Show me the money… or something else useful…

It's not all about the money... photo credit: Flickr user "401(k) 2013" - used under Creative Commons

It’s not all about the money…
photo credit: Flickr user “401(k) 2013” – used under Creative Commons

In Sir Ken Robinson’s (@SirKenRobinson) book Out of Our Minds, he describes an economic model for our education system that is grounded in Enlightenment era philosophy.

According to Robinson, The Enlightenment is responsible for the labeling of topics as “academic.” At the risk of oversimplifying it, things that can be empirically supported are academic and things that cannot are non-academic.

For example, imagine a sunny day. According to our Enlightenment-conditioned minds, we could talk about “academic” things like the convection caused by the warming earth, the refraction causing the sky to appear blue, the air pressure causing the gentle breeze or the photosynthesis making the grass grow.

We could also talk about a lot of supposedly “non-academic” things like how beautiful the deep blue of the sky is, the lift in our spirits that comes from the sunshine, or the memories of when we were kids in the summertime. (Of course, we could try to make these academic by talking about the sunshine releasing hormones that effect the brain which lifts our spirits, or something like that.)

We’ve also labeled people as academic and non-academic. You see, anyone can feel the warmth of a sunny day, but only the smart, academic kids can understand and discuss heat transfers due to radiation from the sun, right?

And those are the smart kids who do well in math class. And those are the smart kids who get good jobs. By good jobs, we mean jobs that pay a lot of money. And if, you can make yourself academic, you can get a good job that pays a lot of money. You’ll be a smart person, too!

This message has created websites like this or this .The message: The good jobs need smart people. Math is the key to being (or looking) smart. Be smart and get paid well for it.

This message has understandably fostered a response in websites like this, which exist to assure kids that they are able to make money without the mathematics.

But wait, wait… WAIT! Why are we connecting math class to money? Does my “useless” math class only exist to get people high-paying jobs? Surely their must be a REAL reason that my classroom is full five times every day. What about people who don’t want one of those smart, mathy jobs that pay well? Equating math to money excludes significant chunks of students. It excludes future homemakers, military personnel, farmers, people who intend to follow into the family business, or people whose future goals include jobs that they KNOW aren’t going to pay well (teachers, artists, musicians, trade laborers, to name a few). To these folks, a math class that exists to get them paid well truly is useless.

Have we convinced these people they’re dumb because my math class is useless on those terms?

The worst part is that “useless” math classes (like the ones that I teach) are actually useful to all of those people. Math is more than a future paycheck. It is more than getting labeled smart or dumb. It is more than a key to some future door that you won’t appreciate now, but will be so thankful for later.

Maybe my “useless” math class can be for them. All of them. To use right now. To learn how to solve problems. To develop a linear sense of logic. To practice the art of questioning, of guessing well, and of learning to check an answer. To increase numeracy. To learn to struggle and to be patient. If my math class can do these things, then maybe my “useless” math class isn’t actually so useless after all.

“Useless” Math Class – Misconception #3

Photo credit: Flickr user "Hades2k" - Used under Creative Commons

There must be a reason for doing this homework other some job you’ll get ten years from now, right?
Photo credit: Flickr user “Hades2k” – Used under Creative Commons

In a previous post, I commented on how struck I was upon reading an embittered writer’s rant about having to take a “useless” math class. I mentioned four main misconceptions that we math teachers have allowed to take root in the modern academic mindset. I will now address misconception #3:

“The value of math class is defined by the eventual occupation of the student in the class.”

Okay, the oft-mentioned Sir Ken Robinson (@SirKenRobinson) and Dan Carlin (@dccommonsense) both speak out on this one. This is grounded in an economic viewpoint that education’s role is to provided able-bodied laborers to supply the national workforce. This wouldn’t be a scandalous view of education except that able-bodied in 1900 (when the system was being designed) is not the same as able-bodied in 2013… or 2025 when this year’s kindergarteners graduate high school.

But this misconception is perpetuated by posters like this issued by the State of Michigan’s Department of Education.  There is message sitting under the surface of posters like this, and it isn’t very far under the surface.

The message is that you aren’t going to appreciate this math class until you get to your future job. This math class is of no value to you now. Just invest your time in this class. Accept the challenge. You’ll thank us later.

Is it any wonder that we are having a hard time selling that message to our students? Remember this is a generation of kids who have grown up on online shopping, on demand TV, DVD’s mailed to their house, and texting and social media. This isn’t new to them. The world is an instantaneous place. And we are sitting them in a class with some of the most challenging material telling them, “Just wait ten years. Boy, then, you’ll be really glad you took THIS class.”

But surely that can’t be true. There must be a way to design a math class that is useful tomorrow in any circumstance for a civil engineer or a McDonalds employee. The latter being quite important because several of my students are currently employed at McDonalds.

So what will be useful tomorrow? Well, we math teachers would say they need a general numeracy, the ability to model life situations mathematically, and patiently solve complex problems.

That is, “useless” math classes, like the ones that I teach, exist to provide the general public with the ability to read and analyze statements with numbers, recognize common elements of different life situations, and solve complicated life problems with unknown solutions effectively and patiently. There is no job (or state of unemployment, either desired or undesired) that won’t make frequent use of those abilities.

It seems like if The State of Michigan wants to create a sign listing all of the areas that make use of my “useless” math class, they are going to need quite a bit more paper.

“Useless” Math Class – Misconception #2

In a previous post, I commented on how struck I was upon reading an embittered writer’s rant about having to take a “useless” math class. I mentioned four main misconceptions that we math teachers have allowed to take root in the modern academic mindset. I will now address misconception #2:

“The influx of handy-dandy computerized technology has lessened the need for mathematically proficient common folk.”

This misconception is offspring of the belief that mathematics is all about number-crunching in it’s various forms. If that were true, then there would probably be more truth to the misconception than there is. However, mathematics more than number-crunching. It is also analysis. Analysis needs human beings.

To properly analyze requires human beings because everywhere you look, human beings are trying to use quantitative statements to persuade other human beings. And data and statistics are not trustworthy on their own. In fact, they are included in Mark Twain’s three flavors of dishonesty: lies, damned lies, and statistics.

So, modern technology is wonderfully convenient for helping us deal with this:

photo credit: Flickr user "justgrimes" - used under creative commons

photo credit: Flickr user “justgrimes” – used under creative commons

But is your iPhone going to help you figure out if this chart tells us ANYTHING meaningful?

photo credit: Flickr user "jurvetson" - used under creative commons

photo credit: Flickr user “jurvetson” – used under creative commons

Can you imagine what kind of statement this display will help support?

You know where the general public can practice developing comfort with basic logic and numeracy to debunk crappy arguments that are pitched to us by politicians and marketing departments? You guessed it…

In “useless” math classes… like the ones I teach!

 

Also if you are curious about my debunking Misconception #1, you can go and read all about it

Linear Function Geometry

You know, I was talking to a colleague yesterday and he was commenting on the ways that he is trying to keep skills from previous math classes fresh by integrating a variety of skill sets into the problems he assigns.

I liked that idea. I teach geometry and algebra both. Some of the geometry gets taught before Algebra I, so it get me thinking about ways I could combine the two in away that pushes the skill sets of both, but doesn’t have the same feel as the typical practice problem.

 

So, consider this: Plot four linear functions so that there is a triangle in each quadrant. The smallest triangle is in quadrant 1. The next biggest is in quadrant 2. The next biggest is in quadrant 3. The next biggest is in quadrant 4. Also, design your triangles in such a way that the area of the triangle in quadrant 1 is exactly half the area of the triangle in quadrant 3 and the area of the triangle in quadrant 2 is exactly half the area of the triangle in quadrant 4.

 

Once you have your triangles drawn, find the equations for the four functions you drew to create your triangles.

 

What could be the next steps in this problem? What can we do with the drawing that we have in front us? What do you think?

“Useless” Math Class – Misconception #1

In my previous post, I commented on how struck I was upon reading an embittered writer’s rant about having to take a “useless” math class. I mentioned four main misconceptions that we math teachers have allowed to take root in the modern academic mindset. I will now address misconception #1:

“Math is about numbers. Writing is about words. Wordy people write. Numbery people math.”

I want to start by saying that writing and math can both be treated as stand-alone topics. You can study math or you can study writing… but most of us don’t. We are typically doing either one of those things about something else. Perhaps my situation revolves around a car, but I may need to use math and writing to deal with this situation. At that point, math and writing are vehicles (pun definitely intended), but the car is still the focus of the situation.

Now, it has been said that math is a language of its own. (In fact, here is a book about it, if you want to read it.) I understand the point behind such a statement. However, in the end, math doesn’t have it’s own language. Sure there are mathematicians who can cross cultural barriers by writing everything in set notation, but among “non-mathy” folks,  mathematics requires a common tongue. In this way, math is just like anything else.  “Два яблока добавил еще два яблока в четыре яблока” is meaningless to anyone who doesn’t speak Russian and it wouldn’t matter if that was a math statement, a religious statement or a question about sale on ground beef.

Beyond that,  consider what kinds of mathematics “non-mathy” folks are talking about in everyday conversation. Nay-sayers are correct when they say that it probably isn’t going to be formal mathematics. But, it will be important. The cop gives directions to a lost citizen. The salesman explains a payment plan to a potential buyer. The marketers discuss the exposure rates of a type of advertising. The psychologist explains the results from a study to a therapy patient. The professional athlete figures out how to invest his or her signing bonus. (By the way, these types of communication fall into “mathematical literacy” as discussed by Jan De Lange in this paper.)

Unskilled wordsmiths tying to have those conversations are going to leave with more questions than answers. Those aren’t necessarily simple conversations to have. They require patience, dialogue and WORDS. Good words. Accurate words.

And where do people get a chance to discuss complex mathematical situations? In “useless” math classes… like the ones I teach!

When done properly, math class provides an opportunity for students to struggle and stumble over the wording of math situations. To listen to an explanation and respond with a targeted question. The students develop the use of specific vocabulary and learn when to use it.

So, why do wordy people have to take my “useless” math class? Because we need you. We need you folks who are good with words to help us figure out how to explain the math to the rest of the world. Sure, there are “numbery” people there to figure the tough mathematics out, but without the “wordy” people we are left with Sheldon Cooper to explain the math to the rest of us.

“Useless” Math Classes: How to fix them…

I have Jenn Arch to thank for inspiring this post. I read her post called The Most Legitimate Reason Writers Will Never Use A Math Course and then I posted some tongue-and-cheek smack-talk in her comments. I encourage you to go and check out the post.

Jenn’s post is (by her own admission to me) a bit of a venting session regarding her being required to take a math class as part of her college coursework training for a career in writing, which she feels is completely unnecessary. In her defense, she is also willing to sympathize with math people who are forced by the same paradigm to take required writing courses.

Especially in this day and age, I feel that just because someone wants to move into the work force one day, doesn’t mean they should be forced to take math courses, especially if all the basics were taken in high school. This being said, I’m not taking sides and rallying a war against math (would be nice though, huh?) because I know there are math-minded people who feel the same about writing classes because the particular career they’re pursuing focuses more on numbers than words.

So, math teachers? What have we done? What are we doing? You think Jenn is alone? You think Jenn is unique in this regard? Doubtful… And how many math people will be willing to make the same impassioned (and well-written) argument against their being forced to take a writing class? We need to fix this. The sooner the better.

Here is the main issue: we in the math teaching profession have allowed several misconceptions to prevail.

Misconception #1 – Math is about numbers. Writing is about words. Wordy people write. Numbery people math.

Misconception #2 – The influx of handy-dandy computerized technology has lessened the need for mathematically proficient common folk.

Misconception #3 – The value of math class is defined by the eventual occupation of the student in the class.

Misconception #4 – The main purpose of math class is to transmit skills that can be later used to earn money.

Imagine Jenn (and others in her shoes) taking a math class with those thoughts in her mind. An aspiring writer taking a class with those as the pillars of the hidden curriculum would feel very bitter (especially at a couple hundred bucks per credit hour). Math teachers? We need to fix this.

I will be posting on each on of these individually because I feel like all of these points are misconceptions and I would like to do my part to present an argument that will give a different perspective to these thoughts.

Math teachers? Let’s fix this. We have done a disservice to people who feel like Jenn feels.

Are there other misconceptions that you know? Load the comments with them.