What if this is actually true…?

Last August, Kelsey Sheehy (@KelseyLSheehy) published “Failing a High School Algebra Class ‘isn’t the End of the World’  in US News and World Report. In the article she discusses the arguments of a couple of critics who are essentially arguing that it is time to reassess the long-held tradition that algebra is an mandatory part of a high school mathematics curriculum.

From the article:

“Algebra requirements trip up otherwise talented students and are the academic instigators behind the nation’s high school and college dropout rates, argues Andrew Hacker, an emeritus professor at CUNY–Queens College and author of the much-debated article.” (Sheehy, 2012)

She continues:

“Hacker argues that students should understand basic arithmetic, but memorizing complex mathematic formulas bring little value to society. “There is no evidence that being able to prove (x ² + y ²) ² = (x ² – y ²) ² + (2xy) ² leads to more credible political opinions or social analylsis,” Hacker writes.”

Sheehy is referencing Mr. Hacker’s Op-Ed from the NY Times dated July 28, 2012, which has generated a rather strong response. The comments number 477 and are closed. Some of them are less than cordial. There have also been blog responses like this (which also got 20 comments).

The last paragraph of his piece makes no bones about his point-of-view:

“Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions. Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer.” (Hacker, 2012)

It would seem that the policy-makers across the country would disagree with him, but I’m not sure our policy-makers are any more equipped to make that decision than Mr. Hacker.

I’m also considering Dan Meyer’s (@ddmeyer) rather engaging line: “I’m a high school algebra teacher. I sell a product to a market that doesn’t want it, but is forced by law to buy it.”

So what gives? If Algebra is driving up failure rates, driving down student motivation, and, as Mr. Hacker asserts, isn’t actually useful (a very debatable point but perhaps a debate worth having), why do we continue to insist that Algebra continue to be mandatory?

And if it is going to continue to be mandatory (which might be the right thing to do), what can we do to make it more universally accessible?

Perhaps the question of why algebra is mandatory should give way to the much more meaningful discussion: Why do kids hate it so much and how do we fix that problem?

Increasing Engagement Through Art

A half-hour of drawing might make the difference to whether or not the data table gets filled out...

A half-hour of drawing might make the difference to whether or not the data table gets filled out…

I have a teaching colleague to thank for this idea. He currently teaches all of our Algebra I students, mostly freshmen. We have noticed a struggle-disengagement cycles that is self-repeating and driven by inertia. The student begins to struggle, which leads to disengagement, which leads to more struggling, which leads to… you get the idea. However, my colleague created an art activity that might be a game-changer for some of these students.

It goes like this. First, create an image on a piece of graph paper. Whatever you want. Could be your name or a picture or whatever. But there are conditions. It must include at least 10 line segments. Endpoints must have integer coordinates. It must have one pair of parallel lines. It must have at least one pair of perpendicular lines. After the pictures were drawn and colored, then the students picked 10 line segments and found coordinates of the endpoints, slope, function rules in standard and slope-intercept form.

Doing all of those things ten times over is as good as a practice worksheet, except better! Better because, you activated the right side of the brain for those who need it (which is a healthy portion of our students). There is a greatly reduced temptation to cheat or shortcut because the products are unique (and the more competitive students will see to it that their picture isn’t copied). Plus, like a good billiards player, you are always thinking two shots ahead. By tossing in the parallel and perpendicular pieces, you are running the risk that the student might begin to make some conjectures about the look of lines and their slopes.

How much more Algebra is this student learning now?

How much more Algebra could this student be learning now?

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