Math is Figureoutable!
Perhaps the most impactful expression I came across as a brand new teacher was “Math is Figure-out-able!” Not memorizable; figureoutable. When I was a kid math was taught differently; you had to memorize everything and regurgitate it later. There wasn’t time to think, or play with ideas, or problem solve- just drill, drill, drill. The Common Core has changed all that (often to parents’ chagrin!), emphasizing the reasoning and the processes behind what we do, rather than just memorizing unfathomable procedures. And the very idea that we already know what we need to solve a tough problem can instill confidence right from the start.
The best tool I’ve found for shifting this mindset is in the Common Core itself. Take a look at the Standards of Mathematical Practice. They are not very user friendly, but when translated into actionable phrases they can be used as lifelong problem solving skills that we practice every single day. Here is the list I use:
- Try Stuff! (MP1 Make sense of problems and persevere in solving them.)
When you don’t know what to do, try something! There is always something to try, even when the initial panic of a new problem feels paralyzing. Trying literally anything will often get the ball rolling.
- Break it Down (MP2 Reason abstractly and quantitatively.)
Can you break it into smaller steps that you know how to do, or smaller problems that you can do one by one?
- Does This Make Sense? (MP1 Make sense of problems and persevere in solving them. & Reason abstractly and quantitatively.)
Before you go down a rabbit hole, ask yourself if it makes sense to do what you are doing. Does your solution actually answer the question?
- Justify My Answer – Demand Proof (MP3 Construct viable arguments and critique the reasoning of others.)
In math we always have to “show our work,” but what we’re really doing is justifying our answer. How did I get my answer? If your answer is different, whose is right? Explain your thinking to me… our discussion will help us both!
- Model with Math (MP4 Model with mathematics.)
Math is so useful! It can take complicated world relationships and conundrums and turn them into an equation we know how to solve. Powerful!
- Use My Tools (MP5 Use appropriate tools strategically.)
We have so many tools at our disposal: pencil & paper, calculators, multiplication charts, rulers, our fingers, class notes & examples, the list goes on. Try one!
- Check My Work (MP6 Attend to precision.)
This is related to several other “figureoutable skills” – does your answer make sense? Glance quickly back over to catch any silly mistakes. (2 + 5 does not equal 9…)
- Look for Patterns & Shortcuts (MP8 Look for and express regularity in repeated reasoning. & MP7 Look for and make use of structure.)
If something is happening over and over, notice it! There’s no need to reinvent the wheel every problem. And often, it turns out to be a lead-in to tomorrow’s lesson.
I have these posted in my classroom and I refer to them all the time. (Here’s a printable to use in your own classroom, too.) I try to congratulate my students anytime I notice them using one of the skills- especially when they don’t have the right answer yet. These skills are foundational for discovery lessons, where students have to dig into their past to decide how to attack something new.
My hope is that these habits will become so automatic, students will use them anytime they face a new problem, whether on homework, standardized tests, or in future classes. At the very least, if they get stuck during an in-class test, they can look at the wall for inspiration.
Here’s a really fun problem to practice with that I’ve adapted from a MindYourDecisions post. This works for an after school club or a day just before a holiday break. The kind of thinking needed to solve it takes time, so there’s plenty of opportunity to point out the different skills and showcase how they help.