I can’t imagine a scenario where a teacher would not want a student engaged in deep thinking about the math question on the board, except maybe during a fire drill. We all want our students to be able to solve serious mathematical problems. We know that when a student figures something out for themselves with a reasonable amount of effort, they tend to get excited about that, are proud of themselves, and are likely to remember better than if they were just told what to do. Having students figure stuff out, though, typically takes whole lot more time than if we just tell them. Even with the Common Core, we still have to be careful with time. We want our students to perform well on standardized tests, and some of those tests are still plug-and-chug.

I figured out where to get the time to use carefully chosen PBL and discovery activities with my students: not just because of what research tells us, but also because of what I see in my own students. Here’s where I get the time:

- By Anchor theory, I just have to say to my students, “remember the Soda activity,” and a flood of information becomes re-accessible. These activities elicit more focused thought than strictly procedural problems and review many skills at the same time. Practicing a variety of skills at the same time builds connections (similarities and differences), so the amount practice time needed becomes condensed.
- Students don’t wonder when the skills in the activity are used in real life because they experience the value. Because they see the need, they tend to practice more intentionally.
- Check-off points where I sign off on activities assure that students are learning concepts correctly so we don’t waste time reteaching.
- Khan Academy assures accurate practice. By assigning and monitoring electronic homework, my students don’t waste time writing out problems inaccurately, not checking their solutions, and ignoring their errors. When students are unaware of their errors, they can develop further misunderstandings by inventing rules that don’t work consistently. Unlearning ingrained habits is time-consuming.
- I rarely answer homework questions in class. If my students have difficulty with their homework, they are expected to request help electronically.

As my students find themselves doing less “grunt work” to master math, their enjoyment of the class improves. They become confident in their ability to be successful and begin seeing themselves in careers that require some college mathematics. They start setting goals and they become even more motivated. All of these things work together to make learning more efficient, more powerful, and skills more useful. Ultimately, math is the gateway to STEM jobs, so efficient learning becomes a social justice issue. Time cut from less efficient practices is, therefore, well diverted.

We often hear stories of “discovery learning” thrust upon teachers with insufficient training. Students get frustrated and give up. Then the teachers just give them the answers. No one learns. It doesn’t have to be that way. Teachers can learn to captialize on and encourage students’ natural curiosity by coaching instead of always just telling. It takes practice. I am collecting simple activities that replace a direct instruction lesson with an exploration here: Got It =>Get It Transfers. Please submit one of your own to build the problem bank.

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