By Jana McAdams, Math and PE Teacher
Here is a checkerboard. How many squares are there on the board?
If there are three bats that can see from their left eye, one that can see out of its right eye, and four that cannot see out of their left eye, how many potential bats are there?
A farmer dropped and broke all of her eggs. She knew that in certain groupings, there were some eggs left over and in other groupings, no eggs were left over. How many eggs did she have?
Instructions: Explain every step you went through to solve the problems. Write down what you thought, when you thought it, and how you thought. Is there a correct way to solve the problem? Is there more than one solution? Illuminate your thinking. Expand on it. Tell me more.
This is a sampling of “Problems of the Week” (POWs), which are a regular part of the math curriculum at IVA. From a teacher’s perspective, giving students POWs is an opportunity for them to think like a mathematician. It aids them in systematic processing to think through problems in a deep and meaningful way. As students progress through POWs during the year, the goal is for them to come away with tools that they are able to pull out and use when confronted with any type of difficult problem. We are asking students to tap into the intellectual virtues that will ultimately help them in pursuit of becoming a lifelong learner.
In a recent reflection on POWs, one sixth-grade student realized the value of a growth mindset. She commented: “I was able to realize that a growth mindset can help you expand your curiosity and weaken your fixed mindset.” She also recognized the importance of curiosity in aiding her toward success, saying that “you had to be able to have many questions and thoughts when you write your prompt ... I had ideas and thoughts on how different ways could work to solve the problem.” The natural outpouring of this growth mindset contributed to the demonstration of intellectual virtues which led to deep understanding.
The POWs are structured in a way that is intended to lead students towards deep understanding; it just does not happen at first glance. Along the way, students must also demonstrate intellectual humility in recognizing that they may be incorrect in their original thinking. Another comment from this student put it beautifully: “When you solve a problem ... be honest with yourself and write down what you don’t know for sure and what you think; you could be correct. That may make you feel better and stronger about yourself.” Sometimes original ideas can be correct and sometimes they are not, but students must be able to be intellectually humble in admitting that they are attempting an idea that could be wrong. Many times, growth in learning happens when students see how they were incorrect. If one is not willing to accept this failure, there is little chance to grow.
At the end of the process, it is a teacher’s hope that students come to understand themselves better as thinkers and learners. It is a long process that involves many roads with blocks or bumps along the way, but it eventually leads to a clearing. As students come to understand their own selves, their road may still contain struggles, but these struggles can now be met with confidence. The same student explained how this self-understanding has made her a better thinker overall: “I have discovered the true mind I have, where I am able to think and learn thoroughly and let my strengths grow and my weaknesses die. That is because what POWs try and teach you is that your abilities are a big part of what’s inside you and that you can think deeper when you are into learning. If you make learning fun, then your brain can become curiously expanded to any subject.”
What does your road to learning look like? When there are detours in the path, are they met with confidence?