The math we should have been taught in high school

I love The Oatmeal and they have a funny little bit about what they think should have been taught in high school. I just posted the math for obvious reasons but you can check out the whole strip that covers all the subjects.

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Khan Academy

If you haven’t heard about Khan Academy, then you probably aren’t in the field of education. There has been tremendous criticism of Khan Academy by educators because it ultimately just lectures to students and many educators – at least the ones I keep up with – prefer having students approach math in a different way. Math is often seen as something that you learn and then practice. With more practice, you’re supposed to – with the traditional thought behind mathematics education – get better at math but I don’t think the point of math is to be able to memorize and practice problems over and over until you’ve mastered the skill. Although this can be one way people learn math, I don’t think they’ll truly understand it this way. Many other teachers really like Khan Academy because it does the lecturing for them. The program does have its benefits as it does allow students to work and learn at their own pace. Unfortunately, I’ve witnessed teachers just have their entire class watch a lesson in lieu of them teaching it, then pass out a worksheet for them to practice this new concept that they have just “learned.” While I may not be its biggest fan, I know Khan Academy does help some students. So for those of you that may get some benefit from it, check it out. Here’s a sample of what the videos are like:

Calculus: There’s an app for that!

Every math teacher should go through a series of philosophical questions regarding the purpose of math and how it should be taught.

One of the more common dilemmas is usually: To allow the calculator or not allow the calculator?

Other dilemmas include: Homework, Worksheets, Memorizing the times table, Multiple-choice tests, Proficiency grading…

I came across something interesting the other day when using wolframalpha to check some work that one of the students I was tutoring was working on. Besides finding it hypocritical that I asked that student to work on the problem “the long way” and I just used a website to check the answer, I saw an interesting advertisement on the right side of the screen. After a few refreshes, I found another of a similar peculiarity.

The ad on the left was the first one I saw and it made me genuinely upset. To me, it looks like an app will just give you the answers! It probably won’t even tell you what the answers mean! Students will lose all motivation to actually learn the point of Calculus!

Of course, they don’t need an app to demotivate them to learn about Calculus. Most math teachers do a fine job of that on their own. It also upset me to think that soon computers will just do all the math and students will no longer need to learn it. But then I realized that this is a blessing in disguise! I’m CONSTANTLY asking students to explain their answers and what those answers mean. If I could take away the need for them to consistently get stuck or frustrated in doing the problem itself, we could focus on setting up the problem and then analyzing the meaning behind the answer. Assessments would no longer test if students could perform simple algebra or add fractions, it could test whether or not students could create accurate models and interpret their solutions! That’s what people do in the real world!

I know many teachers will disagree with me because fractions are just so important – crucial to life, really – but I don’t care. I like to live life on the edge.

If any of you are curious about what happens when you click those advertisements, here is a screen shot of the page. It certainly would make Calculus homework much easier, but only if teachers continue to ask students to perform operations. This app would actually be a blessing to those who take my approach. Look at all the ways the math can be represented! Oh, the possibilities!

NASA Has Space Math

Here’s just a quick heads up on the awesomeness that is NASA. They have a page dedicated to math! My favorite are the “Problem Archives” where teachers can present real data, pictures, graphs, etc. from NASA to their students in an already lesson-friendly PDF. There’s nothing better than supplementing a textbook with this kind of stuff!

Space Math @ NASA

When Will I Ever Use This?

It’s the question that makes math teachers cringe: When will I ever use this?

It’s true that many of the exercises that teachers make students go through may never be used outside of math class. What I hope is that students see math as a different way of thinking about problems and how to solve those problems.

“There are people who say, ‘I’ll never need this math. These trig identities from 10th grade, or 11th grade.’ Or maybe you never learned them. Here’s the catch: Whether or not you ever again use the math that you learned in school, the act of having learned the math established a wiring in your brain that didn’t exist before, and it’s the wiring in your brain that makes you the problem solver.”

-Neil deGrasse Tyson

Graphing/Photography

There was an article in Wired Magazine (January 2010) online that showcased a photographer’s art in which she graphed her images. You can also check out Nikki Graziano’s website – which is worth taking a look at even if you don’t like math.

This could be a really engaging project for students in both high and low levels of math. Students in Algebra or Geometry could graph simple lines and curves, while students at more advanced levels could graph more complicated functions and shapes.