What are the characteristics of a highly capable math student?
May 24, 2022
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.
I am often asked how teachers can support a highly capable student and the first thing that comes to mind is the Whole Math Student graphic. I think first we need to ask if the student is well – balanced. Beyond being able to calculate quickly and accurately, can the student engage in the other marks of being a strong mathematician. Can they also construct viable arguments? Can they choose from a variety of strategies when solving a problem? Can they look for and make use of structure? Can they come up with new problems and explore them? (see more about this math practice here) Until a student demonstrates computational fluency as well as facility with the math practices, I don’t consider them well-balanced. To help them grow, we need to identify the math practices that they still need to work on and support them there. These math practices can easily be something a child practices at home.
Using the Standards for Mathematical Practice
Some children are working on MP 1 “Make sense of problems and persevere in solving them.” These students are figuring out what the problem is asking, thinking about how to get started, and learning how to stick with the problem when they don’t know what to do. This can apply to math problems but also other life problems that occur. When a friend says they don’t want to play that particular game, what does your child do? Do they modify the game, suggest alternatives, try a different approach or do they give up and move on to something else? What does your child do if they are playing a game with you and don’t get the cards they were hoping for? Can they adjust their strategy and plan a different way to win the game?
Other children are working on MP 3 “Construct viable arguments and critique the reasoning of others.” Can your child explain their thinking to you and tell you how they got to their answer? Can they create a model with manipulatives to show you their thinking? Can your child respectfully disagree with someone?
Another child might be working on MP 8 “Look for an express regularity in repeated reasoning.” They are comparing today’s problems to yesterday’s problems and finding connections. They are generating their own rules about the work and then testing those rules to see if they always work.
These Standards for Mathematical Practice are used by mathematicians in their real-world work. When students use the practices, they are thinking like mathematicians. They are also practicing skills that will help in math and in life.
Building a Solid Math Foundation
For so long math has been taught as a linear subject with parents and teachers ticking off another box each time students show proficiency with another skill. It is time we start thinking more holistically about math and think about math skills as well as math practices. It is not about getting to the top rung on the ladder as quickly as possible. It is about building a solid and deep foundation as we go. This foundation will serve students in their future endeavors in math, not just help with today’s task. These skills are also life skills that will support the child in many ways as they encounter everyday challenges.
