by Mark Illingworth

Kudos to you for coming to this site and arriving at this sentence. That means you recognize the importance of asking students to think at higher levels in the math classroom as often as possible, and you’re willing to make the effort to learn how to do this better.

That’s what this whole site is about—helping you to let go of tired ways of presenting mathematics that in the best-case scenarios train to students to memorize techniques long enough to perform them on assessments. Still, this approach is safe and comfortable because it’s the one we learned and have been using, and it’s fairly easily to manage. So, you’re brave to be taking a step towards building your classroom around higher-order thinking skills.

Although all the articles on this site are written to help you think about or change various aspects of your classroom in order to make it more problem-solving centered, I’ll offer you a few general tips here that will help get you started.

It’s that simple. You have to practice thinking in the ways that you’re going to ask the students to think. To be clear, I’m not talking about the curated word problems from a textbook; I’m talking about the types of problems that I’ll share on this site that are designed to promote the development of higher-order thinking skills. (It’s also the type of problem on which I based Trapeze Education.) When you have a little window of time, sit down in your home with a beverage of your choice and enjoy some of these problems. You’re a math teacher, so I assume this will be fun for you… providing that you’re not trying to do this when there are dozens of other pressing tasks demanding your attention.

When you’re solving these problems, you have to be two people. Obviously, you have to be the person doing the thinking. You also have to observe the thinker—that’s you. Pay attention to the patterns and structures of your own thought as you develop solution paths.

By being the observer, you’ll accomplish two things. First, you’ll learn what your students have to go through so that you’ll be prepared to employ strategies on the fly for assisting them without giving away too much. (I refer to these as leading questions, which is the subject of another article.) Second, you’ll see firsthand what kinds of thinking your students will be practicing, which will give you an understanding of the ways in which they’re growing.

Once you’re a problem solver, you’ll see the importance of helping your students become problem solvers themselves. It’s obvious that to do that you’ll start giving them better problems—challenges that don’t come with directions or all the data needed to solve them. They often will require multiple techniques, and they may not even have a single right anwer. What’s not obvious is the amount of discomfort you’re going to experience, which is why I wrote Comfortable with Uncomfortable.

When you give students the right types of problems, you have to think of it as an experiment. And the more experiments you do, the more you’re going to learn about the process and about the students. Listen to them. Talk to them. Circulate through the class as they solve problems and ask questions that will tell you more about the ways in which they think. Formative assessment doesn’t get any better than this. Of course, you’re still going to occasionally be the dispenser of knowledge when you’re guiding them to discover or learn new techniques. Good teaching of course requires both talking and listening, but if you’re a problem-solving teacher you start to turn the dial more towards the latter.

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This whole site is about helping you create a classroom rooted in solving problems and developing higher-order thinking skills.

You should be proud that you are brave enough to leave the familiar in order to start dabbling in and eventually perfect the unfamiliar.

Become a problem solver yourself first. Then you'll see the value of this and want to share it with your students.

This whole process will take time, and you'll need to think of the new things you try as experiments from which you'll collect data that will help you do the job even better. Listen more than you talk.