.sqrt(n/(n-1)) def beat(self, val): n=len(self.possibilities) m=len(list(filter(lambda x: x>=val, self.possibilities))) return m/n def remove(self, n): self.possibilities.remove(n) def __contains__(self, n): return n in self.possibilities def __str__(self): return 'The '+str(len(self.possibilities))+' possibilities are: '+str(self.possibilities)+'\n mean='+str(self.mean())+' ; SD='+str(self.standard_deviation())+'\n P(beating mean)='+str(self.beat(self.mean())) if __name__=='__main__': x=Possibilities() while(len(x.possibilities)>1): print('') print(x) inp = input('What value was revealed? ') float_val = float(inp) if float_val in x: x.remove(float_val) else: print(float_val, 'is not a possible value.') print('You win', x.possibilities[0])

## Vedic mathematics

I happened across this YouTube video entitled “multiplication using vedic mathematics”. I’m not an authority in its vedic credentials, but it happens to be a fun visual way of doing mathematics.

## Dimensions

Dimensions is a great site that introduces higher mathematics in tasty video form. It includes some topics not usually seen in high school and so might enrich the academic lives of many interested students. Better yet, the videos are licensed under a Creative Commons license. The films are not flashy and the narrator is a bit monotone, so disinterested students will find no entertainment value here, but they are quite high in quality.

## software facilities for teaching mathematics

Two stories caught my imagination today. One is a geometry program akin to something like Geometer’s Sketchpad, KIG (for KDE Interactive Geometry), described by an article in Linux Journal. The KDE EDU project has a number of great programs available for education.

The other is an idea for talking about averages, expectation, and probability. It uses the TV show “Deal or no Deal” as backdrop, trying to evaluate whether or not to accept the Banker’s deal. I got the idea while reading an issue of Linux Journal with an article by Dave Taylor (subscription required). To my taste the implementation in shell script is a might obscure. I would probably use Python to craft the solution while students described how to calculate the various quantities, as the notation appears (or could be made to appear with a few prior function definitions) more mathematical. The program would ask which boxes we opened and progressively give updated statistics on the likelihood of winning it big.

## Ideas for reforming K-12 mathematics

I first saw this story on Slashdot. Paul Lockhart’s Lament (PDF) appears to have been published in Devlin’s Angle, a column over at MAA Online. There’s a follow-up piece too with some additional material. It seems that the essay has made rounds before, but the Slashdot crowd got hold of it a bit late. One can find many commentaries on it in the blogosphere. Its relevance for me comes at a time when I have witnessed the pale shadow of mathematics taught in schools by teachers who don’t seem to remember or have never been taught how beautiful it can be. Lockhart’s answer to “What is math good for?” is perhaps the best I’ve seen–I won’t spoil it for you.