Here is a tip that I learned as a teacher that has helped me immensely with working with my son.
Early in my teaching career, I believed that the point of math was to learn the steps and learn them well. I had a checklist of procedures that I wanted my students to know by heart. I would have them practice these procedures whenever I got the chance so that they would have them ingrained in their memory.
The one-on-one conversations I had with my students often sounded like this:
If I asked a question and my student was silent for too long, I would start getting anxious.
Did she understand what I asked? Did I ask it in a weird way? Should I have asked an easier question? What is she thinking about? I mean, really. There are only three steps for doing this problem. Is she even thinking about it anymore? Maybe she started thinking about something else, and I am standing here like an idiot waiting for her to answer.
Obviously, something had gone terribly wrong.
Then, I would walk her through the steps, hoping that would jog her memory. Maybe that would help her remember next time.
What I didn’t realize was that she was probably engrossed in solving the problem, but I kept interrupting her thinking. She was considering my question, trying to answer, but very time I gave her words of encouragement, she might have had to start all over again.
When I finally started breaking down the problem for her, I completely derailed her train of thought. She might have been doing the problem one way, like starting with 17 and adding ones until she’d used up 5 ones. But then, I interrupted with questions based on what I was thinking, which was likely unrelated to what she was thinking.
To illustrate, solve the following problem. Then, a few seconds before you're done with the problem, read what follows.
What is 20% off of $135?
Now, let's go over the problem together:
What’s 120 ÷ 5?
What’s 15 ÷ 5?
What’s 120 - 24?
What’s 15 - 3?
What’s 96 + 12?
Are you still thinking about the original question? Are you confused? Do you wonder if I forgot to edit this post?
You might be wondering what the connection between the first question is with the rest of the questions. The rest of the questions are, in fact, another way of arriving at the answer. Of course, I cheated--I showed an especially complicated way of arriving at the correct answer, and didn't give any additional information the way I might have in real life. But this is what happens to kids when we interrupt their thinking with our own thoughts. Before, they are engaged with the problem. When we interrupt, they not only stop thinking about the original problem, but likely start thinking of our questions as new questions altogether.
I had given up on her :-(
In my mind, I was doing good, teacherly things. I was breaking the problem down into smaller, bite-sized steps that she could handle. I was assessing her understanding and re-teaching as necessary. But what really happened was, I had given up on her. I did good things, but the problem was, that I did them when it wasn’t needed. What I failed to understand was that she was busy working through the problem. What exactly she was thinking, I didn't know. But whatever she was doing, she had not given up.
While she had not given up, I had. In my lack of confidence in her, I turned her appropriately challenging problem into several little problems that she could do easily: 7+5, 12+1, 1+1. I had originally trusted her to do a more complex problem. Then I stopped trusting her when I got nervous. Worse, I conveyed that mistrust by taking away that challenge and making the problem easier. It's like when the boss takes away a complex project that you’ve been working hard on, and replaces it with a bunch of simple tasks.
Ask a question. Then stop talking.
One hallmark of strong problem-solvers is that they can work through problems and persevere when they face challenges. Perseverance takes practice, and a lot of faith. To develop perseverance, you must have faith that if you keep working at a tough problem, it will lead to success. The only way to learn to have faith is to have many experiences struggling through problems and experience a sense of accomplishment.
After a while, I learned to ask appropriately challenging questions, and then…stop talking. And wait. And wait. As long as my student didn’t stop thinking, I stayed out of the way. Only when my student asked a question, was ready to respond, or started getting visibly upset did I try to redirect her. I learned to embrace the awkward silence. This silence meant that my student was still working on it and hadn’t given up.
I knew I had mastered this when I was tutoring one student who, whenever I asked a question, would go dead silent and stare at the ceiling. For an insanely long time. Like eyeball-drying-amounts of time. If I’d had a SmartPhone, I could have read and responded to three parent emails by the time he finished adding ¼ to ½. And then, invariably, he would come out of his stupor and croak the correct answer.
With him, I mastered a more advanced skill: feeling awkward and anxious without his noticing.