A recent article published by Jo Boaler on the youcubed website entitled “SEEING AS UNDERSTANDING: The Importance of Visual mathematics for our Brain and Learning” has really got me thinking about the direction that math education is heading and I AM EXCITED!!!
As a young student I recall my teacher constantly telling me to stop counting on my fingers and that I had to memorize the facts. Memorizing became a useful tool for me as I progressed further in my education that I feel as though it wasn’t until I started teaching that I truly began to understand math. I recall during my student teaching experience (in a 6th grade classroom) my master teacher reading the book “Sir Cumference and the First Round Table” and it was during his reading that I first understood what pi represents. Prior to hearing this book pi to me was just a never ending decimal that we used when dealing with circles.
In a nutshell, Jo Boaler’s article focuses on how the brain truly LEARNS math and the importance of visualization and the use of manipulatives in the learning process. It gives three recommendations to teachers and parents: Encourage and celebrate students’ visual approaches, focus on finder discrimination and encourage finger use, and math teaching and learning needs to become more visual.
A few summers ago I had the privilege of taking a course entitled Patterns 1: Foundations for Algebraic Reasoning offered by Ruth Parker and the Mathematics Education Collaborative (MEC). This class completely changed the way that I teach and started moving me down the path of visual mathematics and using manipulatives to help students better understand the concepts of Algebra. This class focused on using tasks to help students explore and make sense of patterns and how those patterns are represented in different functions. Since integrating patterns tasks into my classroom, students have had a much easier time learning the concepts that will lead to upper level mathematics.
The state has jumped on board the visual mathematics bandwagon and thanks to the legislature is offering a paid opportunity for all high school math teachers to learn more about some of the productive routines that can help promote reasoning and student discourse in the classroom. The course (which can be taken online or in-person) is entitled Developing Conceptual Understanding through Productive Routines. The productive routines covered in the training partner nicely with the patterns type tasks promoted by both YouCubed and MEC. (Depending on the time you read this article, you may still be able to register for the course)
This shift from memorization to conceptual understanding with a focus on visualization and using manipulatives is a welcomed change to the rote memorization of formulas and theorems that mathematics has historically been. The Standards of Mathematical Practice that was introduced along with the Common Core State Standards has helped in facilitating this change.
I highly encourage all math teachers to strongly consider implementing more patterns tasks, number talks, and manipulative usage. Ever since I started integrating the concepts and ideas into my classes, I have seen tremendous growth from my students in their understanding of concepts which, I have been told, has continued on into upper level math courses.
Aside from teaching, I also coach baseball (JV for the high school and AA for American Legion) and enjoy spending time with my wife and son.
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