Sunday, March 4, 2012

MW's Math Library

Arranged in no particular order, this is a list of some of the math(s) books on my shelf, piles actually, that I am currently reading, have read, or to be read. Ok, so its the pile within reach of my favorite chair. As time allows, I will create a more complete database and share it. These are the books that I read and reread as I am planning my lessons or simply want to escape into the world of math literature. There are fun problems, human stories, histories, theory... These are some of the books I routinely pull excerpts from to share with my math students to help the see the beauty of math and learn that math is more than arithmetic. They are the source of inspiration for challenging problems for my students, and me, to chew on. They are inspiration. I thought my followers might find something interesting here. Please use the comment box below to share some of the titles in your piles, or comment on how you make use of books like this with your students.

The Math Book From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, Clifford A Pickover

The Mystery of Numbers, Annemarie Schimmel

The Golden Ratio, Mario Livio

The Man Who Counted, Malba Tahan

Fascinating Fibonaccis, Trudi Hammel Garland

Sacred Geometry, Stephen Skinner

The Num8er My5teries, Marcus du Sautoy

Finding Moonshine, Marcus du Sautoy

The Music of the Primes, Marcus du Sautoy

Symmetry, Marcus du Sautoy

Zeno's Paradox, Joseph Mazur

Cabinet of Mathematical Curiosities, Ian Stewart

Hoard of Mathematical Treasures, Ian Stewart

Number Theory and it's History, Oystein Ore

A Mathematicians Apology, GH Hardy

The Man Who Loved Only Numbers, Paul Hoffman

Number, John McLeish

Fermat's Enigma, Simon Singh

Thursday, February 2, 2012

MathCast Project

After exploring the concepts of equivalent fractions and the fraction, decimal and percent forms of rational numbers, I asked my 5th grade math students to create a brief video that explained or demonstrated one of these concepts of their choosing.

The first thing we did, was take a look at a video (Ma & Pa Kettle Do Math: see below) that used humor to explore a math concept. In this case it was the concept of place value, percents, fractions, and division.

We discussed the clip, how humor was used to illustrate the key concept of place value. We discussed the use of a concise story, simple dialog, and the brevity of the piece. Also part of the discussion was video as a visual medium and the considerations necessary in translating a written script to video. 

Students broke themselves into groups of two or three and were given the following outline of steps to get past the producer (me, the teacher):

Treatment & Script Writing
They first had to write a brief summary of the math concept being presented in their MathCast. Each team met with me to go over their concept to ensure that they had an understanding of it. Once that was approved, they were given permission to write a one-paragraph treatment of the video. After approval of the treatment, they set to work scripting out their production. Scripts were written in a collaborative fashion using GoogleDocs on iPads. 

Filming and Editing with iMovie
After approval of scripts by the producer/teacher, teams created props, sets, etc. and began to rehearse. When each team felt they were ready, they filmed their MathCasts using the video camera on an iPad. Scenes were shot as individual clips. In some cases, multiple takes were filmed. In other cases, the MathCast was shot as one continuous clip. Using iMovie on the iPads, clips were assembled, transitions and still frames were added and final productions completed. Each MathCast was uploaded to a class Vimeo site and embedded in pages on the class Moodle site. 

Screening & Evaluation
Students were notified by email when their video was posted and given an access code to view their MathCast. As a nightly assignment, all students were asked to view one MathCast and respond on the Moodle to the following questions: 
  1. What is the math concept presented in this MathChat?
  2. What about the MathChat helped you understand the math concept being presented? Be specific.
  3. What suggestions do you have that might make this MathCast better? 

A class discussion also took place to evaluate the process as a means of math learning. Notes from that meeting are included below along with the guiding questions.

Project Timeline

Week 1: Production
Day 1: Introduction, Brainstorming, Treatments
Day 2: Treatment approval, Script writing
Day 3: Script writing, Script Approval, Start Filming
Day 4: Script Approval, Filming
Day 5: Filming, Editing

Week 2:
Days 1-4: Nightly homework, view and respond to one MathCast each night
Day 5: Class discussion evaluating process

Here is one of the finished productions:

Class Discussion Evaluating Process

How did the MathCast help you deepen your understanding of rational number concepts?
  • I got to listen to the ideas of the others in my group. Get their ideas and put them together with my own.
  • A different way to learn the concept. You get to learn how other people beside yourself say and understand it.
  • Having to perform it helps me understand it. Easier to get the understanding than just copying notes.
  • You have to make sure you really know it or you risk presenting false information. Makes your explanations better.
  • In our notes we don't always record all that we know and understand. This forces us to explain everything completely, as if to a younger student.
  • Helps me remember the information, rehearsal of script.
  • We think we know it, so thinking, "how can I explain this and have it make sense?"
  • Have to put the ideas into our own words, forces you to really think about it.

What did you like about the project?
  • The process of making a movie: creating characters, writing script, using iMovie...
  • Not just putting down notes. Not JUST math, have to learn to use the technology. Cool to learn how to link the math to the movie idea.
  • I can use the technology to say what I've learned. Don't really do that in other [academic] areas.
  • Like doing something creative in math.
  • Most fun thing I've ever done in math. Had to do a lot of math, but also got to include the arts.
  • Liked that there weren't so many boundaries. We just had to include the math.
  • Liked that it was all our own ideas.
  • Fun way to express what I know and creative.
  • Would like to do this in EVERY unit. I think it should be LAW.
  • It's cool to watch others' projects.

Why should we do MathCasts? How do they benefit your learning?

  • Learned a lot from other groups movies.
  • Makes math more fun.
  • Like freedom of choosing my topic.
  • Getting to work with others and hear their ideas. Learn how they thought about the topic.
  • Collaborative group process. Have to work together. Have to learn how to compromise.
  • Helps me think about more ways to understand a topic by listening to others' ideas.
  • Hearing the ideas of others and putting them together with my own. I talked.
  • More freedom, being able to use humor and entertainment, but still making sure we communicated some math.

Closing Thoughts...
I don't know what more I can say that my students didn't say above to illustrate the power of this project. Yes, I made a deliberate decision not to go on to a new topic and spend another week on these concepts. However, this was incredibly powerful and worth every class minute. Whatever items I don't get to this year are insignificant in comparison to how much they learned in creating these MathCasts and how it deepened their understanding of basic rational number concepts. Using the iPads and the various apps that students employed in their productions was a perfect vehicle for the project. It could of course be done with nothing more than pencil, paper, and a video camera, but having everything needed in one convenient tool helped make it more accessible to the students. It encouraged them to experiment. And, while they were learning, they were having a lot of fun! I encourage any of my followers to give this project a try. Feel free to send me an email if you have any questions about the specifics. Special thanks to my curriculum supervisor for sharing the MathCast idea, and thanks to our two wonderful instruction technologies specialists for helping me think through the technical details of the project.