What are the characteristics of a highly capable math student? Does it mean that the student can calculate quickly or accurately? Does it mean that that student is the first in the class to answer a question? Does it mean that the kindergartener can do multiplication problems, or the first grader can do division problems?

Habits of Mind of Mathematicians

Current thinking about math skills calls upon us to consider not just ability with the operations but also habits of mind that support a student in thinking like a mathematician. Can the student construct a viable argument? Can they create a mathematical model to explain their thinking? Can they choose the appropriate tool or strategy for the problem at hand?

These habits of mind are called the Standards for Mathematical Practice. There are eight standards that name all the things skilled students should be able to do in addition to the math skill standards. The Standards for Mathematical Practice are always presented in a list but thinking of them as a circle conveys a better model of visualizing a child’s growth. We want children to be supported and grow in each area. There is not one area that is more important than the others. Becoming skilled in all of them is key to becoming a well-rounded mathematician. I created this graphic to show this idea.