Often in math we only think about the content to be taught at each grade level. Third grade learns multiplication; sixth grade learns negative numbers, etc. In reading, there are common learning themes that follow students from kindergarten through twelfth grade; these include fluency and comprehension. Students continuously work on these skills to become proficient readers. The same is true in math. There are 8 specific mathematical practices that students work toward using to think more like a mathematician than just as 2nd grader or a geometry student.
How students use mathematical practices
Teachers of math focus on not only what each child needs to learn each of their 13 years, we will also focus on instilling these mathematical practices. Some simple ways they can be supported is through questioning and creating a positive attitude toward math. Consider the following interactions with a student
“I can’t do this, it’s too hard.”
Response: Don’t give up. Think about what makes sense. How can you think about this problem?
“Is this right?”
Response: Does it make sense? Can you prove your answer by explaining it, doing it another way, or drawing a picture?
“I found an easier way to do it.”
Response: Does that work just for this problem or have you found a mathematical rule? Will it always work? How do you know?
“That’s not the way we were taught in class.”
Response: There are multiple ways to solve a problem. Can you show me the way you did it in class and we can compare it to the way I learned it? Why do both ways work? How are they the same?
“I didn’t learn how to do this.”
Response: Think like a mathematician. Let’s reflect on what you already know and see if we can figure it out by looking for patterns or applying rules we know are true.
“I don’t get it.”
Response: What part is difficult? What do you know you can do and where does it get hard? Can you create a picture or model that can help you ‘see’ the problem differently so you can think about it?
These approaches to math frustration can trigger efficacy in students so they feel capable of working it through. Even though math can be difficult for some students (and frankly many adults), sometimes the struggle pays off. When students are coached through the math, they’re more likely to master their own learning than just watching someone else do it or listening to someone tell them how.