Working Backwards

From high achieving students to the kids who really struggle in our math classroom, they are all focused on one thing – the answer! Think about it, student who get good grades are continually reinforced to keep working hard when they see that they are getting the correct answers. While students keep getting that wrong answer (usually without understanding at all why it’s wrong) continue to get more and more frustrated and often lead to just giving up. And can we blame them for putting so much of a focus on the answers? Yes we ask them to show work on homework and tests, we praise effort and hard work in the classroom, but how are they graded? How have they been graded for the past six years? What do their parents really care about? In fact, what do entrance exams for honors classes or colleges look for?

At times it seems absolutely impossible to fight the beast of grades. I see the efforts of many schools trying to open up their view of grades and recording progress, but as a society we still put a lot of value on getting the correct answers – no matter how you get them.

To try and open up the minds of my students I have been including some classwork where students work backwards. I present them with a problem and then give them the answer outright. It was hilarious to see how my kiddos responded the first time I tried it. It was as if they thought I was helping them cheat! The great thing about giving students the answer is that I think it helps turn the problem into a puzzle. They know the problem (a box of mixed-up jigsaw pieces) and they know the answer they need to arrive at (the beautiful picture on the front of the puzzle box), so now the fun is in figuring out how to put the pieces together just right. I hope I didn’t lose you with that analogy! My point is that when students don’t have to worry about what the answer is they are freed up to experiment with the process. That experimentation is what leads to a deeper understanding of the problem.

This is just one example of a way to prioritize teaching problem solving skills. To take the focus off of being right or wrong, and put it on the beauty that is found when students persists, learning from their mistakes, and work out a viable solution to a problem.

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