I was recently asked to tutor a high school student who was struggling with natural logarithms and the number e. My first reaction was, “Oh. Crud. I don’t remember that stuff very well.” My second thought was, “Not an issue! My schedule is packed, and I’m not even available to tutor!” My third and more thoughtful reaction was, “Wait. If I can relearn this, I can better help her learn this.” So, I did some exploring and found an explanation of natural logs that I found useful and interesting and very different from simply memorizing a process. I passed it along.
Not long after that, I was talking to a friend who also tutors. He was lamenting that he no longer feels comfortable helping students with calculus because he is out of practice.
Yes, this makes sense. From one perspective, it is necessary to have the expertise at your fingertips in order to most efficiently teach another person. When you tutor, you want to be efficient for the sake of the student who is learning and the parents who are paying. Time is money.
But from another perspective, demonstrating to another person how you learn can be revealing and inspiring. Some of my most effective teaching moments have been when I said, “I don’t know the answer to that. Let’s figure it out together. How could we begin? How would you begin?” (I’ll admit…often times I fake it. Sometimes I pretend I don’t know what I’m doing so that I can demonstrate the learning process or inspire a kid to help me. Other times I pretend I do know what I’m doing because, well, don’t we all??)
So, how does this matter at all to you if you are not a math teacher…or even a “math” person? At the very least, it means that you CAN be helpful to your child’s mathematical learning (and any learning, for that matter) even if you haven’t mastered the material. Even if you don’t consider yourself to be a “math person.” Beyond simply supporting your child in any subject, you can also shift your own perspective so that you understand that you are setting an example for your child that learning is a lifelong experience, that it requires persistence, and that problem solving takes precedence over “answer getting.”
- Remember to never say “I am not a math person.” Don’t pigeon-hole yourself or your child. And while you’re at it, don’t do that with other things either. This is a general approach to life, not just a mathy one. Keep the doors of possibility open for your child (and yourself.)
- When your child asks for your help with math, try. If you don’t understand the material they are working on, ask them to explain what they know. Ask them to teach you as if you were a new kid in class. If you do understand the material, take the exact same approach – ask your child to explain what they know. You are playing the coach, not the expert.
- If you both are stuck, brainstorm. Can you draw pictures of the problem? Can you look it up online? Does that intimidate you? Imagine how your kid is feeling. Pretend it doesn’t intimidate you, and do it.
- At some point, your child is going to get frustrated and say, “Can’t you just TELL me the answer??” Maybe you could. But you won’t. Because you are trying to demonstrate that it’s NOT the answer that’s important. It’s the process of learning how to problem solve. How to persist. How to think.
- At some point, YOU will get frustrated and want to say, “Here’s the answer.” Don’t do it. Remember that you are trying to demonstrate that it’s NOT the answer that’s important. If the problem solving process is backing up against dinner time, take a break. Call it a break. We all need to learn how to take breaks.
- Start this process early with your young children so that you can easily apply it when they are in high school. Or better yet…if you have done this when they were young, they will know how to do it themselves when they are older.
- WARNING: This approach requires time. With your children, you have to have the patience to let them be wrong. If you’re not ready to be patient, don’t attempt this…you’ll just get frustrated.
And what about when you run into ways of learning math that you are unfamiliar with? Even math teachers do. That’s when you double down on the approaches above. That’s when you don’t have to pretend you don’t know, and you can honestly coach your child.
Keep in mind the difference between a fixed mindset and a growth mindset. When I’m teaching, if I always have the answers at my fingertips, then perhaps my students are under the impression that I just know this stuff and have always known it easily. They haven’t seen how I have had to work and struggle to understand the concepts that they now struggle with. If, on the other hand, they see me go through my own problem solving process, they learn that there is a pathway to knowledge. They might follow mine. Or they might gain the confidence to try their own.
The other day I tutored a student who needed help in trigonometry. It’s been 9 years since I’ve taught trigonometry in a classroom. I no longer have all those facts and formulas at my fingertips because I no longer work with them daily. But I do know how to coach a student. So, as she worked through each problem, I asked questions. “What would a diagram of this look like?” “How can you be sure?” “Is that the only way to do it?” “Is there another problem like this that can serve as an example?” “Would your class notes be helpful to refer to?” “Why does that formula work?” “Could you have used a different formula?” Along the way, she realized she was capable of more than she had thought. So did I.
(Mathematically…math is about so very much more than numbers. Math is patterns and processes and generalizations and universalities and relativities and spaces and…and…so much! You can help launch your child into the adventure of math by coaching them through it, rather than delivering them immediately to the answers. And, if you really feel you aren’t the person to do it, look for this quality in the tutors you hire.)
Photo credit: Silenceofnight on Visual Hunt / CC BY
I love a good roadmap for being a better parent and coach, and this one is excellent. Thank you!
Many roads to your destination…
I learnt math as a set of algorithms, never quite understanding the notations but becoming quite adept at it. Now teaching my kids I want them to understand more than I did and have followed the approaches you’ve outlined without realizing the impact and importance. I have my shortcomings, mainly impatience. My younger kid, 10 suffers math stress and I realize that I will have to learn along and show her that maths is about problem solving and not just number crunching.
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Loretta, thank you for your comment – and your honesty. Your daughter is lucky to have a mother who is willing to learn alongside her! In doing so, you’re also demonstrating growth mindset (rather than fixed mindset) to her…and setting an example that we all learn differently. I hope your daughter begins to have a better math experience at school!