Common Core math

So, Evan (my 2nd grader) had a pretty interesting math homework problem last week.  It presented a math problem and then said a student had made a specific error in solving the problem, i.e., 250-90=140 or something like that, and the homework was to get the actual right answer and explain what the hypothetical student had done wrong.  Common Core math(!!) I thought.  Not just applying an algorithm to solving a subtraction problem, but rather showing that you understand how math/subtraction actually work.  Cool.  Now, in this case, neither Evan, nor myself, nor my wife could quite figure out why the mistake was made, but I really appreciated that a seemingly simple math problem was calling for higher order thinking.

Earlier this week, I came across this nice blog post from a math teacher defending this kind of common core math from right-wing attacks that really puts things in perspective (and I think would have helped me figure out the particular homework problem):

Over the past week, I’ve seen this image multiple times on Facebook and elsewhere, a supposed denunciation of the Common Core version of math that kids are now learning:

That picture is especially popular on conservatives’ Facebook walls… and I’m sure one of your relatives has said something about it, too.

On the surface, it seems ridiculous. The top makes sense; the bottom is silly; screw you, Common Core!

Except that the top doesn’t make sense, the bottom does, and the connection to Common Core is completely misunderstood. (Says this math teacher.)

Here’s what’s going on: The top is how most of us learned subtraction. I’m sure your teachers taught you what was going on mathematically, but do you really remember what they said? Probably not. For us, it’s just an algorithm. You can do it without thinking. You hope there’s no “borrowing” of numbers involved, but if you had to do it by hand, you could probably pull it off.

The problem with that method is that if I ask students to explain why it works, they’d have a really hard time explaining it to me. They might be able to do the computation, but they don’t get the math behind it. For some people, that’s fine. For math teachers, that’s a problem because it means a lot of students won’t be able to grasp other math concepts in the future because they never really developed “number sense.”

That’s where the bottom solution comes into play. I admit it’s totally confusing but here’s what it’s saying:

If you want to subtract 12 from 32, there’s a better way to think about it. Forget the algorithm. Instead, count up from 12 to an “easier” number like 15. (You’ve gone up 3.) Then, go up to 20. (You’ve gone up another 5.) Then jump to 30. (Another 10). Then, finally, to 32. (Another 2.)

I know. That’s still ridiculous. Well, consider this: Suppose you buy coffee and it costs $4.30 but all you have is a $20 bill. How much change should the barista give you back? (Assume for a second the register is broken.)

You sure as hell aren’t going to get out a sheet of paper and do this:

Instead, you’d just figure it out this way: It’d take 70 cents to get to $5… and another $15 to get to $20… so you should get back $15.70.

That’s it. That’s the sort of math most of us do on a regular basis and it’s exactly the sort of thinking the “new” way in the picture is attempting to explain. Granted that was an *awful* example to use, but that’s the idea. If students can get a handle on thinking this way instead of just plugging numbers into a formula, the thinking goes, it’ll make other math skills much easier to understand.

Cool.  I really liked that explanation.  The Tea Party, apparently, wants our kids to be drones who can simply apply formulas they’ve been given.  Personally, I’d prefer my kids actually understand what they are doing and be able to think creatively with that knowledge.  To each his own, I suppose.

Photo of the day

Pretty dramatic Telegraph gallery of the recent mudslide:

The search for survivors of Saturday's deadly mudslide grew Monday to include scores of people who were still unaccounted for as the death toll from the wall of trees, rocks and debris that swept through the rural community rose to at least 14 near Oso, Washington
Authorities believe the slide was caused by recent heavy rains that made the terrain unstablePicture: Office of the Governor via Getty Images

Corporations are people, too (no, really)

So, the big Hobby Lobby case was argued yesterday, and Dahlia Lithwick suggests the good guys are going to lose (let’s just be clear here, at least four justices who hate the ACA on political grounds will find constitutional grounds– no matter how tenuous– to strike at the law).  It was a couple of weeks ago, but it reminded me of the most interesting piece I read on the matter, from Constitutional law professor Adam Winkler:

This conception of corporate personhood has profound and beneficial economic consequences. It means that the obligations the law imposes on the corporation, such as liability for harms caused by the firm’s operations, are not generally extended to the shareholders. Limited liability protects the owners’ personal assets, which ordinarily can’t be taken to pay the debts of the corporation. This creates incentives for investment, promotes entrepreneurial activity, and encourages corporate managers to take the risks necessary for growth and innovation. That’s why the Supreme Court, in business cases, has held that “incorporation’s basic purpose is to create a legally distinct entity, with legal rights, obligations, powers, and privileges different from those of the natural individuals who created it, who own it, or whom it employs.” …

In recent constitutional law cases, however, the justices seem to have forgotten this basic principle of corporate law. In Citizens United, the court effectively held thatcorporations enjoyed the same free speech rights as ordinary individuals. Contrary to popular belief, however, the court did not base that holding on the idea that corporations are people. Instead, the justices said that corporations are “associations of citizens”—and those citizens who make up the corporation have constitutional rights…

In the Hobby Lobby case, the owners of the craft store chain make the same mistake. The owners claim that their personal religious beliefs would be offended if they have to provide certain forms of birth control coverage to employees. Yet Hobby Lobby’s owners aren’t required by the law to do anything. The legal duty falls on Hobby Lobby, the company, not its owners. If Hobby Lobby fails to provide the required insurance, the company, not the owners, is responsible...

Hobby Lobby should only have the rights of legal personhood that are essential for its operations… Hobby Lobby is a for-profit corporation whose business doesn’t require it to have religious freedom…

Religious liberty is certainly appropriate for some not-for-profit corporations, like churches or nonprofits with a religious mission. If Hobby Lobby’s owners wanted to form such an organization, there was a convenient and readily available option: They could have incorporated as a nonprofit. They wouldn’t be able to make the same kind of money, but they’d have a corporation with an explicitly religious mission. And under the Affordable Care Act, they’d be exempted from the birth control requirement.  

Hobby Lobby’s owners, however, formed a business corporation. By asking the Supreme Court to let them enjoy all the protections of this corporate form, but not all of its duties, Hobby Lobby’s owners want to have their corporate cake and eat it, too.  [emphases mine]

As Lithwick states to find for Hobby Lobby has some potentially insidious consequences:

The rights of millions of women to preventive health care and workplace equality elicit almost no sign of sympathy or solicitude from the right wing of the bench today. Nor does the possibility that religious conscience objections may soon swallow up the civil rights laws protecting gay workers, women, and other minorities. Religious freedom trumps because we’re “only” talking about birth control.

Something tells me Alito, Scalia, et al., would not be quite so concerned with “religious freedom” it it were about liberal, rather than conservative policy preferences.

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