This is the look that makes my job worth it, when a student finally gets it!
I have the fortune of working with very dedicated students at Shanghai American School. Most of them have been working on mathematics since the young age of two. They start counting with their grandmas at the park. They start adding numbers. As soon as possible they start working with tutors. However, there are plenty ocassions when they do not know why something works, or how it works. That is where the magic happens. When we are able to listen to our students, to find out where they are in their understanding of mathematics. Some of them know the answer, they just do not know how they got it, they do not know how that looks like, they have trouble explaining their reasoning, and most importantly they struggle with making connections of different mathematical concepts.
When teachers are listening to their students, they can ask questions and guide their student to discover HOW math works, and how all mathematics are connected!
Let’s provide all our students with plenty of opportunities in the classroom to make sense of mathematics, by allowing them to experience some productive struggle while solving an authentic problem, a messy problem some call it, a problem that allows them to make connections, to solve in different ways, where students can focus on MAKING SENSE of what the problem is about.