#PassionDriven – The Brutal Truth About Teaching

I recently came across an article  titled “How I Became an Unfair Teacher”. It was written by a primary school teacher who was trying to understand the influence that a teacher has with their students. One particular section was telling:

Classroom lessons may slip quickly through students’ fingers, but the classroom experience lingers in memory. Each teacher offers students a different model of authority and justice. We set our own standards of fairness and sometimes fail to honor them. A teacher swings a heavy club, and we can leave big, purple bruises if we’re not careful.

Ideally, we’d consider every student’s perspective, every moment of the day. But that effort is difficult with the limits of our time, energy, and imagination. In practice, it helps to adopt rules of thumb, rehearsed habits of fairness that can spare students undue suffering—and keep us from living on as demons in their memories of school.

Even though I teach at the undergraduate level, I’ve noticed the same things in my work. You get so focussed on getting through the material that you forget that you are serving your students’ needs and you can’t do that until you pay attention.

It’s a very good article and I encourage everyone to go read it, but that’s not what inspired me to write this post.

That happened when I read the comments.

Specifically, one comment in particular:

And this is why we have raised a generation of emotional weaklings who give up after the first shock–not making first team on the varsity, not having the work ethic to pass an AP test, not having the intelligence to make it through the first quarter of community college.

Every year I see the kids in my high school leave and 90% of them claim to be going to this or that college. Within a year 70-80% of them have dropped out. Your teaching philosophy/worldview is a huge part of the reason why they drop out. They have no guts. No determination. Emotionally stunted, they can’t handle setbacks. With massive egos, the moment they encounter this indifferent thing (which far surpasses your own perceived indifference) called reality they throw their hands up and quit.

Surprise. You…and your students are specks of cosmic dust. You’re not important. So buck up and realize that in life you’re going to get your feelings hurt.

Or you could just keep setting your kids up to fail because there are way more emotionally difficult things waiting for them in this place where the training wheels come off called adulthood: stagnant wages, student loan debt, the destruction of a middle class life, breaking of unions, loss of health care benefits, the pension that vanishes the moment you go to collect it, skyrocketing inequality.

Working to reverse these trends will be even harder than keeping your eyes open in class because you had to work the night shift.

It took me a while to figure out why this comment bothered me. At first I thought that it was needlessly cruel. Then I realized that it was worse than that. It was lazy. True cruelty requires engagement and this commenter couldn’t even be bothered. They just wrote off everyone who wasn’t them. In other words, this person took 253 words to just say “Meh”.

When I was younger I might have speculated about a person with this sort of attitude – what’s their background, why do they think this, etc. Now I just call it as I see it.

You may think that you’re delivering ‘tough love’ to the kids to ‘scare them straight’ and ‘give them some backbone’ something something get off my lawn something FREEDOM! But you’re just a lazy, indifferent d-bag.

Whatever happened to making a better world for our kids? I realize it’s much easier instead to try and drag them down to our level but I don’t think that was always the case.

My mother was an environmental activist. She did this while taking care of her husband, five kids and living in a town where the primary employer was also the region’s largest polluter and hence a major target for her activism.

This had a cost. She got screamed at when she was buying groceries. The priest at our local church told her she was no longer welcome at Mass. My father, an independent businessman, lost customers. We kids were teased and bullied at school (by students and faculty) because of what our mom did.

But we supported her and her work, despite all that. When we asked her why she put up with all of this crap (in addition to the mind-numbing amount of work involved in serious activism), she would tell us that she wanted to make a better world for her children and for her children’s children.

That lesson stuck with me. While I can’t say that I have made as big a difference in the world as my mother, I put in what effort I can in as many ways as I can to make things better. For me this is the primary goal of teaching – to make a better world. It’s hard work and it doesn’t always pan out. But, like my mother, you keep going back and you keep trying.

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#WeHateMath Calculators Considered Harmful

“For this invention will produce forgetfulness in the minds of those who learn to use it, because they will not practice their memory. Their trust in writing, produced by external characters which are no part of themselves, will discourage the use of their own memory within them. You have invented an elixir not of memory, but of reminding; and you offer your pupils the appearance of wisdom, not true wisdom, for they will read many things without instruction and will therefore seem to know many things, when they are for the most part ignorant and hard to get along with, since they are not wise, but only appear wise.”(Phaedrus 274c-275b)

 

The above quote is Socrates complaining about the invention of the written word. He claimed that allowing students to write down facts instead of memorizing them would weaken their minds.

I’m reminded of this when I see some of the reactions to suggestions that we embrace the use of computer technology in the way we teach math. The most noted advocate for this is Conrad Wolfram, who described his philosophy in a 2010 TED Talk.

My first introduction to technology-assisted math was in my high school chemistry class, where we learned how to use a slide rule. (Yes, I’m thatold.) We didn’t have them in math class (or calculators for that matter) so all calculations was done by hand. I didn’t get my first calculator until I went off to college. As this technology got cheaper and more readily available, it began to filter down towards K-12, where I recall a lot of controversy over allowing their use in class. It was felt at the time that it would make students unable to do arithmetic by hand and therefore become dependent entirely on machines to do it for them.

Back in 1957, Isaac Asimov wrote a short story “The Feeling of Power”, about just that kind of future and how society had to rediscover the technique of doing arithmetic by hand. The comments at this page about this story are…..okay, I’m trying to think of how to say this….well, let’s just say there’s a certain ‘you kids get off of my lawn’ quality to them.

Please don’t misunderstand. I absolutely believe that grade school kids should learn how to do arithmetic by hand, to start. But I don’t believe that it’s as simple as we either do all of our math by hand or become completely dependent on machines.

First of all, I have no problem doing arithmetic using a machine. Arithmetic is a very mechanical activity, which is one of the reasons why teaching it involves so much memorization. It isn’t something that comes naturally to us humans. However, we should be comfortable with arithmetic so that we can visualize what our answer should look like and to make sure the problem was entered correctly.  (I prefer using a text editor to writing by hand. This doesn’t make me illiterate.)

Math, on the other hand, involves intuition, creativity, imagination and logical thinking. Machines can make the arithmetic part of it easier but you still need to understand the problem well enough to explain it to the machine. We teachers don’t have to fear the use of calculators or computers in a math class if we use them intelligently. Where these machines can be used to our advantage is to reduce student anxiety about the mechanical parts of the problem so they can focus on the part requiring human-based thinking.

In my experience, students hate math because they fear arithmetic. They are so scarred by their grade school arithmetic classes where the slightest error in a long chain of arithmetic would ripple down and cause them to get the problem wrong (and fail the test) that they don’t want to be anywhere near any class that reminds them of that.

I encourage the use of calculators (and spreadsheets and Wolfram Alpha) in my college math class. They take away fear and give us more time to actually talk about math.

#WeHateMath Math without Calculations?

I ran across a couple of articles that discuss something that I’ve been pondering (and talking about on this blog) for a while now. That is, teaching mathematics without requiring that students do the final calculations by hand.

Here’s the basic idea. Computation (formulating solutions to problems) is more important now than ever. However, since we have calculators, computers and even Web sites to crunch the numbers for us, doing the calculations by hand is out-of-date and should be de-emphasized.

This idea was recently promoted by Conrad Wolfram, the head of Wolfram Research, which produces the software package Mathematica and the math engine Wolfram Alpha. Here’s an interview with Wolfram where he describes his idea in a bit more detail.

I’m not saying this is a bad idea, but I can see that there are any number of ways for someone to take this in a negative way. It takes a while to think this through for those of us who (like me) were raised and educated in the traditional math curriculum.

I teach undergraduate math, so I’m always on the look-out for ways to improve my classroom content. That means that sometimes I use my classroom as a lab for a little empirical research.

For example, this term I’m teaching College Mathematics. This is a 100-level class aimed at non-technical students (we’re a career college) and my students are in a mix of majors like Medical Assisting, Graphic Design and Business Administration. The course description is as follows:

 

This course develops problem-solving and decision-making strategies using mathematical tools from arithmetic, algebra, geometry, and statistics. Topics include consumer mathematics, key concepts in statistics and probability, sets of numbers, and geometry. Upon successful completion of this course, students will be able to apply mathematical tools and methods to solve real-world problems.

 

So it’s essentially a course in functional numeracy. For most of these students, this is the only math class in their program.

I decided to test the theory that the thing most people who claim to hate math actually hate arithmetic. My personal opinion is that arithmetic is unnatural and mechanical (since the learning strategy consists of memorization) and that math places more emphasis on creativity, intuition and critical thinking. With this in mind, on my first day of class I did the following:

  1. Explain the difference between math and arithmetic.
  2. Set a policy of ‘no arithmetic by hand, unless it’s absolutely convenient’. (For example, I’m not going to grab a calculator to multiply 9 by 5.)

For each session, I start with a “Math Minute” where I present a short puzzle or thought experiment to get students thinking and discussing some math concept. For the rest of the period I discuss this week’s subject (I can’t change the text or the lesson plan). However, I keep the conversation focussed on concepts rather than calculation. When we work through problems, we spend most of the time thinking through the set-up and then use a calculator (or spreadsheet or Wolfram Alpha) to get the answer. (This is only for problems where the calculation isn’t obvious. See 2 above.)

As you can see, I haven’t made any big changes (evolutionary, not revolutionary). I still have to pay attention to different student learning styles, encourage group participation, share problem-solving tricks and all of the other classroom techniques I’ve been using for years now.

As expected, there was some resistance. I was taking an unusual approach by de-emphasizing those parts of a math class that are traditionally the focus. But overall the response has been positive.

Now I don’t think that all classroom math should be abstracted to machines. In my class, we still use decks of cards and dice to talk about probability, count floor tiles to think about surface area and lots and lots of whiteboard work complete with diagrams. The point is to get students to connect with math and I’m just shifting that connection to the problem set-up process and I’m a fan of whatever works.

 

#WeHateMath Blog Review – Finding Ways to Nguyen Students Over

Ever since I started this blog, I’ve been on the lookout for other sites that talk about math and math education. I’ve covered a couple before now, but Finding Ways to Nguyen Students Over is my latest crush. Fawn Nguyen is a middle school math teacher from California and judging by the tremendous amount of great content on her site, she has apparently discovered the secret of going without sleep.

Not only does it have some great classroom exercises but there’s a good, common-sense interview with a middle school teacher about Common Core and one of my favorite posts, entitled “Blessed”, where she shares a couple of lovely hand-written notes from her students. Here’s a quote:

I’m crying and thinking I should quit teaching because it can’t get any better than this — like quit while I’m ahead.

As if that weren’t enough, there’s a section known as Math Talks, where she shares student voices as they discuss a math problem. It’s great to see the different ways that students take to approach a solution and it’s a good reminder that everyone has a slightly different learning style. In fact, there’s so much available here that I’d encourage anyone to just click on over there and start digging. If you’re like me, you’ll come out hours later wondering where the time went and you’ll be a better person.

By the way tell Fawn I sent you. (Trust me, I’m trying to start a thing.)

#WeHateMath Book Review: Street-Fighting Mathematics

Street-Fighting Mathematics by Sanjoy Mahajan is probably the least intimidating math book I’ve ever read.

That’s meant to be a compliment, by the way.

The subtitle to this book is The Art of Educated Guessing and Opportunistic Problem Solving and Mahajan sums up his philosophy in the very first paragraph of his preface:

Too much mathematical rigor teaches rigor mortis: the fear of making an unjustified leap even when it lands on a correct result. Instead of paralysis, have courage—shoot first and ask questions later. Although unwise as public policy, it is a valuable problem-solving philosophy, and it is the theme of this book: how to guess answers without a proof or an exact calculation.

This book weighs in at a scant 135 pages including the index. The title comes from a short course of the same name taught by Mahajan at MIT. The makeup of the class ranged from first-years to grad students in a wide variety of academic programs. The course was designed to focus on techniques for using math to solve real-world problems.

This may seem odd at first because we already use math every day to solve real-world problems.

Don’t we?

Well, yes. But, as pointed out above, there is a time and place for mathematical rigor (as taught in traditional classes) and at other times you need to be able to feel the answer. It’s kind of hard to explain but Chapter 4 (“Pictorial proofs) suggests what the author is trying to achieve:

Seeing an idea conveys to us a depth of understanding that a symbolic description of it cannot easily match.

Make no mistake. This is not a book simply listing short-cuts or “cheat codes” that we can use to avoid math. This is instead a different approach to mathematics by way of mapping math to our life experience and giving us a way to internalize it, giving us a sort of sixth sense.

Let me give an example. A bookshelf that is out of alignment and unstable can be described by a series of geometric expressions, involving lengths, widths, angles and so forth. However, an experienced carpenter can tell if a bookshelf is out of alignment and unstable by looking at it and touching it. Now the carpenter certainly knows the mathematical properties of a well made bookshelf but she has internalized the math so that now she can ‘sense’ when something is wrong. It doesn’t add up, so to speak.

The book covers a wide range of topics, from economics and Newtonian mechanics to geometry, trigonometry and calculus. Yet it’s very reader-friendly, written in a clear, engaging style with plenty of examples and even some sample problems. There are only six chapters and you can dip into the material in almost any order. The book has been published under a Creative Commons license so there is a PDF version that is freely available for download. If you’re like me, however, you’ll also spring for the paperback edition.

Street-Fighting Mathematics is a unique book that will reward you with hours of thought-provoking (and practical) reading.

 

References

Mahajan, S. (2010). Street-fighting mathematics: The art of educated guessing and opportunistic problem solving. Cambridge, MA: MIT Press.

#WeHateMath Blog Review – Math With Bad Drawings

As readers of this blog can probably guess, I’m very interested in math education. I teach undergraduate math and I’m always on the lookout for a fresh perspective. One such is the blog Math With Bad Drawings by Ben Orlin.

As the name suggests, it’s kind of hard to describe this blog with words. Each post is illustrated with photos of a whiteboard with really crude drawings (stick figures with giant heads and cartoon text bubbles) but together with the content it somehow becomes something quite sublime.

For example, his latest post is The Calculus of History, a contemplation on what sort of paper he’d assign to his calculus class. It begins with this line:

 

Forget the history of calculus. Write me a paper on the calculus of history.

 

Orlin then goes on a wonderful journey of pondering the implications of viewing history through a mathematical lens. Consider history as an integral, an infinite series, a solution to an enormous set of partial differential equations. It’s not a long piece but it’s poetry.

Not all posts are this philosophical. Some are downright funny. Consider The New Math Teacher (hint: he’s a TeleTubbie whose stomach plays Khan Academy videos), A mathematician is a machine for turning coffee into theorems (not to mention cookies into corollaries) and The Argue-About-Anything Club. He mixes these in with insights from his teaching experiences.

One in particular I love is 39 Ways to Love Math. Orlin went to a recent mathematics conference in Baltimore and put out papers, markers and the following invitation:

In one sheet of paper, capture why you love math.

Then he posted the results, creating a truly charming read as all of these very smart people try to communicate through words, pictures and sometimes equations their passion for mathematics.

So go over there and give his blog a read. Tell him I sent you. (He has no idea who I am, but I’m trying to start a thing.)

 

 

#WeHateMath Book Review – Good Math by Mark C. Chu-Carroll

Talking (or writing) about math in an interesting, engaging way is hard. It’s also something that is very important. Math is more important now than ever before but we haven’t changed the way we teach it in decades.

That’s why it’s a pleasure to find a book like Good Math by Mark C. Chu-Carroll. As a self-described ‘geeky kid’, Chu-Carroll took an interest in the work that his father, a physicist, would bring home from work. This started Chu-Carroll’s life-long love of math and inspired him to create the blog Good Math/Bad Math. Good Math (the book) is his attempt to bring his love of math to a wider audience.

One of the qualities that makes this book a delight is that you don’t need much more than high school algebra to follow along. (Naturally, the more math background you have, the more you’ll get out of it.) In addition, you don’t need to read the entire book in sequence. It’s designed for you to dip in at any point, find something that catches your eye and then move on. Some sections refer to other parts of the book but you can follow them or not as you wish. In addition, some sections include computer code if you want to extend yourself and experiment a little bit.

The writing is friendly and accessible, with plenty of diagrams and examples. The book is divided into six parts: Numbers, Funny Numbers, Writing Numbers, Logic, Sets and Mechanical Math. Chu-Carroll presents a broad look at the foundations of modern mathematics. I recommend this book to anyone who likes a good casual read that makes you smarter.

 

I’d also like to take a moment to give a shout-out to The Pragmatic Bookshelf. I’ve loved their stuff since reading The Pragmatic Programmer and they’ve only gotten better with their expansion into e-books. As you might expect, most of their publications are aimed at programmers but they have content aimed at beginners as well as books to help you ‘take care of your body and expand your mind’.


(Chu-Carroll, M. C. (2013). Good math: A geek’s guide to the beauty of numbers, logic, and computation. Dallas, TX: Pragmatic Programmers.)