At the end of my first year of teaching middle school math, my biggest takeaway was that trying to teach something quickly was worse than not teaching it at all. Every lesson I tried to hustle through or shorten by cutting questions was a disaster and, to mitigate the resulting confusion, we ended up doing the problems and activities I’d trimmed from the original lessons . . . and then some.
Grade levels have a full year’s worth of learning packed into their standards, so it makes sense to try to be as efficient as possible. But if my bare-bones, hurried classes made things worse, what would make things better?
Scaffolding!
How Are Scaffolds Used in Math Class?
Scaffolding is the inclusion of temporary supports to help students access and complete grade-level work. Examples of scaffolding include:
- Asking questions that guide students’ thinking
- Giving simpler versions of problems before introducing more complex versions
- Providing a worked example
- Preteaching vocabulary
- Breaking learning content into smaller pieces
While scaffolding can look very different from one class to another, it always involves more questions, not fewer.
On its face, it sounds like adding questions to scaffold a lesson should make it go slower, not faster. More problems, more time, right? Well, that doesn’t seem to be true. In The Great Courses® lecture series, The Philosopher’s Toolkit: How to Be the Most Rational Person in Any Room, Patrick Grim, Ph.D., a professor at State University of New York, Stony Brook, discusses scenarios in which scaffolding made problem solving faster overall.
In one example, Grim references a study by Dr. Johnathan Sweller in which students were either given a complex problem to solve or two less complex versions of the problem leading up to the same ultimate task.
Complex Problem Only:
- Transform the number 8 into 15 in exactly six steps. In each step, either multiply the value by 2 or subtract 7.
Scaffolded Version:
- Transform the number 8 into 9 in two moves. In each step, either multiply the value by 2 or subtract 7.
- Transform the number 8 into 11 in four moves. In each step, either multiply the value by 2 or subtract 7.
- Transform the number 8 into 15 in exactly six steps. In each step, either multiply the value by 2 or subtract 7.
On average, the participants who received only the complex problem took more than five minutes to solve it. Those who received the complex problem after the two simpler problems needed only 90 seconds to solve it on average, with an average of three minutes to solve all three problems.
Using scaffolded problems allows students to learn underlying concepts they can apply to more difficult problems, making the entire process more efficient.
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