Becoming Mathematicians

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.

~William Paul Thurston

So often in mathematics students experience the same learning routine where skills are modeled and practiced, while being guided by the teacher as needed. While there is nothing wrong with having students learn math this way, I have found, when I implement this approach solely, many of my students rely too much on me when the assessment comes around. They can solve the problems using the given equation or the computation that was taught, but they don't truly understand why it needs to be solved a certain way or when to solve it a certain way.  One could compare the situation to a robot; the robot performs the task you tell it to complete, but it doesn't understand the reason behind the task.

My goal is to have students leave my class thinking as true mathematicians. Long term learning sticks when students are able to struggle and work through their experiences to gather knowledge versus knowledge being bestowed upon them. I have been working closely with our district math specialist, Mrs. Manjarres, to create an atmosphere for my students where they have the opportunity to explore new skills and concepts on their own and at their own pace. By no means did this mean we were not teaching, or doing any work, rather we creatively and effectively crafted situations for the students to explore these concepts and actually learn the skills. We chose to use a unit on rational numbers because it focused more on the understanding of vocabulary rather than procedural problem solving. We thought this unit would be a good place to dip our feet in, before jumping in head first!

The students worked through several activities that were posted on Google classroom. In addition, we checked in on the students understanding and learning in one-on-one meetings and small group discussions.  We had some terrific thinking happening in the classroom, and great questions being asked throughout the unit. We enjoyed being able to appropriately challenge each student independently by asking them deeper and deeper questions about the skills within the unit. The greatest thing was when students started finding cool videos and/or websites and began sharing with their classmates what they found. At the end of our hour and fifteen minute class, we would hear: No! I don't want math to end yet!

When the assessment rolled around, the students really thought like mathematicians! I saw a great change in the confidence level going into this test compared to the ones they took in the past. The students took the time to think more about the questions being asked rather than just solving the problem to get the right answer.

Mathematicians solve problems that have no “right” answers; the students worked through the unit as problem solvers, A.K.A. mathematicians.