Think back to math class for a minute. Any math class will do.
When the teacher asked a question or presented you with a problem to solve, was it understood they were most often looking for an exact answer? The ONE correct solution.
As someone who spent some years leading math classrooms, I know this answer is YES. It’s one of the ways I evolved as a math teacher. Of course, in the beginning I was structuring my class and my questions based on how I had been taught, because that’s what I knew and that’s how I thought it was supposed to be done. This might be one reason so many people aren’t confident in their ability to do math. Because they often made mistakes in the calculations and arrived at a different answer than what was expected. How would the experience of math class be different if the focus was on getting close to the answer rather than expecting an exact solution right off the bat?
Stick with me here for a minute. I haven’t gone completely off the rails. Yet.
I am NOT proposing we take the exactness out of math class.
We know there are situations where being off by the tiniest bit can lead to disaster. The bridge might collapse. The car might not run correctly. A recipe might not turn out well. While I absolutely believe understanding the concept and the thought process is often more important, especially when learning a concept or skill, there is absolutely a time and place and necessity for exactness in solutions.
The truth is, though, for most of the math you do every day, a rough estimate is enough. You don’t need to know it will take 52 minutes and 38 seconds to arrive at your destination. It’s enough to say it will take ALMOST an hour to get there. We say things like, “it will cost ABOUT” this amount and “bake for 25 to 28 minutes” and “your package will arrive in 7-10 days.” All of these are estimates.
Examples of when close enough is sufficient.
We’ve talked about how nearly everything in math comes back to a pattern and recognizing and making use of patterns is an important part of understanding mathematics. My argument here is that estimation is one of the most important math skills we bring into our daily lives. In my experience, it’s also one of the most misunderstood and underutilized skills in math class.
I remember teaching estimation to middle schoolers and being confused by how they approached it. The idea of estimating is to get a general idea of the answer, whatever the task or problem might be. In math class, estimation is useful to judge the reasonableness of the solution you eventually arrive at. So, if your answer is way different than your estimate, you’ve probably made a mistake and need to revisit your work. Estimating BEFORE working the problem gives a general sense of where the solution will fall.
What I found these students did, and maybe you’ve done this too, is confuse rounding (another useful math skill) with estimating. They would work the problem, arrive at their solution, and then round that exact answer to make their “estimate.” This rounded answer isn’t really an estimate that’s useful in math class. It’s simply rounding off your answer, which robs you of the opportunity to potentially find and correct your mistake. Thinking of estimation in this way also undermines the importance of how we use it outside of math class.
In your everyday life, you estimate all sorts of things ahead of time to get an idea of just how much of whatever might be needed.
How much food to make for a meal.
How much time is needed to complete certain tasks.
How much money is in your budget for your kids’ new shoes.
How many cans of paint will cover the living room walls.
None of these scenarios require an exact solution. If you make too much food, you’ll have leftovers. Too little? Then you’ll need a few snacks and you’ll adjust the amount next time. Didn’t allot enough time to finish your task? You keep working or you stop and come back to it later. You get the idea.
Estimating is often so automatic, you probably don’t even notice you are doing it most of the time. At work and at home, estimation is essential to your daily life.
And that, my friend, makes you a math person.
Did you know you have thought threads in your mind that sometimes tie themselves up in knots? These threads hold the belief that you aren’t a math person. My hope is this discussion about estimation empowers you to pull one of those threads just enough so that your knot can begin to untangle. That’s actually the entire point of these posts and one of the main reasons I created the I See Math People podcast. To get you thinking about your relationship to math in a way that begins to untangle those thoughts.
Your brain needs evidence though. Proof that what you are thinking…or want to think…is true. Lots of proof. Give it enough evidence over the course of an extended period of time and you will begin to believe you are a math person.
To that end, I have a task for you. As you go about your days, each time you notice yourself making an estimate, stop and acknowledge it.
Say to yourself, “I just used estimation. I am a math person.”
If you’d like to continue this conversation, I’d love to hear about some of the ways you find yourself estimating as you go about your day. You can comment on a post or message me on Instagram, I’m apocketfulofpi over there. You can also email me at Je******@************pi.com.
