The War on Structure

Here is a partial list of subjects that have been seemingly expunged from primary and high school in the fairly short time since I was in those institutions:
  1. Phonics
  2. Multiplication tables
  3. Algorithms for addition, multiplication, long division, etc.
  4. Grammar
  5. Logic
What do all of these topics (and more) have in common? They are all structure-oriented. They require attention and focus to a fairly small number of rules about the proper order and organization of written symbols. The are all detail-oriented. To the extent that American education-school philosophy is to disparage such issues under a "holistic" approach, I reject that as terribly flawed and respond that, "you need both!".

It's particularly aggravating that several of the issues cut to the very heart of why our writing systems in numbers and words are originally designed as they were: to support simple adding, multiplying, and division procedures by hand; to easily convert spoken sounds to writing by way of phonics. Lose sight of that, and you lose the very essence of those systems of writing.

So doesn't this explain why remedial algebra is the single-most devastating course in the university curriculum, preventing about half of all community college students from ever graduating? After all, it's now the first time in their academic career that students are finally forced, inescapably, it attend to the detail and structure of things. And they've been set up for failure; when our students cannot actually parse the structure of a sentence (don't know what a verb is, what clause connects to what, how to diagram a sentence, etc.), then it's impossible for them to translate word/application problems to math (to say nothing of actually solving them). And it's very sad and heart-wrenching to watch.

What is particularly galling about all this is that this has occurred precisely at the same time as the world around has become more driven by machines, computers, technology, and an increasingly technocratic government structure. All of our young people carry computing devices at all times as a very intimate part of their lifestyle, but their understanding is at about the same level as a cargo-cult. This is why "STEM" academic careers are held out as some kind of bizarre alien life-form that the normals cannot hope or imagine crossing into. To the extent that we have removed the capacity to understand structure from our students, we are making them unavoidably victims of the highly technocratic society that controls their lives, without any hope of understanding it.

Obviously this painful disconnect between prior classes and the introductory algebra course cannot last -- and all signs are that, long term, the algebra class will likely be removed as a requirement even for a college degree (my prediction). And thus a mile-high iron wall will be put in place between the unlearned masses and the elite who are educated in the "real deal" of structure, mathematics, language, and computer skills.


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Online Remedial Courses Considered Harmful

Online remedial courses are inherently absurd. Even though this is UDacity's (for example) great-white-hope moment, as it has begun offering elementary algebra courses for college acceptance in California (link), it practically beggars the mind that this will help the crushing wave of need that students in such courses evidence.

The reason why is that everything that online courses do well is precisely the opposite of what remedial students need. We know that online courses require a higher level of discipline, dedication, and self-starter initiative than in-person courses do. Online courses are inherently tougher to follow than live courses. You also need a certain technical proficiency just to interface with the platform (and occasionally troubleshoot problems). This is all well and good for high-functioning academic-types who fundamentally love to learn on their own.

But our remedial students have none of that. One of the first overwhelming problems is that they don't have self-discipline in schedule or study habits -- frequently helping with this is itself part of the remedial math course. And they don't like the subject; surveys routinely show an overwhelming and long-seated hatred for the discipline; often a large proportion of a remedial class doesn't show up for the very first class. Minor technical problems will routinely frustrate them and throw them off completely.

Frankly, what the remedial student needs is clear -- if we were serious about getting these students educated, then they would need more individual, one-on-one interaction to address their deep level of need (not less). They need a personal touch to get them over their often pathological resistance for the technical subject matter. They need personal tutors -- but the cultural structure is not one that is interested in paying for that.

Here is a quote, based on the reform experience at a community college near Philadelphia, as they focused effort on the classes with the highest failure rates throughout their college, and in many cases improved their statistics by as much as half (based on interventions such monitoring no-shows on the first day, requiring early evidence of class participation, academic probation communication procedures, etc.):
In some cases, Hayden said, the college's analysis has led officials to believe that some courses were being offered in inappropriate formats. For instance, several of the highest failure rates were in online developmental courses (around 60 percent) -- and various reforms didn't budge those numbers. So the college has ended online remedial education. "The failure rates were so high that it seemed almost unethical to offer the option," Hayden said. (link)

This quote inspired me to write this post tonight. "Unethical to offer the option" (for online remedial education) seems about right. We'll see how quickly MOOCs such as UDacity, and those partnering, paying, and linking their reputation with them, re-learn this lesson.


Facebook Removes Downloads of Your Posts

This post isn't exactly about math, but it is technical in nature, so I figured I'd get it out there. As part of my regular data-backup process, I routinely download my information archives from whatever online presences I can, such as Facebook (which I've been on since early 2010), Google Blogger (this blog you're reading right now), etc. Obviously on Facebook the thing that I'm most interested in is what I actually write, which are usually called "wall posts" (as opposed to photos or media, which I retain locally anyway). Once in a while I've found it very useful to pull up the downloaded posts file and search it for some particular bit of info, contact, or date. What I seem to have discovered is that sometime in the last few months, Facebook silently and completely removed our ability to download that "wall posts" information.

This first dawned on me the other day when I used the Facebook "Download Info" process (Gear icon > Account Settings > Download a copy of your Facebook data), and tried to search for a particular post. Well, the normal file was just entirely missing. You can see the difference below in the downloaded archive from March 2013 versus the download from June 2013. The file "wall.html" -- which actually contains all of my posts and is by far the largest data file in the old archive -- is missing from the new archive.

Now, initially I thought this was some kind of temporary glitch. (In the three years that I've been on Facebook, occasionally  the "wall.html" file has mistakenly contained just a few days worth of posts. Or for several months in 2012-2013 the download seemed to just fail completely any time I tried to use it.) But if I now go to the top-level "index.html" of the download, then I find that the reference-link to the wall posts has also been removed there ("Wall" used to be the second link but is now missing; before-and-after shots below):

So at this point I poked around a bit on Facebook's information pages, and landed on the page where they supposedly tell you what information is included in this and other resources ("Accessing Your Facebook Info", which I find at this link). This page currently describes three repositories of information: (1) "Downloaded Info", the archive which I've described above, (2) "Expanded Archive", another download which includes more transaction and login information, and (3) "Activity Log", which is an online-only manipulation of the Facebook timeline (not part of any download). What I see here is that "Your Posts" is now categorized under "Activity Log" (and note that this entry is also out of alphabetical order, possibly evidence of some change, and making it a bit harder to find in the list):

So what this means is that Your Posts, the things you've actually written on Facebook, are no longer included in the "Downloaded Info" which allegedly includes all of your info (and did from at least 2010-2013). The posts are not in the "Expanded Archive", either (I checked to be sure... it has dozens of files including Ad Clicks, Apps, Facial Recognition Data, Poke Data, Relationship Info, etc. ... but no wall posts). The "Activity Log" in which they are now categorized is online-only at Facebook, can't be downloaded, doesn't show all your posts at once, and can't be searched unless you know the date of the post that you're looking for in advance.  (I considered trying the Wayback Machine to find a date when this was altered on the help page, but of course Facebook bricks off any internet crawlers by way of its robots.txt file.)

In short: Facebook seems to have silently locked up everyone's personal posts in their system, with no way to get them out or search them, without any comment or notification of the switch that I can find anywhere online. The "Download Info" process screen itself remains unchanged, so potentially people could keep using it, not knowing that the largest and most fundamental type of data, their posts, has been stripped out of the archive.

Perhaps equally disturbing is how this hunt highlighted for me the fact that Facebook makes it totally impossible to search your own data (in any way other than tedious manual scrolling). I had flatly assumed that any digital entity would have this capability, if perhaps in a difficult-to-find location or UI. But Facebook apparently doesn't let you digitally search your own information in any way, and now they've removed the capacity to archive your information outside their system, too. Perhaps if attention is brought to this matter they might reverse course (as in some past cases) and restore the ability to truly "Download Info" from the largest and most fundamental aspect of your personal account.

Or can you now find any other way to download all the wall posts that you've written on Facebook?

Edit 6/13/13:  About a week now after I first posted this, and a fresh download does include the "wall" posts file. If this was a bug (see comments from Facebook associates, below), then we much appreciate this being resolved and hope the function sticks around in the future, too. Thanks!


Semester-End Teachable Moments

At the end of a semester, math students become extremely eager (or anxious) to know about the details of how their grade will be calculated, what their chances are of a particular grade, and what they need on the final exam in order to achieve a particular grade. In the past I would just fire back the answer to such questions in order to have time for other matters, but now I realize that this may be the most fruitful "teachable moment" of them all. Such questions are, after all, algebra questions, and so any of our remedial-or-above students really should be able to answer them for themselves -- and nowadays I require them to do just that.

It's particularly advantageous, because the customary reaction to the incessant "what good is this math for?" question is usually to introduce application/word problems into a course, but frequently to students this looks even more tangential, abstract, and unearthly than the original math it was meant to demonstrate (particularly for any students lacking background familiarity with the given application area, which is almost guaranteed to be most of them). But here we have a concrete example of intense interest that is being brought up by the students themselves -- and therefore it represents a matchless opportunity to hammer home exactly what the utility of basic arithmetic and algebra is, in a way that is hopefully intense and thus memorable.

Likewise, I used to presume this was trivial for higher-level students and so I'd scribble out the math quickly to not be mutually bored, but then I'd find that even my college algebra and statistics students were stunned by what I was doing. So that's the kind of basic thing that warrants time to make totally ironclad. Two cases that come up in my remedial classes:

(1) The university elementary algebra final exam has 25 questions, and at least a 60% score is required to pass the class (among other requirements; link). Common inquiry: "How many questions do we need right to pass the final?" So my answer is now to write on the board "60% of 25" and ask the students to translate that to math as a word problem, and then compute the decimal multiplication by hand. Some are very rusty, but parts of that process are obviously on the final itself; so, good review.

(2) In my classes, I usually compute the weighted total for the overall grade by taking 15% of a quiz average, 50% in-class test average, and 35% of the final exam. Common question near the end of the course: "What do I need on the final exam to get a B grade?" (or whatever). So my response now is to say, "Well you're asking me an algebra question, and you should be able to solve that yourself", writing on the board "W = 15%Q + 50%T + 65%F", and then assisting them in substituting the decimals, desired W, and known Q and T values. Then I tell them to apply the basic solving process (likely with a calculator), and once they know F, then they have the answer to their question.

In fact, I feel that this latter case is such a golden opportunity that I've modified my class procedures in at least two small ways to highlight it. (a) I used to have a policy where I might possibly replace one test score with the final exam if it was significantly higher; but so as to make the test average definitely known prior to the final, now I just drop one test score outright for everyone (which is nicely handled by our Blackboard grade center). (b) I actually spend a half-hour block on this very topic in the early part of the course, as a prime application of the basic algebraic solving process; I get some resistance due to the longer-seeming equation (compared to simpler drill exercises), but -- you'll get resistance anyway for any application problems, and when it truly comes up at the end of the semester suddenly it seems a lot more relevant.

So in summary -- I used to think that these questions were trivial and uninteresting, but it turns out they're very much not. Most of my students, either in an algebra class or thereafter, can't recognize such inquiries as a basic application of algebra that they should be able to solve. Instead of firing off the answers as an aside so as to cover more literal coursework, I now take the opportunity to leverage that intense interest into making it abundantly clear what kinds of important questions can be translated to math and solved by algebra.

Can you think of other inquiries that you commonly answer in grading or course procedures, that are really opportunities for basic math reviews in disguise?