Musings on Teaching Math
I have read several recent commentaries on techniques for teaching math more effectively, including one entitled “Why Do Americans Stink At Math?” by Elizabeth Green which appeared in the New York Times. As the title would suggest, in general, Americans are not math literate. Indeed, we kind of suck at it (you may be relieved to hear that you are not the only one!). Our children perform poorly when compared to their same-aged peers in other countries. So what are we doing to undermine their performance? Or, perhaps more importantly, what are we not doing to boost motivation and enthusiasm for solving mathematical problems?
The answers to these questions are complex, but several promising ideas are presented in the article referenced and others; ideas that are central to Guiding Curiosity and easily adopted by parents.
One core suggestion is that teachers should be coaching kids rather than merely disseminating information. Children from countries performing well on tests of mathematics can be found in classrooms where they are encouraged to invent, think, and talk about solutions to problems. These children initiate solution finding, and in doing so, realize when they are on the wrong track and are motivated to explore different strategies and find the correct answer. Their teachers don’t show them how to solve a problem and expect them to follow that lead. Instead, these students are presented with a problem and invited to solve it first their own way and eventually as a class. Teachers guide these students to discover the algorithm for themselves. Our children here in the US are more likely to be found doing rote tasks, solving page after page of equations. In doing this work they are disconnected from other students in the room and real world problems.
For parents and other caregivers (that’s you grandpa), this observation suggests that you should be listening carefully to your child’s musings about any problem, not just math problems. Listen then ask questions, encourage talking, even arguing about a solution. Do not automatically give an answer, but rather structure the problem as a challenge or even a game, guiding your child to his own solutions by making suggestions, inviting new approaches, or providing tools to explore and discover. Create an atmosphere where problem solving can involve creative and inventive thinking, as this is stimulating and fun. Mistakes are okay, as long as your child made the mistake on his own terms and not following your agenda. Instead of pointing out a mistake or a wrong answer, steer thinking in another direction with simple comments beginning with “I wonder what would happen if..,” or “I am thinking it could be more like…”
The second message from musings on teaching math that translates well for parents across all interactions with their children is that we can’t really teach kids to do things well or perform as an expert. Rather, we can teach kids to persist and practice problem solving (versus rote practice). The Guiding Curiosity approach invites you and your child to rehearse the steps of inquiry. Asking questions, developing observation and measurement skills and making comparisons. Do this daily, even several times a day. By repeating these steps you are honing critical thinking. Effective experimenting depends on trying out different approaches, or applying what works and realizing what does not. Persistence over time (not in one sitting) builds knowledge. So revisit problems or topics. If your child does ask the question, you can remind him that you were discussing birds, shells, or space, and prompt for another question.
The final message relevant for caregivers is that effective teachers are often talking to other teachers about their approaches. They exchange information on promising tactics, as well as those strategies their students reject or ignore. So, talk with other parents or grandparents about forming effective questions, stimulating observations and finding the language that captures those sensations. Trade ideas for measuring and experimenting. Most importantly, use these conversations to become excited about how to explore with your child (grandchild) the world around you both. Excitement is motivating and contagious. You too are learning and discussions with other parents or caregivers will highlight new options and hopefully motivate your own practice and persistence.
Take a clue (or two or three) from math teachers at home and abroad and try out new ways to motivate learning.