Google Sketchup

Dr. Heigle told me about Google Sketchup.  It's a Google application that you can download for free and use to create 3-dimensional models.  I was hoping it would be a little more intuitive to use.  It took me quite a while to figure out how to construct a fairly simple pyramid, but upon reflection, I think it would be hard to make a program in which constructing a 3-D model would be simple.  The third dimension adds a complexity that is kind of hard to simplify.  Anyway, I did manage to constuct a square pyramid that I then used to show my geometry class the three right triangles in a pyramid that can be used to find different missing dimensions.  It was pretty cool to be able to actually show them this in 3-D.  In the past, I've always done my best to draw a pyramid and the inner right triangles, but I've always felt like only the kids who are naturally good at visualization really get it.

Although it took me a while to figure out some of the basics of Google Sketchup, it was really fun!  I'm pretty sure I could spend hours on end creating things with it.  And it seems to have a lot of really cool features and tools, that I would like to explore if I can find the time.  I would like to be able to use Sketchup next year when we do volumes of solids of revolution in my calculus class.  There is a Google 3-D warehouse with models that have already been created by other people, so I will definitely be perusing that for good geometry- and calculus-related models.

TED Talk: Arthur Benjamin's Formula for Changing Math Education

In this talk, Arthur Benjamin argues that we need to fundamentally change the progression and focus of high school mathematics courses.  In the current system, high school math courses are designed, in large part, to prepare students for the study of calculus, so they focus heavily on algebraic reasoning and manipulation of algebraic expressions and equations.  Many students do take calculus, either their senior year or in college, and some will use it in their careers, but those students, in reality, are few and far between, contends Benjamin.  He asserts that statistics is a branch of mathematics that is much more useful in everyday life, and that is important for people to understand in order to be informed, critically thinking citizens.  A good understanding of statistics, he feels, should be the culmination of high school mathematics, for the majority of students.

I agree with Benjamin.  Statistics is a much more applicable field than calculus for the vast majority of people, and it seems to me that beyond Algebra I, what is learned in high school math classes is not used in everyday life or in a career except by a small number of people who go into math-intensive careers such as engineering.  It doesn't seem like a productive use of educational time for a student to spend three years learning the prerequisite skills to calculus if that student will never take calculus, or will take it but will never use it afterward.  Obviously, some students need to be prepared for and take calculus (we need engineers, physicists, astronomers, economists, etc.), but most students don't need to.

I have always felt that it was unnecessary to require all students to learn algebra to the level that they are required to in the United States, but it had never occurred to me that the reason students are required to do this is because our system of math education is based on an ultimate goal of learning calculus.  It makes sense, though, and I agree with him that it would be better if all of our citizens had a good understanding of statistics, as this helps people to understand political and social issues and many other day-to-day concepts.

Is It Time to Make Mathematics More Fun?

This article, from the March/April issue of ISTE's Learning and Leading, discusses whether math should be taught in a more technology-based, application-based, real-life relevant way.  I certainly agree that it should.  Especially at the high school level, it seems, math is usually taught as a series of algorithms students must learn to “solve problems” that are actually merely exercises without a basis in an actual problem situation.  Even when those algorithms are applied to real-world problem situations, this is often done in a way such that the student doesn’t have to actually determine how to solve the problem, because the problem was chosen because it can be solved with the algorithm the student has been practicing.  When this happens, student don’t actually learn authentic problem-solving skills.  Currently, one of my main goals for improving my teaching is to incorporate more authentic problem-solving experiences into my curriculum.

I think, however, that the author of this article misses a critical point.  She mentions that “Americans tend to think of themselves as good or bad at math,” whereas Asians “think that if you try hard enough, you’ll get it.”  She goes on to say that as a student, she didn’t work hard at math because it was boring.  I think, however, that often an even more significant demotivator for math students is a lack of confidence in their own ability to do math.  If a student has labeled him/herself as “bad at math,” then he/she won’t work hard to understand it, and therefore won’t understand it!  I agree that the way in which math is taught can be made more interesting and relevant, but I think that helping students discover that they can be “good at math” is equally important.

Calculator.com not as useful as I had hoped!

While perusing the eduTecher website, I came upon calculator.com.  Hoping to have discovered a great new online resource, I clicked on the link, but was disappointed.  Calculator.com has many different types of calculators, but is pretty unprofessionally done.  Many of the calculators don’t include any instructions for use.  The “graphing” calculator, in particular, doesn’t seem to have any instructions, and I honestly can’t figure out how to graph an equation with it!  (Granted, I wasn’t willing to invest an exorbitantly large amount of time into trying to figure it out.)  And even if I could, it looks like all it can do is graph; it doesn’t seem to have any of the other many useful functions of an actual graphing calculator (like the TI-84 that my students and I use).  And several of the “calculators” are really just conversion tools.  I feel like this site is trying to be impressive and make it seem like it offers more functionality than it actually does…