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What Really Is the Best Way To Build Number Sense?

I’m always amazed when students who struggle with math haven’t got a clue about how to use a number line. I’ve been teaching my ninth grade intervention classes how to add and subtract using a number line. I was at a loss for words when one of my students proclaimed, “I don’t know where to start?” 

I stood there for a second then said, “What do you mean you don’t know where to start?” This poor child didn’t know if she should begin counting from the number or the tick mark after the number. Not only was she confused, but all of them were the difference between them and her is she asked the question.

After the students left, I sat down to gather my thoughts. I was in total disbelief! I couldn’t understand why these now ninth graders didn’t know how to do basic things with a number line.

The Research

Before children enter school without knowing they have an understanding of cardinal and ordinal numbers. Some students  may have difficulty grasping these early number concepts. To prevent future difficulties, these children need instructional support to help them make connections between their concrete experiences and abstract mathematics concepts (Geary, 1993).

The students  who consistently have  difficulties with early numeracy concepts  may be at risk for mathematic disabilities. Research suggests that incorporating visual representations and using  critical features of explicit and systematic instruction support the opportunities that young children who are at risk for mathematics difficulties, including those who have been diagnosed with learning disabilities (LD) or mathematics difficulties (MD), have to access and learn from core mathematics instruction (Bryant et al., 2008).

Number Lines Are Powerful

I cringe every time I see a teacher in K-2 say, “Number lines aren’t introduced until…or they should be number paths.. ” According to the authors of, Elementary and Middle School Mathematics-Teaching Developmentally, one of the best ways to think of real quantities is to associate numbers with measures of things. In addition to measurement data collection and analysis are also good ways to connect students’ worlds with numbers and relationships.

A number line is  powerful, because it can be used to teach a variety of skills. Not only can you teach several skills with a number line it can also be used to help struggling learners with reasonableness.

As students learn that each equal-size interval on a number line represents a specific unit, they can extend their counting skills from (a) counting a number of objects in a set to (b) counting units of length (Van de Walle, Karp, & Bay-Williams, 2012) 

Learning these concepts and skills by working with number lines may help students develop a mental representation of the order and magnitude of numbers that can then be used to make comparisons, understand place value, and model mathematical operations (Diezmann & Lowrie, 2006). As Engel et al. (2013) noted, purposefully targeting these concepts during early mathematics instruction may support students’ conceptual understanding of more advanced concepts as early as kindergarten.

Instructional Support for Learning Disabled Students

Special education students tend to get overlooked when it comes to in class instructional support. Often times Special Education students are denied access to the general education curriculum through the lack of instructional support from the general education teacher.

My introduction to number paths came in the form of a comment on my Facebook Page. I have a product for using number lines and the teacher pretty much told me that children in the early grade shouldn’t use number lines. They should be using number paths instead. This sort of thinking denies 504 and learning disabled students access to math general education curriculum.

The math instructional tools and strategies that a general education teacher chooses to use in his/her classroom can cause more harm than good. Let’s take number lines for example. In some of the states’ in the  first grade curriculum number lines are NOT to be introduced to students. The curriculum writers don’t take into consideration the needs of special populations such as, 504 and Special Education students.

Studies have shown that students with LD in mathematics are less accurate than their typical peers in their number line representation and, consequently, may benefit from explicit and systematic  instruction on how to interpret and use the number line (Geary, Hoard, Nugent, & Byrd-Craven, 2008).

I cannot stress enough how important it is to use number lines as a math tool for teaching number sense. Number lines can teach students’ understanding of cardinality, quantity comparisons, and operations. Your curriculum may say NOT to introduce number lines to first graders but at the end of the day we teach children not just curriculum.

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