Grumpy Thoughts, 4th Edition

• I happen to think it's bad when a Republican politician assaults a reporter. I also happen to think it's bad when leftwing activists respond to the imminent speech of a controversial guest by breaking windows, lighting fires, and bashing potential attendees with bike locks. Unfortunately, there are a shockingly high number of people out there who seem incapable of holding both thoughts in their heads simultaneously. It's not okay to hit people you don't like unless they hit you first. And no, words are not violence and not grounds for a beating. Jesus H. Christ!
• Just in case I haven't made it clear before, I think the whole concept of "cultural appropriation" is bullshit. Like many leftwing enthusiasms (see my previous post), it posits a zero-sum game where one does not exist. If I use African mythology in one of my stories, that doesn't stop an African writer from doing the same. If I decide to open a Mexican restaurant, that doesn't mean a Mexican can't open his own. In neither scenario have I actually "stolen" anything; in a free market economy, the African or the Mexican are still 100% free to sell the products of their own cultures and reap the benefits even if I too am competing in that market. On the other hand, if we seal off each individual ethnicity in its own hermetic bubble, Africans and Mexicans will lose customers and, consequently, needed profits -- which will surely make things worse, not better, for those minority groups. How do I know this? Well, when was the last time you've heard of a fully segregated, supposedly "self-sufficient" community becoming wealthy and enjoying a first-world standard of living?
• The people who insist that traditional math is racist and/or sexist are making this female math teacher scream -- and aren't helping. Seriously, they aren't. Math is the language of science, and science is the reason we have airplanes, dishwashers, antibiotics, and every other modern-day convenience that has granted us more free time and longer, healthier lives. Do you really want to lock minorities and women out of STEM and the possibly lucrative careers therein? Because if you stick members of "disadvantaged" groups in mathematics courses that waste time on social justice politics, you will render them unable to study science for the rest of their lives. Want true racial and gender equality? Teach the tables, not critical theory. (Please, please, please teach the tables. I'm begging you. If you don't, only rich kids with tutors and/or extremely competitive parents will learn them.)
• Lastly, a general note to the left: Your double standards suck, and frankly, a lot of people are tired of abiding by them. If you don't police your own people and quit that shit, more and more folks on the right are going to start punching back. Trust me: I know people who are itching for an excuse to start crunching "commie skulls." Don't give it to them; you won't like the result.

Making Math Stick

Hello, all! I'm back!

I'm not going to talk about the news today because, quite frankly, it has emotionally exhausted me. Besides, there are other people who've said what I would say anyway, so why fill the ether with something repetitive?

Instead, I'm going to touch on something a little more prosaic: the math wars.

I follow Barry Garelick (author of Letters from John Dewey/Letters from Huck Finn and Teaching Math in the 21st Century) and Katherine Beals (author of Raising a Left-Brain Child in a Right-Brain World) because my own experience has led me to sympathize with their instructivist point of view. From 2006 to 2012, my Virginia county's school board backed the reformist Investigations in Data, Number and Space as its elementary math curriculum, and from my vantage point, the result has been an overall decrease in conceptual understanding and fluency and a corresponding increase in calculator dependency. When an otherwise bright fifteen-year-old reveals - as one did the other day - that he's never learned his times tables, that, for me, raises a blazing red flag.

Of course, the reformists aren't wrong to note that students often skate through our still largely traditional high school math curricula without fully absorbing the material. I think, however, that they fundamentally misunderstand the reasons why this happens and consequently propose the wrong solutions. We don't need more time-consuming constructivist exercises in which students are asked to "discover" the principles of mathematics on their own; on the contrary, we just need to be smarter in how we deliver direct instruction.

In my county, high school math is taught in a very disjointed way. Individual topics are covered in isolation in brief "units" and then, for the most part, are never brought up again until it's time to take the state's End-of-Course assessments. Our standards documents do allude to the vital connections between concepts and courses, but as far as I can tell, only a few exceptional teachers are pointing out those vertical articulations to their students. This needs to change. In order for teens to "get" math, they need to see how it all fits together -- and they need regular cumulative assessments of their understanding to combat forgetting. A few class periods of discussion and a few nights of practice simply won't cut it for most.

It would also help if teachers routinely threw monkey-wrenches into the works to force teens into more abstract modes of thought. Our state's algebra curriculum does this already with linear equations when it demands students solve an equation like (ax-b)/c = d for x, but we could do that with other concepts as well. For example, after giving students a firm grounding in the quadratics unit, ratchet up the difficulty level: ask them to solve 2(x+3)²-(x+3)-6=0 for x and see what happens. And as for "explaining your reasoning," why not bring back the traditional two-column proof? 'Tis simpler and far more elegant than an undirected group discussion.

Lastly, I think we need to approach math education with a good heaping dose of humility and not allow perfection to be the enemy of the good. In truth, no math program is going to successfully educate everyone because no math program can fully control the extra-academic factors that influence math achievement. We can do our best to motivate our kids by challenging them and building their competence, but in the end, some students will remain unreceptive. We can work hard to battle the American perception that math is something only brilliant nerds can master, but some folks will refuse to be convinced. We can preach at-home reinforcement 'till we're blue in the face, but some parents - for a multitude of reasons - will not step up. This is our reality; it sucks, but we have to face up to it. Revolutionaries have gotten into trouble before for presuming to upend entire systems to fix their "flaws." Let's read their failures as cautionary tales and not let starry-eyed technocratic schemes short-circuit our wisdom.

Links of Interest: Cultural Appropriation, the Tao, and Math Education Myths

I'm going to be busy with this particular book today, so please enjoy the links I share below!

All Cultures Are Mine, David Marcus, The Federalist

"Nobody gets upset when Yo-Yo Ma plays the hell out of Bach. Nobody asks him to pay homage or royalties to white culture. As a result, white culture is open to everyone. It is the cultural lingua franca that binds together Americans’ understanding of the world.

The proponents of privilege theory and the concept of cultural appropriation seek to decentralize whiteness but, ironically, they are doing precisely the opposite. They are guaranteeing the central role that white culture plays by insisting it is the only culture that belongs to all of us. The price of this proprietary power play is steep. It encourages division and denies all of us the full flower of our shared human cultural history."

I couldn't agree more. Why are SJW's so eager to bring back racial segregation?

Life, Carbon, and the Tao, Tom Simon, Superversive SF

"In effect, the ruling classes of Westeros, and many others like them in recent fantasy, are crime syndicates in a world without law. But it is the law that makes the crime possible. The vast majority of the people need the Tao to do business with one another, and to make the whole society function. Part of that function is enforcing the Tao through laws, and resolving disputes between people when reciprocity breaks down. This is not a function that we ever see the epic gangsters performing. They are too busy planning murders and rebellions. Real criminal gangs are only able to function because someone else does the hard work of holding society together. They never exist as a ruling class; and when they do temporarily become rulers, as with the Barbary pirates of the eighteenth century, or the Somali warlords of our own time, the society breaks down, the people perish, and the profits of crime disappear. Without the Tao, there is no trust between people; without trust, nobody can work and create wealth; and without wealth, there is nobody for the criminals to rob."

A powerful critique of grimdark fantasy. As Glenn Reynolds might say, read the whole thing.

The Myth of "I'm Bad at Math", Miles Kimball & Noah Smith, The Atlantic

"Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence."

Yes: Average students can learn algebra. It does require a firm foundation in arithmetic that many of my students do not possess, but the correct response to this difficulty is to fix the gaps in their elementary education -- not to remove algebra from the high school curriculum entirely.

Plug and Chug on the Current SAT? I Don't Think So!

So I've been reading some of the pro-College Board propaganda regarding the SAT redesign, and where the math is concerned, I feel the writers in question must hail from some bizarre parallel universe. I've been preparing students for the SAT for nine years, and quite frankly, the claim that the current test favors plug-and-chug mathematics over "deep understanding" and "real world problem solving" (God save me from empty buzzwords!) simply does not jive with my own experience.

Clearly, many of these folks have never worked with actual teenagers in an actual classroom; otherwise, they'd know that the solutions to apparently "simple" SAT Math problems are frequently not evident to the average adolescent and often do require critical thought. For example, take this question:

A string is cut into 3 equal parts. These pieces are then cut into 4, 6 and 8 equal parts, respectively. If the resulting pieces all have integer lengths, what is the minimum length of the original string?

This seems simple, right? Indeed, solving it only requires basic middle-school math. But in order to complete this problem - and others like it - correctly, you have to understand that "cut into equal parts" is referring to division, and then you have to make the connection to least common multiple; in other words, you have to understand what division and the least common multiple are conceptually and be able to recognize how they'd be applied in unfamiliar contexts. And can my students do this? Nope! Most of the time, they get distracted by the odd surface features and fail to grok this question's deep structure.

Real world problem solving? Word problems are already a central feature of the current SAT, and most of them can't be "cleverly back-solved" -- at least, not efficiently. You will not do well if you don't know how to, among other things: 1) calculate percents and apply them in "authentic" contexts; 2) use the concept of the average to find a requested value; 3) write and solve linear equations based on information given in a text; 4) write and solve systems of linear equations, again based on information provided in a text; 5) read tables and graphs; 6) apply basic geometric theorems to complex diagrams; or 7) interpret key mathematical vocabulary and use the basic field properties of real numbers.

There are features of the new SAT that I like. I like, for instance, that they're adding a "no calculator" section, as I think today's students are far too calculator-dependent. But in advertising this redesign, let's not blatantly mischaracterize what it will replace. It is just not honest to pull out the rare odd logic question and argue that the entire old-style SAT is like that. I know this test backwards and forwards, and I can assure you that at least 95% of its content can be connected to the in-school math curriculum -- and no, students can't skate by without thinking carefully about what things mean.