The picture above is of my son doing a Venn diagram challenge problem in the first chapter of Art of Problem Solving’s Counting and Probability. It’s a tough book, and a tough problem, especially for a 10 year-old. He knew exactly how to do it, but had made a few careless arithmetic errors so I asked him to try again and be a little more careful.
He sighed: “Can you just read it out loud to me? I want to do it together.”
By “do it together” he didn’t mean give hints, tell him the answer, or hold his hand through the work. He just wanted to work through his thought processes out loud to someone else. So I read the problem out loud. Then I listened and repeated some of his intermediate steps back to him. A lot of our math work is like this – me right by his side providing feedback or just a sympathetic ear. And that’s ok! I see a lot of parents get wrapped around the idea that their children should be working mostly independently at this age and they get disappointed when they can’t just hand their child a worksheet and have it done efficiently. It’s wonderful if your kid can go off and finish a few worksheet pages by themselves but there’s also nothing wrong if they can’t.
I would also argue that there’s such a thing as too much independent work. Human interaction almost always enhances learning, making math (or any subject) much more pleasant and also helping retention. The ability of a parent or teacher to provide instant feedback should also not be underestimated. Being able to correct mistakes immediately, provide guidance, or simply see where a child is at, are all easier when you’re sitting right next to them.
Working independently is an important skill that all students will need someday, but its important to remember that someday doesn’t have to be today! In my next post I’ll discuss some of the techniques you can use for getting students to work a bit more independently in a natural and gradual way.