In math instruction, everyone wants a “magic bullet” strategy that will help all students understand math immediately–and, I’ve found it!
Many times I’ve had students in my office struggling with a difficult concept we’ve discussed in class or, unfortunately, upset about a recent bad grade on a quiz. After going over the problem and doing some examples, I hear a common refrain: “I understand the problem when we do it together but when I sit down to take the test I forget everything and my mind is a blank. I read the book and the examples and I know I that know the material. What’s wrong with me?”
I can see the frustration in their face and hear it in their voice. And I completely sympathize. Luckily there is a helpful solution. It’s a common phrase among mathematicians: Mathematics is not a spectator sport. To really learn something, to see the pattern of a solution and to internalize it, you have to get your hands ‘dirty’ and do it yourself. I realize that can be a tall order so I follow the advice I was given when I struggled with the same thing as an undergraduate student.
When I work through an example with a student, I’m always careful to make sure they are contributing to the development of the solution. I can see the big picture but in the beginning they can often only help with the small steps. Once we’ve finished with that problem and before we move on to the next question, I put away our previous work and have the student work through the problem again, step by step, completely on their own. Surprisingly, even just recreating a solution they just saw minutes ago can be a challenge. Sometimes I’ll push a bit more and ask how things would have changed had this part been negative, or what if that part had a difficult denominator. By playing around with the material on their own, the student internalizes the procedure and masters the concept.
It may take some time but the good news is that it works! And it works really well! The student doesn’t just walk away ‘feeling’ like they know something or understand what they saw me do. They know it! Because they just did it themselves and they made the process their own.
By Michael Munn, Private Tutor
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