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Matt-a-matical Thinking

Matt-a-matical Thinking
Thoughts about Mathematics and Mathematics Education from a private school teacher in Chicago.

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Highlights Highlight
2008-05-29 07:27:00
My wife and I wrote an article in Highlight s magazine about factorial. You probably know the magazine from the doctors office. You can read the article here Big numbers at a banana-split bar but you miss all the pictures. Guess you will have to find it at the dentists office.

Are quadratics really that important
2008-05-28 16:33:00
If I was a student who had just finished a course in Algebra I in most schools across America I think that I would think that the following were the most important things that we had done. I would think this because we had spent so much of our efforts on it.linear equationsdistributive lawquadratic equationsfactoringThe problem with this list isn't so much what is on it, it is what isn't on it. It seems to me that we simply must include exponential functions and therefore also logarithms. I guess my question is, "Are quadratics really that important?" The only way to add these topics in is to take other topics away. So what can go? Here is a partial list of topics that might be cut or reduced in the standard curriculum.completing the squareconicsrational root theoremlong division of polynomialsExponentials seem like such a natural topic, and one that could be made to support and build on linear equations so beautifully. I will give more of this idea when I write later about ...

Determinants as proportions
2008-05-26 05:21:00
This is a continuation of a discussion of determinants started here. And there is more here.ProportionsSo if determinants are important how important are they and when can they be introduced reasonably. One place that they could possibly come up is in reference to proportions. As a reminder, a proportion is equation where two ratios are equal. One method to solve equations such as this is the Means-Extremes Property. This is more commonly known as ?Cross-Multiplying?. I think I speak for many teachers that cross-multiplying is a ?bane of existence?. Cross-multiplying is a rule that is often overused. It seems to quickly rise to the top of all students list of favorite methods so that whenever in doubt about how to proceed in a problem with fractions teachers often here the idea put forth that the correct method might include cross-multiplying. This is probably because few students really understand what this method does or why it worksConnections between determinants and proportions...

What is a determinant?
2008-05-15 05:01:00
Determinants pros/consDeterminants, for a teacher if I may borrow a British phrase, they are a bit of a sticky wicket. For my teaching, determinants have the qualities that I find makes a topic uninviting for students:? The rules for manually calculating determinants seem arbitrary, and are nearly impossible to motivate.? It is not clear what the determinant means. By which I mean it is not clear what ?natural? meaning might be given to a the value of a determinant, in much the same way that slope can be imbued with the natural meaning of ?rate of change?.But determinants are also tempting:? Cramer?s rule presents a powerful way to solve systems of equations? Matrices are a vast generalization of number systems that have far reaching applications. Can we use determinants as a way to motivate the study of these objects?When teaching we need motivationsThe first question I ask about a topic, is what might lead someone to want to know this? Why have ?slope? or a ?determ...

A tease
2008-02-19 04:15:00
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 textbookBlogging as an assignmentThe genius of EulerFeel free to write in the comments that one of these is more interesting than the next.

More Determinants
2008-02-19 04:12:00
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

Calculator programming
2008-02-15 05:46:00
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
More About: Programming , Calculator

Bear hunting Algebra
2008-02-11 05:50:00
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
More About: Hunting , Bear

Carnival of Education
2007-11-28 07:00:00
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:

Lessons on Lessons while Cooking Mashed Potatoes
2007-11-23 06:03:00
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
More About: Cooking , Potatoes , Lessons , Mash

Carnival coming!!!
2007-11-21 05:24:00
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
2007-11-21 04:40:00
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
More About: Project

Big Idea
2007-11-16 04:14:00
Check out the posting on ASCD Express of my essay about the "Big Idea " in math. I come off a little more strident than I realized at first, but I do believe in these ideas. Check it out at ASCD Express.Powered by ScribeFire.

Fractions Quiz Redux
2007-11-10 05:07:00
As a teacher, who teaches some middle school I am fascinated by this post by Denise at Let's Play Math. The questions here are tremendously important, and I don't think most of us don't have good answers to these. Every middle school teacher must have good answers to these questions. ASCD's journal Educational Leadership has an article this month by Lynn Arthur Steen about math, with a
More About: Quiz

New courses?
2007-11-06 05:25:00
Today was the deadline at my school to propose a new course for next year. I have proposed a few courses in the past and some of them have been accepted. This year I am putting my most ambitious proposal out there. I am proposing a course in mathematical modeling. This course would hopefully be able to handle students who have had Calculus AB or BC, or possibly even for students who are

Classroom Projects
2007-11-05 06:09:00
So late one night last year, I had a strong desire to change the way I teach. In many ways I see myself as very traditional. Some people tell me not so much, but I think at least philosophically I am very much in the land of I have knowledge; their minds are empty; must put my knowledge in their heads. Despite this I definitely see myself as a constructivist. A bad word to many I am sure (I
More About: Projects

Linear Regression and Matrices
2007-10-19 04:59:00
So I know a good amount of math, more than the average guy on the street, but I love to learn new things. This week I passed out copies to the book Supercrunchers to my two kids in math club, and to get the ball started we went over how linear regression is calculated. I had no idea, and I found the following link that does a really great job, but it does almost the whole thing with matrices.
More About: Matrices , Regression

Chat about work with physics teacher.
2007-10-16 15:43:00
I never really understood work. The physics kind too. So I asked a fellow teacher to sit down with me an explain it. I recorded it with ISight, and now I have something to share with my students, and you...
More About: Chat , Physics , Work , Teacher

Small Math
2007-09-24 05:29:00
The idea of "small math" has been bopping around in my head for about two months now. What is "small Math "? Technically "small math" is a neurological syndrome named mathminuitis. I affects roughly 75% of all students ages 8-21. Symptoms include * A desire to learn the minimum amount of math necessary to pass the next test, period. * A belief that roughly 70% of the material studied in
More About: Small

Determinants are calling me...
2007-09-22 03:31:00
Good Story about a class, and my continuing fascination with determinants. I go to class today, and it is Algebra 2, which I am never really sure how to approach. We are doing a chapter on lines. Now I had all this students last year for Algebra I and it is an honors course, so they are all pretty strong. I come in to class and put the following question on the board: Determine if the points
More About: Calling , Term , Mina

Delta/Epsilon in HS
2007-09-16 06:08:00
I was tutoring a AP calculus BC student today that goes to a different private high school. I saw in her notes there the definition of the limit as it regards the definition of the definite integral. It was complete with delta and epsilon, and of course mesh size and all the rigmarole. I am teaching Calc BC at my high school and we had gone over such stuff this week, and I didn't mention this
More About: Delta

Three 3's Competition
2007-09-14 05:12:00
It was parent's night at the school that I teach at this week. There is generally a lot of waiting around for the teachers. So based on the brainteaser over at Text Savvy I decided to give my colleagues a little competition. Just as at Text Savvy the rules were: 1. Write a mathematical expression that evaluates to 9. 2. Use exactly three 3's and no other numerals. 3. Use no plus signs.
More About: Competition

The Scrap Heap of Mathematics
2007-08-24 05:06:00
My nomination for the scrap heap of mathematics, the rational root theorem. It is a lovely pile of math that is collecting all of the math that is no longer relevant, no longer valued to be a part of the K-12 experience. Upon inspection of the heap we find: calculating square-roots by hand, manipulating a slide rule, and if not on the heap lying right next to it balled up like a piece of used
More About: Mathematics , Scrap

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