Algorithms: Good for machines, bad for people

Algorithms: Good for machines, bad for people

This headline is a lie. It’s not that I think algorithms are bad. They’re not. Honestly, I think that’s how many of us move through our days without killing ourselves or someone else. We habitually take the medications prescribed by our doctors; we cook our eggs (and avoid salmonella); we follow the steps for safely backing our cars out of the driveway; we put on our socks before our shoes.

Even certain mathematical algorithms are very useful, like the order of operations (or PEMDAS).

But in the end, I think that dictated algorithms are not so great for people, especially people who are learning a new skill, and especially when the algorithm has little to no meaning or context.

Don’t know what an algorithm is? Check out my earlier post defining algorithms. 

People Aren’t Machines

There are many different educational philosophies that drive how we teach math. For generations, teachers worked under the assumption that young minds were tabula rasas or blank slates. Some educators took this to mean that we were empty pitchers, waiting to be filled with information.

This is how teaching algorithms got such a strong-hold on our educational system. Teachers were expected to introduce material to students, who were seen as completely ignorant of any part of the process. Through instruction, students learned step-by-step processes, with very little context.

In recent years, however, our understanding of neurology and psychology has deepened. We understand, for example, that children’s personalities are somewhat set at birth. And that their brains develop in predictable ways. We are also beginning to realize that certain types of learning and teaching promote deeper understanding.

The result is a better sense of students as individuals. Instead of a class filled with homogeneous little minds, we know now that kids (and grownups) are wildly different–in the way they digest information and approach problems. (To be fair, this is closer to John Locke’s original theory of tabula rasa, in which he states that the purpose of education is to create intellect, not memorize facts.)

In terms of a moral, there’s not much I recommend in this Pink Floyd video, but I can certainly identify with the kids’ anger at being treated like cogs in the educational system. Besides, it’s cool.

A Case for Critical Thinking

Certainly critical thinking is not completely absent in the teaching of algorithms. It’s marvelous when kids (and adults) make connections within the steps of a mathematical process. But critical thinking is much more likely, when the process is more open-ended. Give kids square tiles to help them understand quadratic equations, and they’ll likely start factoring without help. Let students play around with addition of multi-digit numbers, and they’ll start figuring out place value on their own.

You can’t beat that kind of learning.

See, when someone tells us something, our brains may or may not really engage. But when we’re already engaged in the discovery process, we’re much more likely to make big connections and remember them longer.

That’s not to say that learning algorithms is bad. But think of the way you might add two multi-digit numbers without a calculator. Instead of stacking them up and adding from right to left (remembering to carry), you might do something completely different, like add up all of the hundreds and tens and ones — and add again. In many ways, you’re still following the algorithm, but in a deconstructed way.

And in the end, who cares what process you follow–as long as you get to the correct answer and feel confident.

Teaching Algorithms is Easier, Sort Of

So if discovering processes is so much better, why does much of our educational system still teach algorithms? Well, because it’s more efficient in a lot of ways. It’s easier to stand in front of a group of kids and teach a step-by-step process. It’s harder–and noisier–to let kids work in groups, using manipulatives to answer open-ended questions. It might even take longer.

But I say that based on what we now know about kids’ personalities and brains, we’re not doing them much good with lecture-style classes. So in the long run, it’s easier to teach with discovery-based methods. Kids remember the information longer and get great neurological exercise. This allows for many more connections. At that point, the teacher is more of a coach than anything else.

In the end, we all use algorithms. But isn’t it better when we decide what steps to follow, through trial and error, a gut instinct or discovering the basic concepts underlying the process? That’s where we have a big edge over machines. After all, humans are inputting the algorithms that machines use.

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Math at Work Monday: Matt the Quality Control Specialist

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Quality in our car parts is important, would’t you say? I don’tknow about you, but I don’t want to drive down the road using mis-manufactured car parts. Today I had the pleasure of interviewing Matt Case who has been a with American Honda Motor Company for more than 15 years. He is a quality control specialist. Let’s hear about how he uses math at work.

Can you explain what you do for a living? 

I work as a quality control specialist for American Honda Motor Company, correcting supplier and packager errors. A supplier error results when we receive a notification from a supplier or dealer that a car parthas been mis-manufactured, meaning it wasn’t produced to Honda specifications, or that their is an error in the part’s packaging. My job is to investigate problems stated by dealer analysts and report my findings to them. I also give the recommendation for how to handle the mis-manufactured parts and packaging errors.

When do you use basic math in your job? 

I use math when creating end-of-month reports using Excel. I also have to measure parts when investigating the claims. I compare the part to the manufacturer’s drawing detail by detail. I need to know how to find diameters and measure in millimeters as well as use calipers. At times I have to convert mm into inches.

Do you use any technology (like calculators or computers) to help with this math?  Why or why not?

I use Excel, calculators, and of course, a computer. I use a multiplication formula on my computer to do conversions.

How do you think math helps you do your job better? 

IMG_1659Math helps me ensure that parts are acceptable. If I didn’t have basic math skills, I wouldn’t know how to read the manufacturer’s drawing and compare it to the actual measurements of the part.

How comfortable with math do you feel?  Does this math feel different to you? 

I feel comfortable with basic math like addition, subtraction, multiplication, and division. I’m not comfortable using algebra or more advanced math. Math doesn’t make me nervous at work or anything.

What kind of math did you take in high school?  Did you like it/feel like you were good at it?

In high school, I pretty much took basic math classes. During junior and senior year, I went to a trade school (Miami Valley Career Technology Center) where my math correlated with my trade which was engine rebuilding and machining. I can’t say that I liked math, but I did feel that I was competent in it.

Did you have to learn new skills in order to do the math you use in your job? Or was it something that you could pick up using the skills you learned in school?

I already knew how to do the math that I use at work.  Going to the trade school helped me learn how to use the tools that I use in my current position.

Anything else you want to mention?

Even though math may not be the most enjoyable subject, it is important to pay attention and understand the basics of math in order to further your skills as an adult and have a career.

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Interested in finding out more about this type of work?  Let me know any questions you have for Matt.

What is an Algorithm?

What is an algorithm?

For years I’ve been telling people that allowing people to discover mathematical concepts is way better than teaching an algorithm. And a few months ago, a smart friend of mine asked, “What’s an algorithm?”

Duh. I should probably explain that part, right?

It wasn’t that she didn’t have a vague sense of what algorithm means. But in some ways, I was using the term as educational jargon. That’s not cool, so I’m here to correct my bad habit.

Is it better to show kids a step-by-step process for solving problems? Or should we give kids the space to discover mathematical concepts and how to apply them?

In its most basic sense, an algorithm is a set of steps. These steps might be followed by a computer or by a person, depending on the situation. In some cases, you can think of an algorithm as a formula.

Algorithms in Everyday Life

You encounter algorithms all the time. On Facebook, an algorithm determines which posts and advertisements you’ll see in your feed. In Weight Watchers, an algorithm outputs the points value for the food you eat and another spits out your weight loss trajectory. Google uses algorithms to determine search rank. (The more popular the site, the higher its rank.)

Algorithms can make your life easier (or harder, depending on how you look at it).

In these cases, you might consider the algorithms to be formulas. And they are proprietary. There’s no way Facebook, Google or Weight Watchers is going to share these processes.

At the same time, these algorithms can make your life easier (or harder, depending on how you look at it). Certainly, before computers, crunching these kinds of numbers was way more tedious.

Take the enigma decryption project during World War II. (This is the story told in The Imitation Game, a new movie starring Benedict Cumberbatch as the mathematical genius, Alan Turing.) Enigma was a rather brilliant German code that was considered impossible to break. That’s because the code changed every day. Before it could be cracked, the code was altered slightly, always leaving the allies a little bit behind.

Once Turing built his code-breaking machine, the process sped up considerably. With a few standard clues, his invention could spit out the decoded messages in a matter of minutes. Suddenly, the allies had an advantage, which ultimately saved millions of lives.

But Turing likely had a greater effect on our modern lives. He published a paper considering the reliability of certain algorithms–an underpinning of Google’s search algorithms. Turing was one of the first to see the benefits of building machines to follow algorithms that were too complex or tedious for humans.

Algorithms in Math Education

But as a math educator, I’m not so keen on algorithms. That is, I don’t think that teaching certain algorithms is very productive in the classroom. And this right here is one of the cornerstones of the Math Wars: Is it better to show kids a step-by-step process for solving problems? Or should we give kids the space to discover mathematical concepts and how to apply them?

I would say that we need both, but we should rely more heavily on discovery.

So what is an algorithm in the math classroom? The classic example is long division. Most grownups have this process down cold. But it’s incredibly difficult to explain to young students. In fact, it takes most students several years to really internalize the steps.

So what’s the problem? Well, the algorithm isn’t intuitive, and it doesn’t have meaning. That’s no big deal when a machine is doing the calculation–or when the algorithm is so ingrained that the human brain goes on auto-pilot to find the solution. But that doesn’t happen quickly during the learning process. It’s like learning a new language through rote memorization.

In addition, division is a tool that allows us to solve more meaningful problems. When the tool is difficult to learn how to use or must be learned completely out of context, we risk losing kids’ attention in the process.

I’m not completely against teaching mathematical algorithms. I’ve certainly employed long division from time to time as a grownup. But I’m more likely to give that task to the little computer in my smart phone. And at some point, kids should too.

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What do you think? Can you describe any mathematical algorithms that you use in your everyday life? When do you let the machine do the work? And when do you do the calculations by hand? Share your ideas in the comment section.

Math at Work Monday: Audrey the Birth Doula

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As a woman, I know there is nothing more life-changing than giving birth to a child. It’s a time when you most need the support of people around you. You need encouragement. I had the pleasure of interviewing Audrey Kalman for this week’s Math at Work Monday. She’s been a birth doula for twelve years so she’s been the support for countless women (and watched a lot of lives enter the world!). What does this have to do with math?  Let’s find out!

Can you explain what you do for a living?

I support women who are giving birth and their families as a birth doula. Birth doulas are non-medical support people, hired by families, who provide informational, emotional, and physical support before and during birth. I meet with families before their babies are born to find out what they’re hoping for; I help ease anxieties and point them to resources. Once a woman goes into labor—or thinks she’s in labor—she contacts me. I then join her at her home or at the hospital and stay with her and her partner until a couple hours after the baby comes. That could be a few hours… or a few days. I do everything from reassuring her (and the dad!) that everything is fine to massaging her back to talking her through a particularly painful or challenging moment. I often describe my role as a “professional sister.” I have up-to-date training and come without the “baggage” of a family member, but I bring the same kind of caring and compassion you might expect from a close relative.

When do you use basic math in your job?

Because I’m self-employed, math is part of the equation (pardon the pun) that helps me figure out how to set my rates and how many clients I need to work with to meet my income goals. For example, when recently deciding whether to raise rates, I researched living wages in my area. I then calculated how many births I would need to attend to make a living wage, looked at fees charged by doulas just starting out, and used a multiplier developed by another doula to account for my years of experience. Then there’s all the lovely arithmetic that goes into tax calculations, though I use a tax calculation program for that.

Do you use any technology (like calculators or computers) to help with this math? Why or why not?

I don’t know where I’d be without Excel spreadsheets. Since I also serve as the administrator for a small group of doulas (we back each other up), I’m responsible for maintaining a spreadsheet to track all of our clients and tallying up who owes what to whom at the end of each quarter. We serve about fifty couples each year so this can get complicated. Using a spreadsheet is the only way to keep track of everything—not only who owes what but also other information like due dates.

How do you think math helps you do your job better?

I absolutely think it helps me do my job better. The hands-on work of being a doula is very intuitive, but the rest is like running any other business. I believe it’s important to be professional which includes creating contracts and invoices for which basic math is certainly required.

How comfortable with math do you feel? Does this math feel different to you?

I’ve always felt comfortable with math. (My mother was a college professor who taught physics and mathematics.) The math I use now feels somewhat pedestrian—it’s really just glorified arithmetic. What’s interesting to me is using problem-solving concepts to help me figure out big-picture questions (as with the rate-setting example I gave above).

What kind of math did you take in high school? Did you like it/feel like you were good at it?

I have always really enjoyed math. I had an unusual education in that I attended an early college now known as Bard College at Simon’s Rock so I took only algebra in high school. I went on to do some interesting math in college, including systems dynamics, but I didn’t pursue higher level math since I was a creative writing major. I did take statistics for my graduate degree in journalism. I think all citizens should be required to take basic statistics!

Did you have to learn new skills in order to do the math you use in your job?

I definitely picked up my spreadsheet skills post-school since nobody was using personal computers when I went to college, but the big-picture thinking and problem-solving skills which I consider to be part of math were definitely something I honed in school and have used ever since.

Anything else you want to mention?

I want to mention another kind of “math” that is related to birth. I think of it as “intuitive math.” It’s what allows me to “feel” whether a woman’s contractions are getting closer together and longer (a sign that labor is progressing). It also allows me to help women through contractions by counting their breaths. Perhaps this doesn’t have much to do with what we typically think of as math, but part of math is all about patterns and cycles—and those are definitely relevant to the process of giving birth.

Intuitive math.  Pretty cool!  I’ve never even thought about that. I hope you enjoyed this interview as much as I did. If you have any questions for Audrey, please let me know.

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Math at the Movies

math at the movies

(Photo courtesy of NASA Headquarters)

I love the movies. If I could, I would watch one every single day. I’m also a bit of a movie snob. I like films that surprise me or make me think. And while I don’t seek out movies that feature math, some of the best movies out there do. Here are a few of them.

Good Will Hunting (1997)

Written by Ben Affleck and Matt Damon, Goodwill Hunting won the Oscar for Best Writing, Screenplay. Damon plays Will Hunting, an MIT janitor and math prodigy. Psychologist Sean Maguire (Robin Williams) finally breaks through Hunting’s defenses, helping him to leave his past behind.

Pi (1998)

If you’re looking for something surreal, Pi is it. Filmed in moody black and white, the movie follows mathematical genius, Max (Sean Gullette) , as he searches for patterns in mathematics. At the same time, he’s being pursued by two groups who want his results: a powerful Wall Street firm and a Hasidic cabalistic sect.

 A Beautiful Mind (2001)

Based on the true story of Nobel Prize winner, John Nash, A Beautiful Mind won four Oscars, including Best Picture. Nash (Russell Crowe) is a brilliant mathematician, who has troubling relationships with a former college roommate, a young girl and a Department of Defense agent.

Proof (2005)

As her successful mathematician father, Robert (Anthony Hopkins) descends into madness, Catherine (Gwyneth Paltrow) begins to question her own sanity and mathematical abilities. Proof is based on the Pulitzer Prize winning play by David Auburn.

Moneyball (2011)

The ultimate answer to the question, “When am I ever going to use this stuff?” Moneyball  tells the true story of Billy Beane, the Oakland A’s beleaguered manager, played by Brad Pitt. Given a tiny budget for salaries, Beane games the recruiting system, using a sophisticated statistical analysis program. His methods ultimately change the way all baseball teams build their rosters. Jonah Hill plays Peter Brand, the brains behind the plan.

 The Imitation Game (2014)

Based on the life of one of them most fascinating mathematicians in history, The Imitation Game is the most recent math-centric films to hit theaters. Alan Turing (Benedict Cumberbatch) is the great mind who broke the Nazi’s enigma code, ultimately shortening the war by several years and saving thousands of lives.

With a list like this, you might think that Hollywood is has a great relationship with math. Never fear, this mashup tells the truth. Like much of the rest of society, the movies and television hate or are scared of math. Take a look.

What is your favorite movie or television program about math? What do you think of the movies I’ve listed? Post your comments below!