A tease

I keep forgetting about all the things I want to write about. So I will make a public list and hopefully these posts will come in quick succession.

• Tchebyshev Polynomials (Thanks to Al Cuoco again)
• Combinatorial Game Theory textbook
• Blogging as an assignment
• The genius of Euler

Feel free to write in the comments that one of these is more interesting than the next.

More Determinants

I was at the Joint Mathematics Meeting in January, and their I met an author that I really enjoy. His name is Al Cuoco. He does a lot with mathematics education and his book on Mathematical Connections is a must for any high school math teacher who wants to give their students a hint of the beauty of mathematics beyond high school math. I highly recommend it.

Since he was there, and he was speaking a little bit about linear algebra, I decided to ask him the question that has been bothering me for at least a year. What is the the determinant? Remember from my previous posts that it is not that I don't know how to calculate a determinant, or when to use a determinant. What I don't know is how to explain it to students. How to give it meaning. Al's opinion appears to be that it is most clearly connected to volume. To help prove his point he sent me a graphic which previous appeared on the cover of a math journal. The graphic does a pretty good job of explaining how determinants can be used to find the coordinates in a different coordinate system. It basically comes down to projections.

Pretty cool. I think that I will try to tie together the different determinant thoughts that I have had over the year in one post. I will hopefully be able to add some of the things that I have learned in Al's papers.

Calculator programming

While covering the quadratic formula with my 8th grade algebra students, I decided to show them how to program their calculator to do the quadratic formula. Students had a surprisingly strong response to it. They loved it.

Certainly they love the power of having the quadratic formula in their calculator. And their may be less chance that they will memorize the quadratic formula because they don't have to do it as often as they would have had to if I hadn't given them the formula. But it was a great way to discuss the ideas of input and output. I drew a function machine on the board, and we discussed how other machines can be seen as functions. So this connects this fundamental mathematical concept of function for them to their lives, and it allows them a way to construct a function of their own. We did a problem of finding how long it takes for an object to fall a certain distance. Students really started to get it.

In fact, after we programmed that we wrote a program to find the vertex, both the x and y coordinates. This was great for them because it emphasized that this process of writing a computer (calculator) program is really whatever you want. Got a process that you are doing over and over then make a program. I also indicated that these two separate programs might be merged together to create a bigger more complex program that could do both things. Other teachers told me later that the students were still talking about it several periods later.

On the technology side, it really helps to do this with a smartboard and TI-smartview. I was asked so rarely about what did I type or where that button is on the calculator. It is such a relief to have these tools.

Bear hunting Algebra

I am finding myself more of a shameless shill for mathematics in my 8th grade Algebra class. Want me to jump around like an idiot? I will do it. Want me to make a snowball and bring it in to the classroom? Good as done. So you can see I am interested doing anything that will meet my students where they are...

One more crazy thing I have been doing is trying to connect the kids books I read to my math class. And I think I found out one that actually worked a little bit. It is Going on a Bear Hunt...

You may the know story, you may have been to camp, you may have never heard of it, which may mean that you have never had a child, been to any place where teenagers are asked to supervise young children. If that is you click here to get a sense of what it means to go on a bear hunt.

I use this to remind/reinforce the idea about doing and undoing to solve an algebraic equation. So with the equation:

3x+1=10

I say we are going on bear hunt we are going catch a big one we are not scared. Oh no a times 3!. Can't go over it can't go under it... Oh no a plus 1, etc. And then I said a 10! AAAAAAHHHHHH! Back through the 1 (minus 1), back through the 3 (divide by three). These are the steps (minus 1 and divide by 3) that you need to solve the problem.

Now as many of surely know, much of this is not "necessary", but my students need the background of reading through the problem the first time to understand the order of operations. In fact, many of my students still don't understand that the 3x cannot be undone by subtracting 3.

I hope that this helps them see not only what to do, but why they are doing it.

At the very least I am exposing them to classic literature, well literature, well words.

Carnival of Education

As we approach the end of the year will we be inundated with end of the year awards, and of course not so recently we had the Nobel Prizes. Named after Alfred Nobel the inventor of TNT (Boom!). Well here at the 147th Carnival of Education we are going to have our own prizes. The Noble Prizes, these prizes will celebrate that noble avocation to which we have all taken the time to consider: Education. Education is defined by Miriam-Webster to be:

... 2 a: to develop mentally, morally, or aesthetically especially by instruction b: to provide with information : inform ...

So to all of you that have made Education your passion even for only this week, Thank You, here is a prize.

The first Noble Prize goes to one of my favorite teachers growing up, Brinda Price. She was my ninth grade English teacher. As I remember her she was about 4 feet 10 inches, and she was tough as nails. You had better get your Romeo and Juliet packet in on time or else she wasn't going to take it. On the other hand, she loved us. She loved us with a mother's love. She wanted us to grow, and live, and enjoy life. She had a passion for her subject that was only exceeded by her passion for her students. She is one of my heroes, in the sense that I want to make my students feel the way I did in her class. I want my students to see me as a force of nature that cares about them and about math and mostly about their education. I desperately, forcefully, passionately want them to develop mentally, morally, or aesthetically especially by my instruction.

So the first Noble Prize goes to Brinda Price of Columbus Alternative High School circa 1984. Thank you, and I am sure that the lack of prize money will not surprise you given your choice of profession.

The Noble Prizes are given to recognize the sacrifice that we all make to our charges, you are all working to make the future better, to make each child's lives better.

The Noble Prizes for Valiant Effort go to Henry Cate for Public schools - a Gordian Knot or a Sisyphean activity?, Mike Cruz for Losing Difficult Students - Blessing or Loss?, and Mrs. Bluebird for Playing Principal.

The Noble Prize for Growing and Becoming More Zen so that Your Students Can Have a Good Day goes to Siobhan Curious at small tasks.

The Noble Prize for Improving the Profession goes to Bill Ferriter for The PLC Mandate. . ..

The Noble Prize for Literature goes to Rebecca Wallace-Segall for Schools: Celebrate Teen Writers and Lessons from the Newest Generation of Writers (& Thinkers).

The Noble Prizes for Teaching Resource Coordination go to ms. teacher for Sharing!, Joel for 50 Classroom Management Tips I Have Learned This Month, and Ryan for Bridging the Research-Practice Gap.

The Noble Prize for Opening a Window into a Soul goes to IB a Math Teacher for The Book of Me.

The Noble Prize for Unschooling goes to Laureen for Bucket-Free.

The Noble Prizes for Elementary Education go to What It's Like on the Inside for The Sad State of Elementary Science, and Ryan for How Kindergarten Has Changed.

The Noble Prize for Anti-Telepathy goes to Mr. Pullen for Hey, Kids: Guess What I'm Thinking!.

The Noble Prizes for Public Policy go to Judy Aron for Tax Credits For Homeschoolers - Bad Idea!, EdWonk for EduDecision 2008: Obama's $18 Billion EduFix?, Joanne Jacobs for Defining dangerous down, and Dave Saba for Math: there is no substitute | American Board for Certification of Teacher Excellence.

The Noble Prizes for Math go to Denise for Fraction models, and a card game, Tony Lucchese for A Letter to a Young Mathematician, and Matt (that's me!) for Lessons on Lessons While Cooking Mashed Potatoes.

The Noble Prize for Art goes to Scott Walker for Some sketches during a staff development session.

The Noble Prize for Thoughtful Homeschooling (is there any other kind?) goes to Dana at A workable solution for American education.

The Noble Prize for Film Advertising goes to Matthew K. Tabor for his highlighting of a Screening of 2 Million Minutes.

While the Noble Prizes for Film go to Larry Ferlazzo at Math Movies and More, and Adam for The Academic Schools.

The Noble Prizes for Humor go to mister teacher for Helpful or Harmful, Smellington G. Worthington III for Welcome, and Carol Richtsmeier for Lists, Parents & Paperwork.

The Noble Prize for Zoology goes to Ms. Cornelius for Wanted: One case of mouse-sized Depends Undergarments.

The Noble Prizes for NYC Education go to Norm Scott for UFT Candlelight Vigil Snuffed, Woodlass for Sacrificing the learning years — Why?, and NYC Educator for his accounting of 7.2 million dollars in What A Bargain!.

The Noble Prize for Statistics goes to Edwonkette at Lies, Damned Lies, and NAEP Exemptions.

The Noble Prize for Networking goes to Pat for Networking is Important for All Teachers.

The Noble Prize for Civics goes to Matt Johnston for Not Every Education Problem Begins and Ends at NCLB.

Then Noble Prize for Homework goes to michele lestage for Too Homework Much Help Can Result In Failure.

The Noble Prize for Identifying Hypocrisy goes to Right on the Left Coast for Teachers in My District Say Teachers Don't Care About Students.

The Noble Prize for Foreign Language goes to Maria Fernandez for Free Spanish online lessons on mp3.

The Noble Prize for British Education goes to oldandrew for The Two Discipline Systems.

The 148th Carnival of Education will be at So You Want to Teach. Entries are due at 5pm Central on December 4th.

Reading the submissions was a great honor. I learned a lot, and that is what is all about. Thanks to all our contributors for their thoughtfulness and their giving hearts.

Lessons on Lessons while Cooking Mashed Potatoes

I hope you had a wonderful Thanksgiving. We had a wonderful time here. We didn't go anywhere we stayed home, my Mom came, and we cooked here. As often happens, while discussing making mashed potatoes with my wife, I had a little epiphany. Maybe it isn't an earth shattering discovery, but I love a metaphor and I think this is a good one, so bear with me and I think you find a story that all teachers can use with their students.

As I said we made Thanksgiving dinner here this year. My wife picked the recipes, and it just happened that we picked all of our recipes from a cookbook we have from America's Test Kitchen. One of the things that we love about this cookbook is that it tells you their theories about "why" they do things. My wife were talking particularly about the mash potato recipe. I am sure that many of you know this, but it is important to add the butter BEFORE the milk. This has to do with "coating starches, etc., etc.", and my wife noted that it was not something she knew about. I told her that I had shared that same information, about the butter before the milk, with my wife's mother. My mother-in-law seemed to think that this was not interesting news of any sort, but something everyone knew. Of course, her own daughter didn't know it.

What does this have to do with teaching math. We often show students what to do. And often we are surprised by the ways they fail to do what we show them. But in this example my wife watched her mother make mashed potatoes many times, but because she didn't know why the butter went in before the milk she didn't know that there was any importance to the order. Since then, my wife has been mixing mashed potatoes, milk, and butter all at the same time. The Horror.

Well the mashed potatoes were great, and I believe that my classes will be improved because I have been reminded one more time that the model of teaching math where you ask students to just do what you do, and not show why is forever deeply flawed. Why is it flawed? Because it leads to lumpy mashed potatoes.

More secrets of mashed potatoes here.

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Carnival coming!!!

The Carnival of Education will be hosted here next week. Can't wait for the submissions. Check back here on November 28th to be shocked, entertained and amazed by how much can go on in world's finest, absurdist institution: the school. Entries are due Nov 27 at 11:59 pm EST. Send entries to mbardoe (at) att (dot) net.

Project Redux

So my fun projects/presentations are almost all in and on the whole they are: alright. I thought about classifying them as "not bad", but that sounded too good. I thought about classifying them as shockingly medicore, but I realize now I should not be shocked. Though I tried, I did not do a good job of giving feedback and guidance along the way. So in the end I think that each student group in their own earnest way did really work hard to learn about the things that I had asked them to learn, but what they didn't do was learn it well enough to explain it to others. There explanations were on the whole subpar. I found myself sitting there wondering if this is what they experience everyday from me. I think I will delude myself with some of my student evaluations from previous years to stop that thought. As usual my students failed in planning their presentations to think about one important thing: the audience. Most talked directly to me the whole time, or to the board. They expected me to say things like "right", "wrong", "yes", and, "I see". I ended up saying some of that stuff, oh well.

So how do I feel about the experiment. I think that I have to do it again. It can be better, and they can do a better job of communicating their thoughts. If they can't they desperately need the practice. What was also interesting was how the students went about using technology. Some eschewed it completely. That didn't necessarily help their presentations. They argued while they gave a team presentation, they said "I don't really understand this". They didn't rehearse. All in all there was room for improvement. But I did help one group make a mathcast of an argument to show that the square encloses the largest area of any rectangle of a certain perimeter. And after we were done the student was so excited to see what they had made. It was pretty dry mathematics, but they were excited to see what they had done with it. Sort of made the whole thing worthwhile.