Making Sense of Number Sense: Understanding Dyscalculia (LD in Math)
Some people are just better at math than others! And just like with other types of learning disabilities (LD), there is no precise “cut off” for when someone might qualify as having a learning disability in math. In addition (no pun intended) not all features of a math disability persist over time or remain problematic (at the same magnitude); newly acquired skills, practiced over time, make future learning easier and more “automatic.” That said, the deficits underlying LD in math often do not go away. Work-around strategies and accommodations help, and just like in the area of reading, math LD is not a prescription for failure.
Starting With 1-2-3: Number Sense
It would never occur to us to lead a child to a piano keyboard, hand over a sheet of music, and give the instruction to “play.” What’s a keyboard and how does it work? What do those black lines on the page mean, and what meaning is there to the different kinds of dots? And what does any of this have to do with the keyboard? Without a sense of how the language of music works, the system used for representing sounds in relation to one another, and how this language also communicates information about how long notes are held, which fingers to use, and when to start and stop, the child is clearly going to be lost. Playing by ear or watching and modeling others and just “winging it” is an option, but not for long and not if deep understanding is the goal.
Number sense is just that; an intuitive understanding of numbers, their magnitude, their relationships, and how they are affected by operations. It has also been described as a well-organized conceptual framework of number information that makes it possible for a person to understand numbers and number relationships and to solve mathematical problems (not just do calculations). Many individuals with dyscalculia struggle to grasp these very basic concepts, and resort to going through the motions of computation and problem-solving without understanding why and how it works.
Experts in math learning have also described the importance of number sense as the underlying ability a person has in fluidity and flexibility with numbers. They talk about how important it is for a child to develop a sense of what numbers mean and to be able to perform mental mathematics, looking at the world and making comparisons. More information about the importance of developing number sense is highlighted on the National Council of Teachers of Mathematics website.
Number Sense Explained
For those us who do not have dyscalculia, a sort of mental number line is ready and waiting for us to use whenever we need to engage in math thinking. We don’t have to work hard to realize that some numbers represent larger quantities than others; we don’t need to resort to counting on our fingers and toes when making change, or worrying about estimating ingredients for a recipe or the time it will take to travel from point A to point B. Not so for individuals with dyscalculia.
A few of the key concepts that are essential to developing number sense are:
- magnitude: how one thing (or amount) compares to another of the same kind in terms of size or rank
- ranking: think “higher than”, “lower than”, “equal to”
- comparison: evaluating features of things to make a judgment of some sort
- measurement: associating a physical quantity (i.e., length, weight) with a unit that describes it (i.e., inch, pound)
- rounding: replacing one quantity with another that is simpler but still meaningful
- percents: expressing something as a value of some amount compared to 100
- estimation: finding a result even though it may be imprecise or incomplete
For individuals with LD in math (dyscalculia) poor understanding or incomplete mastery of these concepts and skills can make math learning extremely frustrating. There are components of these skills that can be seen in very young children, and struggle during the kindergarten and elementary school years should be a sign to parents and educators to take a closer look.
Here are a few resources about how to expose children to the kinds of activities that can help build early math skills and provide a window to possible risk for LD in math: