The myth that some students cannot be successful in math because they lack some inherent talent, skill, or intuition for numbers is all too persistent among kids and adults, writes John SanGiovanni, an elementary mathematics supervisor in Howard County, MD, in McGraw-Hill’s Medium.
The answer is far simpler: Anyone can be a math person if they have time to experiment with numbers and strengthen their number sense. As an elementary teacher, I found that my students really struggled in this area. I was in graduate school at the time, and I wanted to find some tools to help my students, so I studied number sense. Here’s what I learned:
Number sense is an awareness and understanding of what numbers are, including their relationships and their magnitude, what happens to numbers when we operate on them, and the use of mental mathematics and estimation.
Number sense is also mental calculation, computational estimation, recognizing part-whole relationships and place value concepts, and problem solving. Opportunities to play with numbers are how we strengthen our number sense. It’s not done in one lesson.
That’s where number routines come in. Number routines are familiar, yet adaptable, protocols that provide structure and flow to a mathematics classroom. They can be leveraged for developing number sense, problem-solving, and language development. Teachers can use them effectively by learning about them, planning for them, modifying them, and simply using them every day.
They’re brief, but these bursts of practice add up over the course of 180 days or more.
Routines are an important supplement to games. Games are a great way to practice number sense, but you’ll find that games aren’t a good fit for all students — some find games intimidating, or get caught up in concerns that other students are faster, winning, etc. If you’re a teacher, you know what I mean.
Let’s take a step back and consider what exactly we mean by routines.
A routine is a familiar, adaptable protocol for engaging students in learning through thinking and discussion. Routines help us establish expectations for engagement and participation, support classroom management, and foster positive relationships with mathematics. They’re particularly effective for reinforcing underemphasized skills.
There are routines for language, fluency, problem-solving, reasoning, and, of course, number sense.
Teaching is one aspect of number sense — practice and play is another aspect, and an important one.
Historically, math programs in the United States have placed a greater focus on written computation than mental math. Over time, we’ve trended back to a balance in curricula between mental math, written computation, and estimation.
And while no program is perfectly balanced, a consistent commitment to routines really does add up.
Let’s use our number sense: If we spend 10 minutes a day on number routines, throughout a K-8 program, or 9 years, for 180 days, we’d spend 16,200 minutes, or 270 hours, or about 1.5 school years just on practicing our number sense.
Here are a few elements that should be in place for number sense practice:
- Engagement: Have you captured your students’ attention?
- Interest: Is the context or content of the problem interesting to them?
- Intention: What exactly are you having them practice? Why?
- Relevance: Do your students know why they are learning this? Have they considered how they will use it in their daily lives?
- Opportunity: Have you given your students the opportunity to play with and think about math? Are they listening to their peers think about math, too?
Number sense becomes an equity issue when not every student has access to:
- A teacher with a deep understanding of number sense and fluency
- High-quality instructional materials for components of number and fluency
- A reasonable amount of time to learn
- Practice opportunities that are engaging and risk-free
- Responsible and complete assessment; and
- Intervention when needed that focuses on number and strategy instruction rather than procedure and abstraction.
Students’ math identities are their deeply held beliefs about themselves as mathematicians. Every student deserves to have a strong, confident math identity, and number sense can help. Understanding how numbers work and how they can be manipulated shapes confidence and competence inherent in a positive student identity.
Mathematical agency (which we can think of as identity in action) is the ability to participate and perform effectively in math. We want students to be able to make choices about math, including how to perceive numbers and what to do with them, rather than just mimicking what adults do. Number sense empowers students to make informed choices, develop agency and fluency, and utilize their deep understanding of numbers to select effective strategies, act flexibly, identify efficiencies, and solve problems.
McGraw-Hill
