The core of visible thinking is writing. One creates a complete thought when he or she formalizes it into tangible words but that is only half of the job of writing. The other role is to communicate the concept to a reader or listener. If the recipient understands the concept as the speaker formed it then the communication is successful. This dialogue is clear in directive statements such as when my wife asks me “Can you take out the trash?” and I do so in some hurried and confused mess at some point, though not always right then. Communication is less clear when we are working with concepts, stories, feelings, and all the other things that make it fascinating and frustrating to be human. We have art to help us through these challenges. I want to spend time on the non linguistic arts later but not today.
I teach math. The beauty and challenge of math is that it is a study of carefully ordered thinking. We have all kinds of rules, terms, properties, and muck but it is at its heart a system of logical reasoning and problem solving. Math is not “the” system but it is the most universally accepted one. As a math teacher, I answer lots of questions. So many questions. Too many questions.
Only teachers can understand the litany of questions students ask during a class. That blaze of interrogatives accosted in my first days in the classroom. As I look back, my steady need to respond was probably the most exhausting part of that first year. What harm is there in questions?
Not much but a great deal can come from the answers. People often ask before thinking. We also answer before doing so. If they do not immediately grasp the concept, they ask for further explanation. These questions are a cue that they need guidance. Embrace these for they are easier to work with then the other people who think they understand and don’t ask. Regardless, you know can now make thinking visible and, if done well, can bring the whole class along. Your motive is to direct the students to ask the right questions. You are the guide in a Socratic dialogue. Avoid responding with an explanation since that didn’t work so well the first time around. Try to ask simple questions that guide the student to respond with answers that build toward understanding. You may also want to ask other students to respond and have the process lead to a discussion. This process takes a profound understanding of the material and some flexibility. There are wrong answers but rarely is there one right one. I have learned a great deal about math by following a student’s line of reasoning. You can make quick assessments of understanding through this process and you can also find the elements that confuse students and lead to faulty reasoning. This second part is extremely useful moving forward because you can present material to address those errors.
However you present the material to your class, this dialogue is a powerful tool and one that inspires strong discussion within the class. It is only as good as the questions are so you may want to start the year discussing how important that all important element is. I am a big fan on this video from Veritasium. You could borrow from him or present the video but the focus is asking the right questions.
More to come one art as visible thinking…