Read more about how approaching math from multiple entry points and using different strategies and tools to solve problems turned educator Lynn Smith's world around.
Author's Note: This piece was largely written before the COVID-19 crisis closed schools across the country. However, many of the practices highlighted here are more important than ever. The impact of COVID-19 will be felt for many years to come. The education of our nation’s children has been upended and their well-being deeply impacted. The disparities in access to high-quality instructional materials as well as inequities in implementation have been forced into view. The educational and social-emotional outcomes for all our children are largely dependent on the ways we respond and the resources we offer to teachers. Our educational first responders (teachers) must be empowered to use high-quality instructional materials so that every child may learn despite these unprecedented times. We owe them no less than this.
Here’s something I don’t often share about myself: I failed my 10th grade geometry class. The truth is I struggled as a math student. I didn’t understand the content, the materials, or the way math was taught. I didn’t recognize the connections to real-world applications, and found it challenging to accept that there was only one way to solve a problem.
Fast forward a few (many) years and to everyone’s surprise (including my own) I became a math teacher for students with special needs, then a math specialist for EdReports, and am on the road to getting my doctorate in curriculum and instruction in elementary mathematics. In order to give my students engaging opportunities to learn math, I first had to learn and understand the content myself. I immersed myself in all things mathematics and found support from fellow colleagues. Soon enough, the way I had once perceived math completely changed, and I was bitten by the math bug!
Like many new teachers, I had a lot to learn when I began to teach struggling math students. But in many ways, I understood where my students were coming from because I had been in the same boat. Just like them, I had a hard time connecting to the content. This experience made me approach my classes in a different way than I might have if I had always excelled.
My goal was to make math meaningful and engaging to my students. To that end, I knew students would need to approach the content from multiple entry points and use different strategies and tools to solve problems. In order to understand math and build critical thinking skills, they needed to know more than calculations and algorithms.
With the help of supportive colleagues, I leaned into college and career-ready standards. The more deeply I studied, the more I understood the benefits for all kids. Ultimately, the standards were key in offering the kind of math instruction I believed would speak to my class.
During my almost two decades in the classroom, I have learned some lessons that I would love to pass along to fellow educators. These best practices have been invaluable to me as I strived to inspire students at all levels to learn.
1. Build a Strong Foundation
The instructional shifts for mathematics focus, coherence, and rigor provide the foundational building blocks for future content that all students need for success no matter what path they choose.
Focus indicates greater concentration on fewer topics with the greatest emphasis on what we call the ‘major work of the grade’ (e.g. problem solving related to addition, subtraction, multiplication, and division of whole numbers and fractions; ratios and proportional relationships; algebraic expressions and equations, etc.). As an educator, it’s easy to get into the habit of treating the standards like a checklist, but we have to remember that not all content is prioritized equally nor should it be. Some topics require greater emphasis based on the depth of concepts, the time it takes to master those concepts, and their importance to future mathematics content.
The second shift is coherence which links concepts and topics within and across grade levels. So often when I was learning math, I didn’t understand how one concept connected to another concept I had learned the week before (much less the year before!).
But for my students, I could see how coherence made a huge difference in their learning every day. When they could connect a familiar concept or skill to a recently introduced one, they were much more likely to grasp the new concept. Our instruction and materials should help students to build an understanding of math by offering opportunities to connect prior knowledge to new content. As teachers, we must help students build bridges and make connections so they may actively engage in their learning.
Then there’s rigor. When most people hear rigor, they think harder problems and more problems. But in the mathematics standards, rigor is not about longer, harder, or more problems. Instead, it’s about ensuring students are able to create a process for solving problems and have multiple opportunities to apply what they have learned through conceptual understanding, procedural skill and fluency, and application. Without rigor, the content of the major work of the grade may never be truly mastered.
Whether I work with students or adults, I always return to these three shifts because I know they build the foundation that lays the path to success in mathematics.
Building a strong understanding of the standards is essential, but too often the standards become immovable and taken very literally. Earlier in my career, I had the same line of thinking. For example, the use of number lines is not mentioned explicitly in the standards until second grade; therefore, I didn’t think a number line could be used at any time in kindergarten or first grade. And that is simply not true.
What I came to learn is that there’s a difference between content and the tools and strategies that help students understand the content. While the number line is first mentioned in a specific standard in grade two, that doesn’t mean the tool itself can’t be used in kindergarten to guide students through grade-level skills such as counting and cardinality. It’s how the tool is used that dictates whether or not the instruction is off grade level or developmentally inappropriate.
What’s more, using a variety of tools and strategies to build students’ mathematics foundations develops familiarity. If a student is exposed to the number line in kindergarten to practice counting then is reintroduced to it in second grade for addition and subtraction, the concept will be less foreign to them.
Strategies, like tools, build upon one another. Using a consistent variety will help students build mathematics knowledge and develop familiarity and confidence. When I was a student, I was often taught one specific strategy or procedure to find an answer. So if that didn’t work, like most students, I was likely to give up. When we embrace the fluidity of the standards, we stop limiting our ability to meet the needs of different students and we allow students multiple pathways to solve problems.
3. Invest in Aligned, Quality Mathematics Materials
If college and career-ready standards are the compass, then high-quality, aligned instructional materials are the paths that allow us to get from one destination to the next. Quality curricula support processes such as mathematical modeling that allow students to find different entry points in solving problems. These materials play a critical role in supporting access to content, tools, and strategies that all students need to succeed in math.
Like me, many teachers in the classroom did not necessarily learn math the way it’s being taught now, and we certainly didn’t have access to the materials being used today. Quality materials can provide support so teachers can ensure there are no gaps in students’ foundations while also freeing up time to focus on bringing lessons to life, differentiating instruction, and inspiring kids at all levels to learn.
When we struggle with math, we tend to believe we are “not good at math.” We equate failing with being a failure. It took years—through college, teacher training, and time spent in the classroom—before I fully internalized that I was not that same student who’d fallen short in geometry.
Now, I am lucky enough to understand that my journey would not have happened without the setbacks I faced as a student or what I learned from the struggles of the students in my classroom. My experiences were integral in shaping the teacher I became and the relationship I had with those I taught.
As I strive toward an advanced degree and spend each day supporting EdReports reviews of mathematics instructional materials, I continue to draw on the lessons I learned about how students and teachers interact with content and materials to build mathematical knowledge. I believe that each child is unique and with robust standards, high-quality instructional materials, and strong instruction, all students have the opportunity to be successful.