When I was working on my Master's degree in secondary math a number of years ago, most of the coursework involved multi-part tasks and open-ended projects. I found these activities to be both challenging and enjoyable - but I also found them to be a very inefficient way to learn new material. Tracking down the information on my own and building new skills with little to no assistance was frequently super-frustrating, with too much of my time being spent on stuff that wasn't learning. 

To make matters more stressful, the all-important Master's assessment was always on my mind, and the closer it loomed, the less prepared for it I felt. I simply wasn't learning enough, fast enough.

I began to suspect that the problem was me.

So I was relieved beyond belief to find that the test prep courses at the end of the program consisted almost exclusively of pre-worked examples, practice problems, and instant feedback. Applying this approach allowed me to start making some serious headway in my own classroom; I learned more in the last two months of the program with pencil and paper (and eraser) than I had in the previous year and a half - far more. Furthermore, what I learned stayed learned. By the time the test rolled around, I felt super-prepared for it - and my results proved my confidence justified. I hate to think of what would have happened without all the examples, problems, and feedback.

Now you might think this is just another rant questioning the effectiveness of things like discovery learning, project-based learning, and the like, but it's not. I genuinely enjoyed the discovery-oriented tasks and open-ended projects from the earlier parts of the program, and ended up learning quite a bit from them. My complaint has to do with the when, not the how.

The visionary and spokesman behind worked examples, John Sweller, has just as frequently spoken of when not to use them, referring to what he calls the Expertise Reversal Effect, which suggests that while pre-worked examples are critical for beginners, they can be detrimental for those approaching expertise. 

Was my Master's program backwards? Should it have delivered the new content with pre-worked examples, practice problems, and instant feedback and then required application and extension of this knowledge with complex tasks and open-ended projects?

Speaking as the subject of this particular educational experiment, yes and yes.

The example/problem/feedback approach is the surest strategy we have for teaching new math content to the point of mastery - and the designers of my Master's program knew it. When it really mattered - when the university needed to be positive that its Master's candidates had the detailed knowledge and specific skills they needed to pass the final assessment - this was the strategy they went with. Good thing too, because the vast majority of the material on the assessment hadn't been covered at all in the tasks or projects.

But, I can hear some of you saying, the point of learning math shouldn't be just to pass tests! And you know what? You're right. Tests are an inescapable fact of life, whether we like it or not; they're hurdles we need to jump. And just as I hate to think of what my Master's experience would have been like without examples, practice, and feedback, I hate to think of how lifeless the whole experience would have been without the rich tasks and open-ended projects.

In "Math Education Land", the argument rages endlessly over direct instruction vs. inquiry/discovery/project-based learning - and even proponents of “both/and” get shot at on a regular basis. What if “all of the above” is the actual answer - but only in a certain order?

After 30 years in the teaching business, and after having examined the process in detail myself from the student side during my Master's program, I'm convinced that it is. John Sweller deserves to go down in history as having gotten it right: pre-worked examples, problems, and instant feedback for beginners; faded examples and more open-ended problems and learning experiences after that.

Horse, then cart.