Stephanie Burroughs, Ed.D.

Curriculum Leader, K-12 Education

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Encouraging our Students to Learn Mathematics

​I've decided to spend some time looking at each of the Guiding Principles for Massachusetts Mathematics Programs. These 6 principles are important statements that shape how we should think about building and sustaining a successful mathematics program, what we should be emphasizing in our instruction, and how we should prepare our students to be citizens that embrace mathematical reasoning. 

I'm not going to define these for you, but I am going to summarize what they mean to me and what I believe they should mean for Mathematics instruction. I assume that, since you're here, you can read and can google search the guiding principles all on your own. The Massachusetts Frameworks will even take these principles and weave in which Standards for Mathematical Practice are associated with them. I love that blue book, it's a great resource and a great starting place when you are trying to unpack this supposed "new math," but I plan on discussing my own philosophy behind these principles and the direction I believe we should be taking. So here it goes...


Guiding Principle 1 for Massachusetts Mathematics Programs:

Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of understanding.


When I read this aloud, I'm thinking "well of course we should be doing this," but it actually is pretty difficult to do using traditional instruction methods. Most of us grew up rehearsing mathematics concepts and not discussing the why, how, or when these concepts are used and for what practical purpose. This method of learning, rehearsing the same problems until you get it right enough to do well on the test, limits the number of students that can be successful in Mathematics and prevents depth of understanding. It also helps sell the story that Mathematics is a subject that not all kids can learn because it is what it is and that's it. 

Mathematics makes sense of the world around us and our students are missing that part of the conversation. For me, this first Guiding Principle clearly points out a need to abandon memorization regurgitation mathematics and focus on inquiry, reasoning, and discussion. We can make mathematics engaging and exciting for students when we start to think about teaching mathematics in new ways. 

Mathematical ideas should be explored in ways that stimulate curiosity.

Let's start asking questions differently. Let's start differently. Instead of coming into class with a warm-up that reviews pre-requisite skills, introduce some vocabulary and processes, and then send the students on their way to rehearse what they've learned, let's create the need for the mathematics they will learn that day through inquiry and discussion. Inquiry based learning gives every student an entry point and levels the mathematical playing field by letting student intuition and reasoning spark a discussion on the mathematics needed to solve a problem. If we pause instruction and ask the students, "what do you think about this?" or "how do you think we could find this answer?" you allow students the opportunity to show what they know. 

I'm an advocate for inquiry because I believe that we will never stimulate a students curiosity by telling them how it is. Any great discussion or debate I have ever been engaged in where I've learned something and felt confident in what I know has been a two-way conversation, not a lecture from an all-knowing source. With inquiry, every student and every teacher is questioning and developing their understanding together. Every student in the room, no matter where they're at in the standard deviation of class performance, has an opportunity to debate a solution strategy before we intimidate them with the "right way" to solve it. 

Mathematical ideas should be explored in ways that create enjoyment of mathematics.

We have to stop being so rigid. We are not our worksheets, our standardized assessments, and our two column proofs. There is more to learning mathematics then being able to perform on a standardized, scripted assessment. It's frustrating to be a teacher, read the research, and then be thrown a state standardized assessment that contradicts that research. We have to work against this and convince our students that there is more to math than multiple choice tests. We cannot let our students believe that mathematics can be reduced to the memorization of formulas and recall of basic three step processes and we cannot let our students believe that if they can't do these on command, then they cannot do math. We're more than this.

Data Science is one of the fastest growing fields in the world right now because there is a need for Mathematics. What does Data Science do? It takes a real world problem with real world data and develops an algorithm that predicts future trends or dissects the meaning of the data and reports out on that meaning. Why aren't we doing this in Math class? Mathematics was created to better understand the world around us, build a better world around us, and we're not telling our students that enough. We should have discussions, debates, presentations, and writing all be a part of the way we assess our students, but we should also make those topics and those projects applicable to our student's lives. We should be giving our students opportunities to create with mathematics.  

Mathematical ideas should be explored in ways that develop depth of understanding.

We are missing the boat when we do not expose students to the true purpose of mathematics instruction: to support the development of logical thinking, reasoning, and problem solving. If you think about it, although Shakespeare is nice to read, English Language Arts isn't claiming that knowing Shakespeare will make you successful in life. I mean it might for some, but for most reading Shakespeare is an exercise in breaking down complex text and deciphering the meaning; this develops depth of understanding. What English Language Arts has been able to do well before Mathematics even thought of it, was make the discussion and the decoding of meaning the focus of instruction. Shakespeare is a vehicle, it's not the lesson. 

Mathematics instruction should be doing the same for students. Just as we do not need to memorize Shakespeare, we do not need to memorize formulas. We need to discuss them, compare multiple solution strategies, and create learning experiences that inspire students to explore mathematics through their own problem solving. We have to stop looking at the quadratic formula as the lesson and start looking at it as an opportunity to have a discussion on the beauty of multiple pathways to the same solution. This will help our students develop depth of understanding.

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