When we are confronted with a problem, we think of potential solutions. If we try a solution and it works, the neural pathways, or schema that suggested that solution become stronger. The next time we are confronted with a similar challenge, that solution will come to us sooner and, if it works again, those paths will become stronger yet again. Basically, the ideas that work grow stronger in our brains each time they are proven to work, while ideas that don’t get reinforced tend to become weaker.
In order for the cycle to go into action, however, the learner must be the one having the idea for a solution and experiencing the feedback, whether it be positive or negative. If a teacher, for example, comes up with a potential solution for a student to test, neither will experience the perception-action cycle. The student will miss out because they are testing someone else’s ideas, and the teacher’s perception-action cycle will not go to work because they didn’t experience the feedback from testing their own idea.
It might be difficult for teachers to give students challenges that will kick their perception-action cycle into math learning gear, but visual models can accomplish the same thing. If you show a student an image of some birds sitting on a wire, and then a second image where some of the birds have flown away, you have a model of subtraction. If you ask students how many birds must join those on the wire to make a total of ten birds, you not only have a missing addend situation, but you’ve asked them to solve a problem—which engages their perception-action cycle.
Shutting the Perception-Action Cycle Down
As with other learning cycles, the perception-action cycle can be shut down from negative emotional experiences at the point of feedback. Imagine a teacher trying something new with their class for the first time and it’s not going great. With the class out of control, the principal walks by and pulls the teacher out of the room to tell them to get it together. That teacher is not going to be eager to repeat the experiment, right?
The same thing happens with students learning math. If they are shamed or otherwise made to feel bad about themselves or their ideas, they are going to shut down. Learning environments need to be free of emotional judgment. To build a conceptual understanding, students need space to explore ideas and see what does and doesn’t work.
Learning by Speaking
Learning by doing is a powerful way to learn but not the only one. Students also learn a great deal by speaking. When you ask a student to justify their thinking, as they explain themselves, they actually create a new mental codification of experience called a schema.
This is why asking students to give a synopsis in an English class is so powerful. Students aren’t just parroting back language without meaning. To give a summary, a student must create meaning from the information they have received and then communicate it clearly to someone else.
Most educators are probably familiar with the Benjamin Franklin quote, “Tell me and I forget, teach me and I may remember, involve me and I learn.” By giving students opportunities to solve mathematical challenges in a safe, non-judgmental environment and then asking them to explain the thinking behind the solutions they arrived at, you’re involving them in their own learning twice. That explanation isn’t just a rehash of what happened; it’s an opportunity to extend, generalize, and reinforce the learning that took place in the perception-action cycle.
Showing Students Math Is for Them
Engaging students in the perception-action cycle and having them explain their thinking is an excellent start, but students must also know that they are “mathematical people,” that they are capable of doing math and that, in fact, they do it all the time.
Something as simple as building an equivalent fractions lesson around the paper fortune tellers many kids fold in grade school can help them understand that math is a part of their everyday lives, relieving some of the anxiety and fear around the subject.
Fortunately, the perception-action cycle is an inherently more equitable way to teach math because every human being is capable of learning this way. It also tends to eliminate confounding factors. For example, on a recent school visit, one of the teachers was a little flustered by a student who had just come to the school a few days prior. He only spoke Cambodian, and his teacher was saying that she didn’t know what to do with him because she had no way to test his math knowledge. She wasn’t even sure if people in Cambodia used the same math symbols because she couldn’t speak to him and ask.
I sat him down in front of a computer with a visual math problem to solve, and he arranged the numbers 1-20 in order on a number line immediately. He had plenty of math knowledge for his grade level, but no one had been able to get past the language barrier to find out. By cutting out all those external factors, visual math challenges that invoke the perception-action cycle can help shine a light on all kinds of interesting thinking different students are capable of.
There was nothing wrong with that student’s ability to learn math. His teacher, through no fault of her own, simply wasn’t teaching it to him in a way that worked for him. Just as we learned 25 years ago that there is a better way to teach reading by focusing on the science, we know today that there is a better way to teach math. Let’s hope it doesn’t take a quarter century to become the norm as well.
- 5 tips to keep online students motivated - June 8, 2023
- Collaborative edtech tools are changing the game for student engagement - June 8, 2023
- How our school handled the chaos of an active shooter hoax - June 7, 2023