Thursday, July 17, 2014

Resources for SAT self-study -- The Khan Academy

I don't want to be too negative here. This is a decent resource and for most students there will be some value in going through these problems. If that sounds like faint praise, that's because it is. What we have here, while nice, simply isn't that much to get excited about. The Academy, it should be noted, is promising a much more complete and sophisticated set of tools next year, but for now, we pretty much have to limit ourselves to the "better than nothing" standard.

I would recommend that you go to the Khan Academy SAT site and do some exploring on your own.

In the meantime, I have included a few examples to get the discussion started.

So what are my concerns here?

I The Medium is the Message

Ideally, we'd see videos that made better use of the medium (more on that later) but the bigger, more immediate concern is is that they have simply chosen the wrong message here. What we have in these two clips is basically a standard problem session with most of the good and important parts left out.

This type of instruction, done properly, is contextualized and highly interactive. Putting problems in context is essential because, even more than drudgery, the thing that drags kids down in math is not knowing why they're doing what they're doing. Working a problem for a class should be a conversation that both frames the question and gives the students a chance to participate in the solution. (For example, ask them "If this length is x, what is this other length in terms of x?" and let them come up with the 2x.) Without the conversation, there's not much point in presenting this information in a video because...

II You've already got the message in a better medium

These clips are basically an instructor reading out loud the kind of solved examples that can easily be found in books or online. The videos add little to the printed version and they arguably lose quite a bit. This will strike many as blasphemous, but for certain tasks, print actually is a superior medium. It's good at conveying precise information and it gives the reader a level of control that is difficult to achieve with pausing and rewinding a video. It offers tremendous variety and availability. It is easily searched and database-friendly. What's more, the ability to pick up a book or go to a website and teach oneself is a valuable skill for everyone and an absolutely essential ability for anyone in STEM.

Is the spoken word ever better than print? Sure, much of the time. If you're going for a conversational voice; if the gist of the message is not dependent on any single word or phrase; if you want a particular emotional tone... Unfortunately, these clips not only do things that print would do better; they leave out the things that their medium would do better than print could.

III Rush, rush, rush

There's a choppiness here both in tone and structure, combined with a hurried quality. The approach is very much "Here's a problem. Do this. Do this. Do this. Here's the answer." No time spent orienting the student. Worse yet, no time spent checking the answer. In terms of  Pólya's How to Solve It, they tend to jump directly to "carrying out the plan" and stop there. That's very dangerous because, even if the students do manage to follow what you're doing, they won't have a firm grasp on why you were doing it and that's going to be a problem when you're not there to hold their hands.

IV Lots of trees, very little forest

If you want students to understand what they're doing and, just as important, if you want them not to feel confused and anxious, you have to give them a sense of the overall problem.

The carton question above is a perfect example of how to screw that up. The instructor jumps directly to the exact variables and equations needed, skipping a number of steps that are not at all obvious to the students. In fact, it is those skipped steps that trip up most of the students who miss these problems.

If you tried this with actual students, they would say "How did you know to do that?" and that's an extraordinarily good question. The answer is that we start with translation from English to mathematics (a faithful but not necessarily idiomatic translation, though I probably wouldn't mention that to the students). "[H]ow many of the $50 cartons did she buy?" suggests number of $50 cartons should be a variable (let's be original and call it x) and it makes sense that the number of $30 cartons would be another (y). "Sarah bought 20 cartons" becomes x + y = 20 and so on.

If students understand the why behind the what, they will be happier and learn better.

I don't want to be too harsh here. This isn't exactly a bad resource and I very much believe that the Khan Academy's heart is in the right place, but when it comes to the SAT, they still have a long ways to go.

Note: I made a few minor wording changes after first posting this.

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