#TheMelvinProject My Apology to Senator Al Melvin

Dear Senator Melvin:

In March of this year, I wrote a post making fun of you and your opinions on the Common Core Standards.

Based on recent events, however, I would like to take this opportunity to apologize.

Sure, you admitted that you hadn’t actually read the standards document and what little you did hear about it, you grossly misunderstood. Certainly it was this lack of understanding that led you to follow your personal beliefs and oppose implementing the standards in your state of Arizona.

However, at least you didn’t say that implementing Common Core would make students gay.

So you’ve got that going for you, anyway.

Sincerely,

Tom

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#WeHateMath Blog Review – Math Babe

I was directed to Math Babe by a link from Fawn Nguyen’s blog Finding Ways to Nguyen Students Over and it’s definitely a different kind of math blog than I’m used to reading. For one thing, blogmistress Cathy O’Neill was a former data scientist who co-authored the text Doing Data Science and before that she was a quant on Wall Street. (“Quants” or quantitative analysts are much sought after in the finance sector.)

Dr. O’Neill is currently the director of The Lede Program at the Columbia School of Journalism and she brings her unique perspective to her MathBabe blog. Primary topics of discussion include data science, statistics, finance, journalism and data modeling. Her writing style is friendly but not oversimplified. Her innate sense of humor always shines through, particularly with her regular feature Ask Aunt Pythia where she takes questions from readers in a mock advice column format (Pythia was the priestess at the Oracle of Delphi).

The questions aren’t restricted to finance wonkery, however. For example, this one from “Breasts of Oppression”:

Dear Aunt Pythia,

I am a female physics PhD student. A colleague once said to me that “If women want to be respected, they should not show cleavage.” What do you think?

Aunt Pythia’s answer?

Dear Breasts,

I’ve always thought quite the reverse. Namely, if men had boobs, they’d be showing them off all the time.

MathBabe has earned pride of place in my RSS feed so head on over there and tell her I sent you. (She has no idea who I am but, as I’ve mentioned, I’m trying to start a thing.)

#WeHateMath How To Start a Lecture on Probability

As my students filtered into the classroom, I was at my desk, idly shuffling a deck of playing cards. When class started, I got up and displayed the deck.

“I have here an ordinary deck of playing cards, which has not been tampered with in any way.”

I continued shuffling the deck and approached one of my students.

“Could you please examine this deck and confirm that it is indeed an ordinary deck, such as you might purchase in any store?”

She examined it, shook it, sniffed it, then handed it back. I approached another student.

“Would you please give this deck a good shuffle, just to make sure I haven’t pre-arranged the cards in any way?”

He grabbed the deck with a grin, cut it, shuffled it two or three times, then handed it back to me. I continued shuffling the deck and approached a third student.

“Please cut this deck to ensure that these cards are truly randomly organized.”

She did so and handed them back.

I held the deck over my head, pointed to a fourth student.

“Name a playing card, the first one that comes to your mind.”

“Seven of hearts”, she said.

“Seven of hearts!”, I announced to the class, “Now I want everyone to concentrate on the seven of hearts. Picture this card in as much detail as you can – color, texture, shape, until you feel you can almost touch it and keep this image in your mind.”

I held the deck in my left palm and covered the top with my right.

“While you are all concentrating on the card, I’m going to use the mental energies of the group to telekinetically move the seven of hearts up through the deck to the top. And I’m going to do this on the count of three. 1! 2! 3!”

I pulled the top card off of the deck and showed it to the class. Queen of diamonds.

“Huh. Do you have any idea how often this happens?”

I grinned.

“Tell you what. Why don’t we figure out exactly how often this happens?

Aaand we’re off to the whiteboard….

 

Teaching: one quarter preparation and three quarters live theater.

 

#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.

Euler11a

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 #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:

(Grades 11-12)

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 Project Euler 8 – Math Makes Everything Better

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

At first glance this appears to be arithmetic which, as we all know, is boring and mechanical and completely beneath us as humans. Well, actually, at first glance the part of our brains that does arithmetic (you know, the boring part) sees this awful number and just wants to shut down. Since I knew it had to be more than just arithmetic, I tucked it in the back of my mind to ferment a bit before tackling it again.

After a bit of thought, I can see the trick here. The problem statement refers to a 1000-digit number but we’re supposed to deal with individual sets of digits. So we can use math to make this more interesting (since math makes everything better) and simply regard this as a string of 1000 digits.

How does this help? First of all, any string of digits with a zero in it we can disregard. In fact, we can discard any ten consecutive digits that have a zero in the middle since any five digit sequence will multiply out to zero. So we look for digits with this pattern:

XXXX0XXXX

Let’s take another look at our number, clearing out digits within four positions of any zero:

731671765XXXX0XXXX19225119674426574742355349194934
969XXXX0XXXXXXX0XXXX23957XXXX0XXXXXX0XXXX478851843
858XXXX0XXXX12949495XXXX0XXXX95833XXXX0XX0XXXX
XXXX0XXXX4715852XXXX0X0XXXXXXXX0XXXX9522XXXX0XXXX7
668966XXXX0XXXX44523161731XXXX0X0XXXX1121722383113
622298934XXXX0X0XXXX336276614XXXX0XXXX486645238XXX
X0XXXX0XXXXXX0XXXXXXXX0XXXXX0XXXXX0XXXXXXX0XXX0XXXX
0XXXX27121883998XXXX0XXXX274XXXX0XXXXXX0XXX0XXXX6
6572XXXX00X0XXXX78XXXX0XXXXXXX0XXXX2XXXX0XXXX52243
52XXXX0XXXXXX0XXX0XXX0XXXX586XXXX0XXXX415722155397
5369781797784XXXX0XXXX51XXXX0XXXX69321978468622482
8397224137XXXX0XX0XXXX0XXXX0XXXX968652414XXXX00XXXX21XXXX0XXXX0XXXX
XX000XXXX2XXXX0XXXX41227588666881
164271714799244429XXXX0XXXX65674813919123162824586
17866458359124566529476545682848912883XXXX0XXX00XXXX
XXX0XXXXX0XXXX6321XXXX0XXX0XXXXXXX0XXXX6XXXX0X0X
0XXXXX0XXX0XXXX554443629XXXX0XXXX79927244XXXX0XXXX
XXXX0XXXXXX0XXXX9133875XXXX00XXX0XXXX99XXXX0XXXX0X
0XXXX116XXXX0XX0X0XXXXX00XXXXX983XXXX000XXXX5729725
716362695618XXXX0XXXX52XXXX00XXXXXXXX0XX0XXXXXXXX0

Okay, I’ve eliminated all strings of digits whose product will be zero so our new string of digits becomes:

73167176519225119674426574742355349194934969239574788518438581294949595833471852952276689664452316173111217223831136222989343362766144866452382712188399827466572785224352586415722155397536978179778451693219784686224828397224137968652142124122758866688116427171479924442965674813919123162824586178664583591245665294765456828489128836321655444362979927244913387599116983572972571636269561852

(I could have written a script to do this for me but pattern-matching is part of my evolution so I can do it myself without much trouble.)

This is a much more manageable number (still 389 digits long, though) but if we’re ultimately going to be doing arithmetic (and it looks like we’ll have to eventually) we have to think about having a machine do the work and that involves explaining the task to a machine in a way that it can understand. But this brings us to a question:

Do we really have to do any arithmetic at all?

A bit of thought tells us that we may be able to avoid arithmetic after all.  Here’s the logic:

Start scanning the string of digits and split off each set of five. For example, if our string was:

73167176

We would pull out the substrings:

73167

31671

16717

67176

Now, remember, I don’t really want to any arithmetic if I can help it so I do a bit of math thinking and rearrange the numbers in sorted order:

Original           Sorted

73167                77631

31671                76311

16717                77611

67176               77661

I can multiply numbers in any order I want so rearranging the digits won’t change the outcome. However, by sorting numerically, the number with the largest magnitude will automatically give me the largest product. 77661 is the largest number in my sequence here but let’s test my hypothesis just to check my thinking:

Original                     Sorted               Product

73167                          77631                882

31671                          76311                 126

16717                          77611                294

67176                         77661                 1764

Sorting has the added benefit of letting us eliminate strings that have the same digits (and thus the same product). So I only need to find the largest five digit number (after sorting) and then get the product of those five digits. I have now knocked my job down to doing a single multiplication and I bet I can get my computer to do even that little job for me if I’m feeling particularly lazy.

So I just whipped up a quick script to dump out 386 separate five digit strings of digits and sort each set of strings numerically. Then I copied and pasted the output into a spreadsheet and did a quick numerical sort to find the largest numerical quantity. Here is my result:

99972

It’s then a simple matter of using my hand-dandy calculator and determining the product, which is 10,206.

So we took a problem that looked like it would require almost 1000 arithmetic operations and knocked it down to a single calculation with just a bit of thought about the conditions of the problem.

If anyone is interested, I’ve posted my script here.

See, math makes everything better!

#WeHateMath What’s the Difference?

The new school term started yesterday and I’m teaching a course called College Mathematics. Here’s the course description, straight off of the syllabus:

 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 this is intended to be a course in functional numeracy, which can be defined as “here’s math you can actually use”. Based on my work on “We Hate Math”, I decided to approach this class in a very different way than I had previously. So my opening remarks (after going over the syllabus and class policies) was an expanded version of this post. The short version was that I was trying to convince them that math and arithmetic are not the same thing and when people think they hate math, what they actually hate is arithmetic (and that’s completely normal).

While I was doing my patter (teaching is one quarter preparation and three-quarters live theater), one of my students raised her hand and asked, “So what’s the difference between math and arithmetic?”

This question stopped me in my tracks. I considered for a moment and this is the explanation I gave her.

Let’s suppose I want to drive to the pet store. I have a choice of two routes to get there, like so:

If I take Belmont, I have a five mile drive but if I take Damon, I have an eight mile drive. I then asked her which route I should take.

“Belmont”, she said.

“And that’s exactly the answer that arithmetic will give you”, I said, “because arithmetic can only really tell you that five is less than eight. Math, on the other hand, knows about speed limits, traffic lights,…”

“Rush hour”, said another student.

Yet another student chimed in, “Road repair.”

“Right!”, I said,scribbling the list on the whiteboard, “so if we go back to our example and I tell you that Belmont has a twenty-five mile per hour speed limit and there are five traffic lights between my home and the pet store. Damon, on the other hand, has a forty-five mile-per-hour speed limit and there are only two traffic lights, one at either end of the route, which one would you take?”

“Damon”, she said.

“That’s the difference between math and arithmetic.”

There’s a reason why the phrase “Do the math” actually means “Think it through”.