#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 Project Euler 11 – Largest Product in a Grid

In the 20 X 20 grid below, four numbers along a diagonal line have been marked in red.

The product of these numbers is 26 63 78 14 = 1788696.

What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 2020 grid?

Yikes.

This is the first Project Euler problem that has personally offended me. That may seem strange but it’s because this is at it’s core an arithmetic problem, not math. At first glance, it seems similar to Euler problem 8, but it’s really a brute-force, grind-out-every-product-and-compare-them, ugly, arithmetic problem. So while I would have preferred a more elegant solution (a scalpel instead of a hammer, as it were), I went with the ugly one.

The perfect programming language for ugly, brute-force hammer solutions is C, so that’s what I used. (I considered Fortran, which is actually better for brute-force math and arithmetic problems but the last time I used it was in 1977).

So when I ground out the answer, here’s what I got:

`MacPro15:WeHateMath tsinclair\$ time ./Project_Euler11`
`70600674`

`real0m0.003s`
`user0m0.001s`
`sys0m0.001s`

So it only took about 3-thousandths of a second to get my answer, but I’m still annoyed.

#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 The Sniper’s Tale

I’d like to tell you a story about a man named Rob Furlong. Mr. Furlong is a Canadian, formerly of Her Majesty’s 3rd Battallion (Princess Patricia’s Canadian Light Infantry) Furlong’s job with the Canadian military was one that most of us (okay, mostly us guys) would think was kind of cool.

Rob Furlong was a sniper.

Well, not just a sniper. It turns out that Furlong was THE sniper. In 2002, he set a record for the longest confirmed combat kill, at 2,657 yards (2,430 meters). Coincidentally (or not), the previous record holder, Master Corporal Aron Perry, was on Furlong’s team. (Must be something in the poutine.) By the way, Furlong’s record was broken in 2009 by British sniper Craig Harrison. Perhaps afternoon tea trumps poutine.

What does this have to do with math? Well, if we take our education about snipers from popular culture, Furlong and his companions are some kind of Jedi Master/Zen Monk types who rely on mystical instincts to hold a stick very steadily for a long time.

Not so much.

Consider gravity. Over 2,657 yards, Furlong knew his bullet was going to drop almost 300 feet so he had to aim high. Wind resistance? Check, adjust for that. By the way, what’s the temperature out? Turns out that gunpowder burns at different rates at different temperatures. Speaking of air, how high above sea level are we? I only ask because the bullet travels farther in the thinner air at higher altitudes. Also, what direction are you facing? If your target is to the east, you’ll have to aim a bit lower, due to the Coriolis Effect.

In other words, Rob Furlong is a highly trained mathematician who can kill you from over one and a half miles away.

#WeHateMath #TheMelvinProject Common Core Conspiracies

There’s a awful lot of hoo-ha going on about the Common Core Standards for Math and English. A lot of people, rightly or otherwise, seem pretty upset.

I thought I’d take a look at some of their complaints and see if I could help. (I’m caring nurturer.)

First up is Conservative Teachers of America. I had never heard of this organization so I took a look at their About page to see if they had a mission statement or something.

It was blank. This is never a good sign.

I searched on “Common Core” and pulled up two entries. Just for giggles, I also looked for posts tagged “Common Core” and filed under “National Standards: Common Core” and both came up blank, even though the two posts I initially found are tagged as “Common Core”.

Fine. Moving on.

Okay, both of the posts I found are also coming up blank. This has gone beyond comedy at this point. Is it some kind of post-modern deconstruction thing that I’m not getting? Okay, if they don’t want me to read their posts, I’ll just look somewhere else.

The Daily Caller – Common Core again threatens to make little kids pee their pants – Apparently bathroom breaks are strictly monitored and measured by our new Common Core Overlords. Or maybe it’s just some jerk-face petty bureaucrat at the single Chicago school where this rule was enacted. We may never know.

The Blaze – Dictatorship 101 – Apparently the Education Overlords are threatening violence against free-thinking citizens who dare to speak out against injustice and…um…I don’t know, algebra?. Oh, wait, it was just some guy being a jerk and disrupting a public forum before being asked to leave by security. Darn it, I was hoping for something dramatic, like Arne Duncan tearing up the Constitution, wiping himself with it and then setting it on fire.

Okay, this one is promising. Town Hall – Common Core Teaches Kids to Hate the Constitution. Now we’re getting somewhere! Let me check those dastardly Language Arts standards:

Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance (including The Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, and Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical features.

Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses).

I seem to be missing the whole ‘make sure the kids learn to hate our founding documents’ thing. Clearly I’m a bit rusty in my ‘reading for understanding’ skills. Well spotted, Townhall guy!

Okay, this is getting silly. As I’ve said before, there are legitimate concerns with how Common Core is being rolled out but these kinds of stories just strengthen the case for improved education standards.

“A system of general instruction, which shall reach every description of our citizens from the richest to the poorest, as it was the earliest, so will it be the latest, of all the public concerns in which I shall permit myself to take an interest.”  – Thomas Jefferson, 1818.

#WeHateMath #TheMelvinProject – Common Core Math Testing

Last week, Stephen Colbert did a bit on the Common Core called “Common Core Confusion”, which was both funny and painful to watch (like most good satire). He took a couple of questions from a Common Core math test and riffed on how weird and confusing they were. He was right, they were awkwardly phrased and asked for odd input from the student. (One of them told the student to write their friend a letter and explain the math problem to them.)

“Great!”, I thought to myself, “I’ve got a topic for the blog, ready-made!”  All I had to do was dig up some of those goofy questions and talk about them and offer perspective and then something something freedom + comedy. So I happened across a site that offered Common Core test prep and thought I had it made.

There was only one problem.

I actually read the questions and they were nothing like the ones that were presented on The Colbert Report. In fact, they were perfectly reasonable and written in a clear, understandable way. For example, this one from Grade 6 Mathematics:

 The balance on your savings account is -50, which means that you have \$50 of debt. A monthly charge increases the amount of your debt. Which of the following could be your new balance? 60 40 -40 -60

It turns out that the goofy questions that Colbert cited (and the ones floating around the Internet) are not Common Core questions at all. In fact, the Common Core standards do NOT specify how the subjects are taught. Every school district (or state or whatever appropriate local education body) is free to present the material in any way that they feel works best for their students. In fact, this is stated right on the front page of the standards document:

While the standards set grade-specific goals, they do not define how the standards should be taught or which materials should be used to support students. States and districts recognize that there will need to be a range of supports in place to ensure that all students, including those with special needs and English language learners, can master the standards. It is up to the states to define the full range of supports appropriate for these students.

So the questions that have been going viral all over the Internet are actually the result of really bad curriculum designers.

Now I’ve worked on curriculum committees. I’ve done course design. It’s a lot of work and you really don’t know if you’ve got it right until you’ve presented it to your students and get their feedback, both through their comments and how well they end up understanding the material.

The point (and I think I have one here somewhere) is that bad teachers are not the fault of Common Core. Bad course designers are not the fault of Common Core. Scam artists who suck up taxpayer dollars and deliver crappy materials and when caught, point fingers at Common Core have been around since before there was Common Core.

Yes, there are legitimate concerns with Common Core (and not a few illegitimate, insane ones). But what this recent brouhaha tells me is that national standards for primary education is just the beginning.

“I know no safe depository of the ultimate powers of the society, but the people themselves: and if we think them not enlightened enough to exercise their controul (sic) with a wholsome (sic) discretion, the remedy is, not to take it from them, but to inform their discretion by education. this is the true corrective of abuses of constitutional power.”