We want students to do challenging things in mathematics, but we also want them to be successful. Its a constant battle between scaffolding too much and not scaffolding enough. I’m always worried about not being clear in what I want, and asking students to do very confusing tasks, but I also don’t want to take them through things step by step, because then they’re not thinking about the math themselves.
What does not help?
Telling students what to do. Giving students exact directions on what to do next. If we have to do this on a daily basis, then we haven’t taught students how to actually think. If we have to do this, then we have to scaffold each problem for our students, because each problem is different. This obviously doesn’t help long term, because eventually we hope that students can do things without us. This involves instructions like:
- create an equation for this sentence
- measure the slope of the line
What does help?
Scaffolding thinking. Using things like the Mathematical Processes to help our students think about big picture mathematics. Having students do things like reflect on the reasonableness of their answer is useful in every problem. Having students understand that we can represent mathematical models in various ways also helps in a variety of problems. Another way to use scaffolding is to scaffold in time during the lesson to have students discuss their own next steps. Perhaps its a few minutes to talk about what should be done next. Perhaps its some time soft students to look up vocabulary words that will help them solve a problem. Here is a great summary of a few of these strategies.
Patient Problem Solving
In the end, its simple. Help students think so that they can solve their own problems. Don’t help them solve specific problems. Long term, that’s not helping. If we scaffold each step, they will never be patient enough to think through something on their own. On the other hand, if we scaffold thinking strategies, they will take the time to reason through their thoughts and work with others to make sense of the mathematics that we’re trying to teach.