Weekly Questions: How do feature low-status students’ ideas as competent? How do we bring out the voices of students who do not always contribute?

 Essential Question: How do we find and feature all students’ competence?

This week, something I've been thinking about that is related to these questions is this Venn diagram I saw on Twitter (source: https://twitter.com/ddmeyer/status/1232449193572261890?s=20):

The reality, which our current education system in many ways likes to ignore, is that mistakes are very helpful for learning. In fact, doing a problem the "wrong" way often teaches us way more about the problem than getting it correct the first time. This is sometimes because it shows us exactly why the correct way is correct, but it also might be because the incorrect way has the most truth to it. Or perhaps the wrong way is true for a differently worded problem, a problem which the student might have assumed was being asked instead. Students contribute smart ideas every day, and often they are ideas that we won't expect if we are only looking for the prescribed method of completion. It seems to me the easiest way to feature low-status students' ideas as competent is to ask for them. To recognize them. To pay attention to them at all. If we think back to the reading about the "whisperers," those students almost never had their ideas actually recognized in front of the class. They had no encouragement, and while it was clear that this didn't completely ruin their confidence, as they kept offering them anyway, it sure was not helpful in developing it and building it into something that would serve them better. Ideas are important. They are competent. Even when they don't directly lead us to an answer, they help us eliminate the answers that are wrong.

When it comes to bringing out voices of students who don't contribute, I think my instinct is always to head for group work. Students often see math as a very solitary, individual trek through algorithms. Why would students want to speak up? If the question is "what is the slope?" when given an equation, they think they either know it or they don't. So if they're afraid they might be wrong, there is no incentive to answer. Group work lowers the social risk because now they are only answering in front of a few peers instead of the entire class. And group work is the perfect time to offer questions that aren't so "yes" or "no" and allow the students to instead work towards an answer and find the problem solving of mathematics. This builds confidence in mathematical work, but it also builds peer-to-peer confidence and might lower the overall social risk just a bit, even if it doesn't last for long.