Stupid “math” tricks

I was a high school math teacher. A former student asked me my opinion on a social media post asking what

8 ÷ 2 (1 + 3)

is, with the common answers being 16 and 1.

I’m sort of a “math person.” Not Phd math solving a Clay Institute math prize get a million dollars math person, but I can do reasonably well through differential equations and teach physics for part of my living. I also write computer code for a majority of a living. So my answer to what that is: It’s a context free meaningless computation, written poorly.

It begs the questions — why are you adding one and three? What do they model? Are there any units on those values?

What’s Math

If we have the concept of counting, and values of one, three, and four, along with the concept of addition, then one plus three equals four, regardless of whether we use words or 1 + 3 = 4 or uno más tres es igual a cuatro.1 That’s math, it’s always going to be true. That’s the way the universe was made.

1. The equation in Spanish, according to google translate.

What’s not Math

Writing the calculation with the plus sign between the numbers is a convention called infix, and it’s what normal people expect.

Infix isn’t the only choice — the postfix expression of that equation would be:

8, 2, 1, 3, +, *, ÷

which means put the four numbers in a pile (a “stack”). Then replace the last two with their sum, making the stack 8,2,4. Next multiply the last two, yielding 8, 8, then do the division to get 1. Calculators that work that way are called Reverse Polish notation (RPN) and I still own (and use) the HP-11C I bought in 1979 or 80.

HP 11C, shinier than mine

So, back to the original question — because of the ambiguity of infix, there’s a generally accepted convention for what to do first, called order of operations. For a programming language, it can run fifteen levels deep (computer nerd link). In the US, this often taught as “PEMDAS.” 2 But this is just a convention, followed sometimes: according Wikipedia, different calculators might calculate the expression differently.

2I hate PEMDAS, but that’s a separate blog entry.

Back to math

Adding some trim

I’m replacing some trim on a cabinet like so:

The wood is $8 / ft, but it’s twice the width I need, so I can cut it in half. Let’s write the equation:

Cost of trim

So now I have some units and, because my goal is to communicate clearly, even if just to myself, I’ve written the first division as a vertical fraction rather than the linear form. This makes it obvious we’re going to end with $16 of trim.

Friends for pizza

So you and your partner are going to invite 3 couples over for pizza. A pie has 8 slices. How many will each person get?

Pizza per person

So now I have some units/labels and, again, the layout of the equation makes the computation clear: each person gets 1 piece.

Math education and social media

Unfortunately, math is too often “taught” as a set of arbitrary rules to memorize than what it is: a cool and fun recognize of patterns in the universe. Addition: beauty. “PEMDAS:” bleh.

Then we get social media posts which really have nothing to do with math, and are just math abuse so some people can feel superior to others because they can memorize some rules better than others. What I hope the two examples above show is this: If you’re actually doing math — solving problems with a context — then the order of operations should just make sense. If you take the effort to write equations clearly, then the reader doesn’t have to rely on some memorized rules to understand what you mean.


8 ÷ 2 (1 + 3)

then sneering if someone doesn’t come up 16 doesn’t make you “smart.” It makes you a jerk.

Common core math isn’t that stupid

People who think common core math is “stupid” are, in fact, …. misinformed.

For example, this guy:

makes fun of a teacher explaining in great detail a method of multiplying 35 x 12 by showing how much quicker it is to do longhand.

So what. It’s 2019. Use a calculator. Ask Siri or Alexa, or use your Google search bar to come up with 420.

The students of the “stupid” teacher are learning:

  • Notions of place value
  • Distributive property of multiplication
  • Algebra

Algebra? Where’s the algebra, you might wonder. Simple. A student who knows how to multiply 35 * 12 as (30 + 5) * (10 + 2) isn’t going going to have trouble multiplying (30 + x) * (10 + y). The “quick” student who is taught multiplication is a mechanical sequence of steps may, or may not, grok the algebra, depending on how much insight they’ve picked up along the way.

Of course students shouldn’t be taught to always do it the long way — just enough until they get the concept.

Trouble with the core

Is common core math perfect? No. It started well with good intentions — get smart math people to focus on which concepts (not techniques) are important to life long understanding of math, with the idea that if students learn them initially, it won’t require relearning later.

The difficulty is the concepts then went to textbook and curriculum companies, who too often boiled them down to a set of mechanical steps (“first draw a box”) that’s not much better than the pen and pencil method it’s replacing. Assessment is difficult — hard to see what’s in a kid’s brain — so evaluation becomes whether they do the unimportant stuff (drawing boxes) “correctly.” Naturally, students who get the idea will become frustrated when force to repeat it overmuch.

There’s also the human element. We expect our elementary teachers to be superhuman — to handle the difficult emotional management of all sorts of kids, deal with the nightmare of educational bureaucracy — because of course our common core math learning must be documented, and be subject matter experts on myriad subjects. It’s not a realistic expectation. I’m not trying to diss elementary school teachers here, just the system that dumps so many expectations on them.

Please don’t follow

On Facebook, sometimes you’ll see comments that say Follow or following, which allow the poster to be notified on new comments. There’s actually a built in way of doing this, which just takes two clicks.

Find the three dots to the right of the post, and then click Turn on notifications from this post.

This will allow you to be notified of changes and make it easier for allow of us to follow the flow of conversation.

Socialized medicine

So apparently, according a recent Facebook meme, I’m not a “decent fucking human being” because I’m not “on board with free health care.”

I’m also not on board with unicorns. There ain’t no such thing as a free lunch, and there’s no such thing as “free health care.”

Socialized medicine “works” by underpaying doctors and rationing care. A private health care provider or insurance company that continually under performs loses customers to competitors. Of course private providers try to cut costs, but it’s a balancing act — performing too poorly loses as much money as not controlling costs. When government is the payer, priority shifts to maintaining costs, not providing care, and fraud is inevitable: “An array of outside contractors used by the government is poorly managed, rife with conflicts of interest and vulnerable to political winds, according to interviews with current and former government officials, contractors and experts inside and outside of the administration.” (NY Times)



United Kingdom:

“NHS delays leave thousands facing long wait for wheelchairs”

Political childishness

So this week the main concerns of politically oriented social media appear to be:

  • How a woman sat on a couch (left wing outrage).
  • Who sat when during a speech (right wing outrage).

To which I must inquire: seriously?

Let’s see what’s going on that’s kind of important:

  • Multiple aggressive nations, with crazy leaders who wish us harm and the ones without nuclear weapons working hard to get them.
  • We are a nation without a real immigration policy.
  • We don’t know how to pay for health care nationwide.
  • We don’t know how to put our working population to work.

What becomes clear is these outrages aren’t about what’s good for the country, but some sort of political counting coup, good — for now — for stirring up people who agree with you but not changing the hearts and minds of anyone else.

There was a time when the system that allowed a minority party to push the majority to the center was called checks and balances. Now it’s “obstructionism” which is the political equivalent of “Waah, I can’t get my own way!”

Every group of people has wacko outliers that are going to say or do stupid stuff. They don’t actually represent the group. So maybe we could stop supporting the latest outrage and encourage our politicians to govern the old fashioned way — respect, discussion, compromise. You know, the boring stuff that has little entertainment value but is actually good for the country.

Why DeVos is education secretary

Some of my liberal / progressive friends have expressed displeasure and / or surprise that Betsy DeVos was confirmed as Secretary of Education. In the perhaps overly optimistic hope that there is still a place for civil political discourse in 2017, I’ll explain it.

First off all, there was a time when the US Senate valued consensus and required 60 votes to confirm a cabinet level appointment. But recently the majority Senate leader changed the rules, after changing the rule that such a change would require a two thirds vote. I’m talking about former Democratic majority leader Harry Reid, who pulled this stunt in 2013. Current majority leader Mitch McConnell was against the move: It’s a sad day in the history of the Senate. So if you’re upset the Rs are able to confirm cabinet level positions without any Democratic support, you can thank Harry Reid.

Secondly — yes, I’ve seen the graphs of DeVos’s political contributions. What’s important to understand is that for years, politically the national teacher unions have essentially been wholly owned subsidiary of the Democratic party, donating millions. Middle America likes teachers — that doesn’t mean it likes teacher unions. An August 2016 Rasmussen poll found only 20% of likely voters think unions do a good job for there members and 50% think they have too much political influence. Union membership remains high only because of mandatory membership rules in many states ; when workers are given a choice in right to work states, enrollment drops … since it’s hard to find anything resembling non-biased (left or right) reporting on that, here’s the google news results. I did find this analysis by a human resources website interesting. By shilling for the losing presidential candidate, and interjecting itself in non educational political topics [1] [2], the National Education Association both alienates part of the public and plays a high stakes, “all in” political game; a good strategy if and only if your picks win. They lost: why would anyone expect anything but an anti-teacher union stance from the (current) powers that be??

Thirdly, because Americans went to school, they think they understand schools. (I did until I started working in them.) The idea of choice has powerful appeal: one current US Senator, in a book cowritten with their daughter, wrote: Fully funded vouchers would relieve parents from the terrible choice of leaving their kids in lousy schools or bankrupting themselves to escape those schools, and that was Democratic Elizabeth Warren.

Of course vouchers are good for kids with parents with the skill set to utilize them, but maybe not so good for society at large; like many topics involving humans, where gold standard scientific processes can’t be applied, research and opinions vary. Nonetheless Trump ran on pro-voucher platform and he won.

Finally — don’t blame Mike Pence for his tie breaking vote. For all the reasons I’ve outlined above DeVos was essentially in as soon as Trump nominated here. Only two Rs opposed, Lisa Murkowski, who owed public sector unions for her 2010 victory as a write in, and Susan Collins from blue state Maine who may be considering a run for governor. McConnell can count — it didn’t hurt anything for two R Senators to oppose, so it’s not that big a deal from the Republican view of things.


Stupid research

So today’s copy of the Journal Inquirer (JI) has the provocative headline: Students mine data to find where unfaithful husbands live: Fairfield County. Well it’s actually a Toledo Blade story — the Connecticut based JI just tacked the “Fairfield County” on the end.

So these kids at University of Toledo use data from hacked Ashley Madison website to determine who cheats most often, noting that “Metropolitan areas with some of the lowest subscription rates were in poor Appalachian and southern locations, strengthening the conclusion that affluence is linked to this kind of online adultery.” The story goes on to note that “The Fairfield County area also topped the list of metro areas in spending rates, doling out $1,127 on the site per 1,000 people.”

Huh. Of course this fits with the usual liberal narrative that rich people are inherently evil and poor people inherently virtuous ….

One thousand, one hundred twenty dollars ? And that’s just on the website — presumably there are other costs in cheating. Or maybe — just maybe — poor people have cheaper ways to cheat. Because the Internet is a tiny place and Ashley Madison is the only way to cheat …



My fitness journey

A while back I posted on social media that I had lost 45 pounds this year. A friend asked “how” and I said I’d get back to him, so here goes.

The brief answer is a combination of motivation, diet, really good luck, and exercise.


Out of respect for the privacy of others, I’m not going go into complete detail of all the factors motivating me, but a key one was the birth of a granddaughter this year.  My focus shifted from a vague “oh, I should get in shape someday” to “I really want to be around decades from now.” My own daughter never really knew her paternal grandfather, and I don’t want that for me granddaughter. I know there are no guarantees, but I wanted to tilt the odds.

Exercise, the beginning

A few years ago, with an obese Body Mass Index (BMI) of 30.7 and arthritis in the right hip, getting up was a 20 minute evolution which consisted of groaning my way out of bed, urinating, grabbing coffee, and sitting while the pain subsided to bearable. I knew I had to do something, had heard positive things about yoga from the daughter, and saw a group on for a place near work. First class March 4, 2013: I liked it, and I liked the “beginner / gentle / slow” instructors. Flexibility increased, pain diminished, and I was able to lose about ten pounds without thinking about it too much.

Diet, part I

On a warm beach last January the wife and I had time to relax from the life / work hamster wheel and admit to each other we weren’t really happy with the shape we were in. I had a good idea, exploiting our own personal proclivities — we’re competitive. We made a bet with each about losing weight. In order to keep it safe and reasonable and challenging, we settled on losing twenty pounds in six weeks. She won. I “lost” — only making it down eighteen. But it got the ball rolling. The diet was basic nutrition stuff — more veggies, less sugar and sweets, more awareness.

Good fortune

A new routine

Due to the unfortunate closing of my first yoga studio, one of my fav instructors started teaching at a hybrid Pilates / Strength Training / Yoga studio, Total Body Pilates and Yoga. The owner and primary coach attended the first several yoga sessions, and, although she seemed inhumanly flexible in yoga class and the online workout descriptions kind of scary, she convinced me to give it a try.  A combo of yoga-ish stretching, weight training, and Pilates apparatus strength, flexibility and balance, a continual variety of exercises –not the same thing every day — and a small core of fellow members who turned out to be fun people to workout with made going relaxing and fun.

I had had a decades old misperception I should only work out every other day — a chance conversation with a friend to be on a Saturday morning in the parking lot clued me in that the studio programming allows daily workouts, so I started going roughly six days a week.

Healthy choices

A shift in work brought me to working in the main building complex at UConn Health; the main cafeteria includes both all the decadent stuff a soul could want (pizza, fries, burgers) and protein rich main dishes (if you leave the sauce off), nicely done veggies and salads. Carb loaded breakfast sandwiches from coffee shops were replaced with freshly made omelets or oatmeal with fruit.

Between the workouts, and better breakfasts and lunches, after a couple months, the change started to become noticeable.

Diet, Part II

September brought a studio challenge to try something called “The Whole Life Challenge,” a combination of sound and fad diet choices, a tracking / game playing / social media site and lifestyle choices. The lifestyle stuff was mostly covered by existing workout habits. The main things I ended up taking away from it were:

  • drink lots of water. A full stomach displaces perceived hunger and thirst for coffee and the like. I guess there’s some calorie consumption heating it, too.
  • you don’t need that many carbs.
  • sparkling water (mainly Pellegrino) adds a little taste and makes a nice substitute for my previous glass a drink moderate drinking which may, or may not be healthy, depending on which survey you believe; regardless not drinking is definitely less calories.
  • cheese should be an occasional flavor treat (like zero to one servings a day), rather than a staple.


Have a grand child. Workout, including strength training, almost daily (whatever works for you). Eat healthy — sort of paleo without being whacky about it. Drink lots water, avoid stress, get enough sleep.