Sunday, 23 April 2017

Why Developing Number Sense Is Crucial

Developing number sense is the first step for children to feeling comfortable with math and everyday calculation, and also the path to developing a fondness for numbers and a flexibility when working with them.   When children learn the names of numbers, what composes them, what they mean, how to use them, and how to apply them to real-world referents, it makes the children feel comfortable and confident and both eager and able to engage with math.

Having number sense allows children to have flexibility with numbers.  It allows them a confidence when working with numbers and a capability to make well judged estimates.

I have based the Number Agents approach on this awareness and understanding.  I believe it is crucial that the 'professional development' presented to the agents takes the form of activities that allow children to do this.  I have developed some key elements within my programme that have a visual component, these work exceptionally well for children when building an awareness of numbers and in their development of the five components of number sense listed in the article below.  My basic pack that explains how I do this and what activities I use can be found here.   Once again I am a big believer in using everyday items and having dice, dominoes, popsicle sticks and tens frames along with regular and irregular subitizing cards on hand are a must in my agency.  

Another key way Agency develops number sense is through discussion.  A lot of what we do centres around modelling and development of strategies and the ability to discuss and explain them.  Cowgirl calculation has been a god send here.  The children love listening to her explain things and are always keen to share how they solved a problem.  The talk moves (also referred to as math talk) has been a brilliant addition to the way I teach maths and absolutely crucial for children when crystallising and consolidating their ideas. 

Cowgirl Calculation - Our Agent Talk Moves expert

The professor also helps out greatly on this front.  He is great at discussing new ideas and presenting new knowledge or exploring and extending on knowledge.  The agents are much more engaged with the professor in puppet form and love working with him.  

The Professor

I am also working on using more open ended problems in agency and would love to get to the point of using numberless word problems this term.  Agent eyes works really well here with children really building on their ability to notice and discuss.  I love the site Have You Got Maths Eyes it is fabulous.  I have also developed my own basic pack here of photos.  Basically the more open the picture is , the more discussion is provoked.  It is also a great way to combine strand and number.  My pack is here.  I find I am constantly seeing images that would make a great visual starter to our discussions.

The whole essence of agency is about bringing an authenticity and purpose to maths, for children to develop number sense there needs to be a purpose for them to do so...Number Agents gives them that purpose in a fun and engaging manner.  I also find that during self-directed play based sessions children are more likely to discuss and share what they are doing on a deeper level and seem to notice much more.  

My goal this year is to continue to build on ways to foster this growth in number sense as I see this as absolutely crucial in developing confident mathematicians. The work of Jo Boaler is a great place to start if you have not done a lot of exploring in this area.

This article can be found here:

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 wayssee 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 (In mathematicsmagnitude is the size of a mathematical object, a property by which the object can be compared as larger or smaller than other objects of the same kind. More formally, an object's magnitude is an ordering (or ranking) of the class of objects to which it belongs.)
  • Operations involving numbers and referents for number  (“Referents” are things in the real world that children and adults understand through numbers. When you see you three dogs, and know that you’re looking at more than two dogs and less than four, and also that if two more dogs join the group there are now five, you’re employing referents (the dogs) for the numbers.)
  • 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 SenseWe 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)

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