Understanding Number Sense

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Making Sense of Math
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Understanding Number Sense

Understanding Number Sense—
It’s Importance and Research-Based Teaching That Improve It

What Is Number Sense?
Number sense essentially refers to a student’s “fluidity and flexibility with numbers,” (Gersten & Chard, 2001).  He/She has sense of what numbers mean, understands their relationship to one another, is able to perform mental math, understands symbolic representations, and can use those numbers in real world situations.  In her book, About Teaching Mathematics, Marilyn Burns describes students with a strong number sense in the following way: “[They] can think and reason flexibly with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different ways, see connections among operations, figure mentally, and make reasonable estimates.”

The National Council of Teachers in 1989 identified the following five components that characterize number sense:

  • Number meaning
  • Number relationships
  • Number magnitude
  • Operations involving numbers and referents for number
  • Referents for numbers and quantities

Why Is Number Sense Important?
Number sense is important because it encourages students to think flexibly and promotes confidence with numbers—they “make friends with numbers” as Carlyle and Mercado charmingly refer to it in their book Teaching Preschool and Kindergarten Math. Students come to understand that numbers are meaningful and outcomes are sensible and expected (Burns, 2007).  Conversely, students who lack
a strong number sense have trouble developing the foundation needed for even simple arithmetic much less more complex math.

In a recent study of 180 seventh-graders conducted by the University of Missouri, researchers found that, “those who lagged behind their peers in a test of core math skills needed to function as adults were the same kids who had the least number sense or fluency way back when they started first grade.”  (Neergaard, 2013) This is particularly sobering when one considers that 1 in 5 U.S. adults lacks the math competency of a middle school student—leaving them unqualified for most jobs.

Teaching Strategies to Build Students’ Number Sense
We know from a wide body of research that number sense develops gradually and over time resulting from an exploration of numbers, visualizing numbers in a variety of contexts, and relating to numbers in different ways. About Teaching Mathematics. A K-8 Resource, 3rd Edition, Marilyn Burns (2007) highlights the following key, research-based teaching strategies to build numbers sense:

  • Model different methods for computing:
    When a teacher publicly records a number of different approaches to solving a problem–solicited from the class or by introducing her own—it exposes students to strategies that they may not have considered.  As Marilyn Burns explains, “When children think that there is one right way to compute, they focus on learning and applying it, rather than thinking about what makes sense for the numbers at hand.”
  • Ask students regularly to calculate mentally:
    Mental math encourages students to build on their knowledge about numbers and numerical relationships. When they cannot rely on memorized procedures or hold large quantities in their heads, students are forced to think more flexibly and efficiently, and to consider alternate problem solving strategies. (Parrish, 2010)
  • Have class discussions about strategies for computing:
    Classroom discussions about strategies help students to crystalize their own thinking while providing them the opportunity to critically evaluate their classmates’ approaches. In guiding the the discussion, be sure to track ideas on the board to help students make connections between mathematical thinking and symbolic representation (Conklin & Sheffield, 2012).  As noted in Classroom Discussions:  Using Math Talk to Help Students Learn, the goal is “not to increase the amount of talk but the amount of high quality talk.”
  • Make estimation an integral part of computing.
    Most of the math that we do every day—deciding when to leave for school, how much paint to buy, what type of tip to leave in a restaurant, which line to get in at the grocery store relies not only on mental math but estimations.  However traditional textbook rounding exercises don’t provide the necessary context for students to understand estimating or build number sense.  To do that, estimation must be embedded in problem situations.
  • Question students about how they reason numerically.
    Asking students about their reasoning—both when they make mistakes AND when they arrive at the correct answer—communicates to them that you value their ideas, that math is about reasoning, and, most importantly, that math should make sense to them.  Exploring reasoning is also extremely important for the teacher as a formative assessment tool.  It helps her understand each student’s strengths and weaknesses, content knowledge, reasoning strategies and misconceptions.
  • Pose numerical problems that have more than one possible answer:
    Problems with multiple answers provide plenty of opportunities for students to reason numerically.  It’s a chance to explore numbers and reasoning perhaps more creatively than if there was “one right answer.”

“Just as our understanding of phonemic awareness has revolutionized the teaching of beginning reading, the influence of number sense on early math development and more complex mathematical thinking carries implications for instruction.”
(Gersten & Chard, 2001)

Sources:
Burns, Marilyn. About Teaching Mathematics: A K-8 Resource. 3rd ed.
Sausalito, CA: Math Solutions, 2007. Print.

Burns, Marilyn. “How I Boost My Students’ Number Sense.”
Instructor Magazine Apr. 1997: 49-54. Web.

Carlyle, Ann, and Brenda Mercado. Teaching Preschool and Kindergarten Math: More than 175 Ideas, Lessons, and Videos for Building Foundations in Math,
a Multimedia Professional Learning Resource
.
Sausalito, CA: Math Solutions, 2012. Print.

Chapin, Suzanne H., and Art Johnson. Math Matters: Understanding the Math You Teach, Grades K-8. Sausalito, CA: Math Solutions Publications, 2006. Print.

Chapin, Suzanne H., Mary Catherine. O’Connor, and Nancy Canavan Anderson. Classroom Discussions: Using Math Talk to Help Students Learn, Grades K-6. Sausalito, Calif: Math Solutions, 2009. Print.

Conklin, Melissa, and Stephanie Sheffield. It Makes Sense!: Using the Hundreds Chart to Build Number Sense. Sausalito, CA: Math Solutions, 2012. Print.

Gersten, R., and D. Chard. “Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities.”
The Journal of Special Education 33.1 (1999): 18-28. Print.

Neergaard, Lauran. “Early Number Sense Plays Role in Later Math Skills.” Associated Press (2013): n. pag. Yahoo! News. 26 Mar. 2013. Web.

Number Sense:  Rethinking Arithmetic Instruction for Students with Mathematical Disabilities, The Journal of Special Education (1999) 33:18-28 © 1999 by PRO-ED, Inc.

Parrish, Sherry. Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5. Sausalito, CA: Math Solutions, 2010. Print.

Schuster, Lainie. Enriching Your Math Curriculum: Grade 5 :
A Month-to-month Resource
. Sausalito, CA: Math Solutions, 2010. Print.

Way, Jenni. “Number Sense Series: Developing Early Number Sense.”
University of Cambridge, NRICH (2013): n. pag. Web. 26 Aug. 2013.