Ed.: This is day 2 of my challenge to post an article to the blog each weekday for one month. So far so good.

I’ve written a lot about Guided Practice, which is the model I have been developing and using for pre-class work in a flipped learning setting. The purpose of Guided Practice has been, and still is, to have students learn enough to “launch” the activity I have prepared for class. That is, the flipped learning design of the class is focused on what goes on in class, and everything that happens prior to class is there solely to prepare students for that experience. (It’s important to make this clear, because too often flipped learning discussions focus on the pre-class work and its logistics. That’s important but not central.)

This semester I’ve noticed that I still have the same conception of the purpose of Guided Practice, but what it looks like has changed. My older Guided Practice assignments were focused on acquiring knowledge and skills needed to launch the in-class activity. Students would read from the book and/or watch a collection of videos that, with the help of a set of exercises, come into class “equipped” with the basics and ready to work on more advanced topics.

This summer, though, I took a Google online course on computational thinking for educators, and after I finished it, it seemed to be that “equipped with the basics” and “ready to work on more advanced topics” are not necessarily the same thing. Computational thinking, briefly, is a way of approaching problem solving – typically computational problems but this can be broadly interpreted – that involves four stages:

  1. Decomposition, or breaking down a problem into simpler parts;
  2. Pattern recognition, observing patterns and regularities in your data;
  3. Abstraction, identifying the general principles that unify the patterns you noticed; and
  4. Algorithm design, devising a process for solving your problem and others that are like it.

Possibly without thinking about it, computational thinking has crept into the way I build Guided Practice assignments. The way I think of it now is:

So rather than focusing on “acquisition” of skills and information, Guided Pratice is about getting to a certain point in a problem-solving process that is then resolved as a learning community in class. Those first two parts of the process are almost always things that students can do individually – in fact it taps into the parts of doing math that students like the most, in my experience, namely computing stuff and noticing patterns. Then the second two parts are harder, and need as many voices in the process as possible, which makes it a perfect candidate for in-class work.

Rather than giving more and more reading and video to students, I’ve found myself giving less and less. Here is a Guided Practice I just gave to my Discrete Structures 1 class, in which I actually forbade students to do any reading or watch any video because I didn’t want them getting spoilers. This is in a unit on basic combinatorics, and there are formuals to learn. But if they don’t discover the concepts behind the formulas – by playing with counting problems and being asked What’s the pattern? What’s the overall principle? – then there’s a good chance they will have only a superficial, mechanical knowledge of those formulas. So the textbook and the video can in some cases do more harm than good.

Here’s another one from the second-semester class where we were learning about properties of relations. There’s an embedded Sage cell in there that generates a random directed graph, displays it, and then tells whether the underlying relation is antisymmetric. Students were asked (among other things) to evaluate the code cell over and over again, and then think about, What’s the pattern? What does an antisymmetric relation look like? In the past I have had a hard time getting students to grasp this idea (they tend to think that “antisymmetric” means “not symmetric”). This time around, nearly 100% of the students isolated the right pattern without any “coverage” of the material. Zen news flash: Covering the material doesn’t always cover the material, and sometimes you cover the material without covering it.

A lot of newbie flipped learning practicioners worry themselves to death ask about how to make sure that students do the readings and watch the video to prepare for classes. Certainly this can be a real problem – if all you do is assign videos to watch and readings to read and exercises to work. Students don’t respond very well to being asked to consume information just because it’s the next topic up. There’s no context.

But students do tend to respond well to things like puzzles, games, and compelling questions. Moving from a model of Read and watch the following items and work some exercises to play around with this model and tell me what patterns you notice taps into their curiosity – in fact it seems to revive it, after having it generally beaten out of them by schooling – and their native abilities and curiosity are generally enough to get to the right point in computational thinking to take the next step.

This approach to Guided Practice reminds me of the study done at Stanford a couple of years ago that suggested that having students get hands-on time with concepts before watching videos – “flipping the flipped classroom” in a way – led to greater learning gains than having them watch videos and do reading as their initial preparation for class. So maybe they will get more out of the time for telling this way too.

Expect to see a lot more about computational thinking in this space in the future, as I really like this framework as a paradigm for all mathematics courses and especially those that are aimed at non-mathematician audiences.