For the 2016 Blogging initiative, Week 3 had the title of Questioning. In the article, it then proceeded to give suggestions for topics to write about. In previous weeks, the prompts were few in number, but I found one that seemed to be a good fit for me. This week, even though there were more prompts listed, I knew I needed to buck the system and write on a related topic that didn’t apply to any of the prompts.
As mentioned before, I teach in an online school. But I haven’t always. I started in a classroom and most of my experience is there as well. One thing I noticed while in the classroom is that students are observant.
If a student provided an answer to me, often they could tell by my body language or my facial expression if they were correct or not.
Slowly over the years, I was able to better mask my excitement or disappointment. If the answer they gave was to the question, “What is the next step?” often I would say, let’s try that and see what happens. Then we work through the problem as if they were correct.
If they were indeed correct, we have success. If, however, their thinking was flawed, I think it was helpful for them to see why it was flawed, or what would happen if we tried their method. Not only helpful for them, but helpful for the handful of other students who agreed with their initial response.
Other times, they wouldn’t be “wrong” per se. But their suggestion wasn’t helpful. For example, if we were looking at the problem x + 5 = 13, they might say to “add 5 to both sides” for the next step. Mathematically, this isn’t wrong. The Addition Property of Equality says you can add the same value to both sides of an equation and not change the answer to that equation (both sides are still equal).
When we use their suggestion, our next step would look like x + 10 = 18. Again, thier step wasn’t wrong; it just wasn’t helpful. I think students benefited for seeing this as well, especially because they have the right idea, just the wrong execution.
So what does that have to do with questioning?
More recently (and part of this is helpful in an online environment where students cannot always see my facial expressions as we work together), I hve started to question everything.
If they got the answer wrong, I would ask how they got their answer.
If they got the answer correct, I would ask how they got their answer.
They couldn’t tell anymore if they were right or wrong when I asked that question. Many students who were wrong were able to find their error and correct themselves as they explained why they did what they did. Even if the student could not find their own error, by asking the question, I (as the teacher) could better identify their thought patterns and discern what the true problem really was.
Although I can’t find the exact resource that lead me to start doing this, I believe it was in a blog post by Marilyn Burns, probably talking about the Math Reasoning Inventory (MRI). Alternately, it may have been from her article “Looking at How Students Reason” (bottom right paragraph on page 29).
Completely unrelated, but funny story. When I was in school training to become a teacher, I had the opportunity to pick up some free resources. Two of the items I chose were the books The I Hate Mathematics! Book and Math For Smarty Pants. I mostly picked them for their titles and fun graphic inside, along with the well written content. Just the other day, I was looking though them again, and I noticed they were written by Marilyn Burns! Who would have thought that she would have had an influence on me at the start of my career, and even now well over a decade later?!