Think about this year. Well, think about each year you have been in the classroom. We spend countless hours, evenings, and weekends considering which tasks, questions, and opportunities would be best for supporting students in mathematics. What is our goal – mathematical thinking.

Now, what I want you to take time to consider is that what we often think is the purpose of our lesson and task, may not be what the student views as the take-away. I have seen many teachers using learning goals in mathematics. They will often write the learning goal at the beginning of a lesson. This learning goal, in student friendly language, is meant to be the compass for instruction and learning. It is meant to provide students with a clear depiction of what they will be learning about and maybe, if success criteria is included, what they will need to demonstrate in order to achieve this particular learning goal. Learning goals can be written as I can… statements or We will be able to…statements, so that students can envision what they will be able to do at the end of the task. It feels good to provide students with insight into the direction and purpose of the lesson. However, what are the impacts?

At the end of a lesson, students, when asked what they learned, will often state the learning goal. They will refer to this as the purpose of the lesson and describe how they have achieved the goal. Ask yourself this: is the learning goal usually content focused or learning focused? I ask because I think it is really important to consider what students are taking as the message of our instruction and of mathematics. Are they viewing the goal as understanding a concept (i.e., being able to record numbers in expanded form) or as strengthening their mathematical processes (i.e., problem solving, reasoning, communicating, visualizing, etc)? This is what I want us to consider.

Now, let’s go beyond the end of the lesson. Let’s consider asking students one question: what did you learn this year in math. I will guess that the vast majority of students will share a particular concept, such as order of operations, comparing numbers, input-output, measuring angles, etc. Is this what we really want? Isn’t our goal to support students in thinking mathematically – to encourage and support them in strengthening their mathematical processes so that they can approach a problem and be able to navigate it, be able to clearly articulate their thinking, to be able to reason through a task, to be able to visualize a concept, etc.

My concern is that while we may think that our instruction is supporting students in strengthening their mathematical thinking, we may only be focusing on specific mathematical concepts in isolation. While concepts are very crucial, it is the processes that we want students to deepen. Mathematical processes are verbs – they are thinking. We want students to be mathematical thinkers not mathematical doers.

What will your students say is the goal of math? What will your students say are the take-aways from this year’s math class? Sometime this month ask your students what they learned this year in math. Be prepared, you may not hear what you expect. Sometimes what we teach for is not what we get.