What is the purpose of math class?

Would you agree with me that many, if not most of us, were in classrooms as students where the purpose of math class was to get answers. We were taught the most straightforward, non-confusing, easy, step-by-step way to get answers. No room for confusion. We’d circle our answers. Take it home. Parents recognize it. Done! 

Consider this: If the purpose of math class is getting answers, is teaching math even necessary anymore? 

We have computers, calculators, cellphones, and now AI that can help us get answers to almost any math problem without us having to think at all. If getting answers is the goal, why do we need math class at all?  

Most classrooms are still organized around answer getting. I recently visited a high school class. The teacher was a great guy and had a good rapport with his students. When they got to work, he walked up and down the aisles “giving feedback”:

• “Hmmm, this, not that.”
• “Ah, add not subtract.”
• “Ooh, first here, then there.”

These were all great directions to give students — to get correct answers. Each changed their work as he instructed, and class went on. 

If our purpose of teaching math is to have students get answers to math questions, then it was happening in this class.

But what if the purpose of math class is not about getting answers?

What if the purpose of math class is to develop mathematical reasoning?

I don’t mean just some fuzzy, think better reasoning. I actually mean reasoning mathematically. That students are using mathematical relationships to logic their way through mathematical problems and in the process creating connections to new content.

I’ve created this graphic showing what I call The Development of Mathematical Reasoning — a nested set of domains that are hierarchical. These domains are built on and based on each other.

It’s not just about students getting answers to addition and subtraction questions, or answers to multiplication and division questions, or solving proportions, or graphing a function. It’s about students creating new ways of thinking, ways of reasoning more sophisticatedly, and ways of reasoning about more complex things. It’s building students' brains so that they’re reasoning with a more dense, interconnected web of relationships that build on each other.

Mathematicians logic their way through problems using what they know, based on the mathematical relationships and connections that they own. This process creates new mathematical relationships.

It doesn’t just happen.

We need to actively, intentionally help students develop their mathematical reasoning.

In our mini workshop  Transforming Teaching 6-12: Small Shifts, Big Impact we help you think about what we can do with students, wherever they are in this set of domains, to be able to learn grade level content and wrap back into building the content that they need from previous domains.

In Summary

If the purpose of math class is about getting answers, students may never develop and use the kind of reasoning that the problems were intended to develop.

Math class can and should be about building mathematical reasoners, math-ers who are doing the mental actions of math-ing. This shift from answer-getting to reasoning-building requires specific teaching moves, and that’s exactly what we explore in the Transforming Teaching 6-12: Small Shifts, Big Impact mini workshop

Make it happen: www.mathisfigureoutable.com/transformingteachingsecondary