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?

Punished for True Math

Reading some Mathoverflow the other day, I ran into some truly blood-boiling recollections in a discussion of "Examples of common false beliefs in mathematics" (mostly at the research level, but the comments diverged), such as that "Many students believe that 1 plus the product of the first n primes is always a prime number". Recollections such as these (link):

When I was 11 y.o. I was screamed at by a teacher and thrown out of class for pointing this out when he claimed the false belief stated (it wasn't class material, but the teacher wanted to show he was smart). I found the counterexample later at home. I didn't let the matter drop either... I knew I was right and he was wrong, and really had a major fallout with that math teacher and the school; and flunked math that year. – Daniel Moskovich May 5 2010 at 1:19   

@Daniel: Sorry to hear that. When my daughter Meena was the same age (11), her teacher asserted that 0.999... was not equal to 1. Meena supplied one or two proofs that they were equal, but her teacher would not budge. Maybe this is another example of a common false belief. – Ravi Boppana May 5 2010 at 2:59   

@Daniel: I've heard a worse story. A college instructor claimed in Number Theory class that there are only finitely many primes. When confronted by a student, her reply was: "If you think there are infinitely many, write them all down". She was on tenure track, but need I add, didn't get tenure. – Victor Protsak May 5 2010 at 5:38   

This false belief leads to a proof of the Twin Prime conjecture: For every n, (p1p2⋯pn−1,p1p2⋯pn+1) are twin primes, right? – David Speyer May 6 2010 at 15:50   

Daniel, about the same age, I was asked to leave class for claiming that pi is not 22/7. The math teacher said that 3.14 is an approximation and while some people falsly believe that pi=3.14 but the true answer is 22/7. Years later an Israeli newspaper published a story about a person who can memorize the first 2000 digits of pi and the article contained the first 200 digits. A week later the newspaper published a correction: "Some of our readers pointed out that pi=22/7". Then the "corrected" (periodic) 200 digits were included. Memorizing digits of pi is a whole different matter if pi=22/7. – Gil Kalai May 11 2010 at 5:45

I guess I had the good luck to not ever have such a completely horrible math instructor, because I think any of these cases would have made me completely lose my mind. (As an aside, I will say that it's routine in my classes that I'll have to disabuse people of the idea that pi = 22/7... perhaps this is more common in Israel, as Prof. Kalai above is, and many of my students are from.) Have you ever seen someone punished, yelled at, or thrown out of class for actually expressing true basic math facts?

Parity of Zero

Did you know: As much as half the population doesn't know that zero is an even number? And that this can cause problems in cases like gas-rationing based on license plates' last digit (as happened here in NYC last fall after Hurricane Sandy).

http://en.wikipedia.org/wiki/Parity_of_zero

Village Voice on CUNY

Here's a very nice cover story from NYC's alternative newspaper, the Village Voice, basically on the subject of my math teaching job at a CUNY community college (and more generally, community colleges across the country):

http://www.villagevoice.com/2013-04-03/news/system-failure-the-collapse-of-public-education/

Some highlights:

• Enrollment at CUNY community colleges is up 33% in the past 5 years
• CUNY has seen a 40% drop in per-student funding from the state in the last 20 years.
• 80% of NYC public school grads who enroll in CUNY need remedial-level instruction
• Just 14% of public school grads pass the CUNY algebra placement exam
• Only 20% of remedially-placed students have advanced to a for-credit class 2 years later
• Only 1 in 4 remedially-placed earn any degree after 6 years.

Regarding NYC public high school statistics: "The numbers are 'better'—there are more graduates—and yet, in an endless loop of absurdity, these students get to college only to be told they haven't finished high school."

Regarding NYC's Harry Truman High School: "Truman currently boasts an A grade from the city. Yet only 10 percent of its graduates are able to enter CUNY without remediation."

Regarding a new pre-matriculation START program which takes small classes and gives detailed basic math instruction: "That process sounds an awful lot like what we used to think of as 'teaching.'"

Everyday LCMs

Here's an exercise that I'm planning to use in my remedial arithmetic class in the near future. The question is: For each of the following number ranges, state (i) the LCM (least common multiple), (ii) some everyday examples that use that LCM, and (iii) an explanation of why that number is convenient.

(a) {1, 2, 3}.
LCM is 6. Examples: Six-pack of soda, beer, donuts, etc. Convenient because you can divide them evenly whether you have one, two, or three people.

(b) {1, 2, 3, 4}.
LCM is 12 (a dozen). Examples: 12-pack of beer, dozen eggs, hours on a clock, etc. Convenient because you can divide them evenly among either one, two, three, or four people (or dishes or periods).

(c) {1, 2, 3, 4, 5}.
LCM is 60. (And see next exercise.)

(d) {1, 2, 3, 4, 5, 6}
LCM is also 60. Examples: 60 seconds in a minute, 60 minutes in an hour, 360 degrees in a circle (6×60), etc. Convenient because you can divide them evenly into one, two, three, four, five, or six periods, as desired. (See also: Babylonian numerals.)