On achieving a definition of Numeracy: hard word ahead

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When I started delineating numeracy in my mind, a definition along the lines of numeracy is the attainment of a number sense wherein one can encode and decode information given through numbers came to mind. Upon learning that numeracy is but one component of a much larger concept, that of ML (mathematical literacy), I reformulated my working definition of numeracy, to state that numeracy would then be an element of ML, one more related to quantity than to number sense and the result of a structural design of teaching practice. On that occasion, I also made a mental note to highlight the idea of insight as necessary to the computational/algorithmic aspect for a full numerical command. But when I learned about the idea of math anxiety and how it shapes much of our collective numeracy development, I had to enlarge these two working definitions to encompass the affective domain involved in dealing with quantities for practical purposes.

The first thing that I considered here, and to me it was a real game-changer, was the notion that math anxiety is diverse from general anxiety and the extent to which this state can affect performance and achievement goes far beyond what research has addressed so far (Berch & Mazzoco, 2007). The reason therein might be better understood if we take the idea that in the core of such anxiety lies a poor or inexistent grasp of the central conceptual structure for whole number (Griffin, 2005). Once hindered by this absent or flimsy grasp, the whole perspective for future success may be jeopardized as elementary math achievement does come as an early indicator of such status (Connell, 2018).

As if that were not sufficient for us all to take a step back and treat such finding with the depth of implications that it carries, there is the added and utterly understandable offshoot of this fact in very real contexts: those of early elementary classrooms worldwide. As Beilock and colleagues (2010) found, the fact that such state (math anxiety) is very common among most of elementary school teachers (predominantly female), female students’ role models for approaching the relationship of concepts that a good grasp of number line entails (Connell, 2018) are very poor. Consequently, much more than capacity or disposition, their future in math performance gets nipped in the bud for what they see right in front of their eyes: their teachers displaying nervousness, insecurity and fear in dealing with Math. That stance, more than materials, technology and whatever else might be of use to those students, is what was found as pervasively harmful to a full attainment of numeracy.

So, before proceeding, let’s recap and realign all that I have said so far regarding numeracy: first, there is the importance of the number sense, a point that lies at the root of many of the problems and disparities between low-income students and their peers (Office of Child Development, 2009). The fact that children need exposure and experience with translating numbers into magnitudes, a point that is very clear from the insights brought by Griffin (2005), is something that no culture or context can leave unnoticed. There needs to be a community that is engaged in fostering the development of this number sense in children, even before they come to elementary school. As happens with literacy, where the earlier one is read to, the better one develops reading (Wolf & Gottwald, 2011) in numeracy, the development of math achievement is dependent on ‘math encounters’ as what happens when parents play math games with their children. This is when the approximation demanded by a full acquisition of number sense takes roots in children’s development.

From that core and primordial concept, I then proceeded on to the idea of approximation that number sense brings and that is central to the development of numeracy, or rather, to mathematical literacy, one that is rooted in our human biology (Dehaene, 2008) and needs the workings of time and the concurrence of help from more knowledgeable ones to come to fruition (Dehaene-Lambertz & Spelke, 2015). Therefore, development and community seem to really make sense for their inclusion in a working definition of numeracy.

When we think of the interdependency of behavior (what one displays), to environment (what stimuli one receives) and cognition (what capacities one develops to understand those reactions and stimuli, manage and cooperate with them), the importance that emotion plays is heightened. So, dealing with the stimuli in a positive manner, one that holds anxiety in place and has mechanisms to counteract its deleterious influences, seems to be coherent in a working definition of numeracy.

Therefore, my final definition of numeracy would entail the following: numeracy is the development of a capacity for understanding what numbers mean, for dealing effectively with quantities in a positive manner, and with the aid of a community that understands the depth and importance of such capacity and displays it in an effective manner.

References

Beilock, S. L., Gunderson, E. A., Ramirez, G., Levine, S. C. (2010). Female teachers’ math anxiety affects girls’ math achievement. Proceedings of the National Academy of Sciences of the United States of America, 107, 1860–1863. doi:10.1073/pnas.0910967107

Berch, D.B, & Mazzocco, M.M.M. (2007). Why is math so hard for some children? Baltimore MD: Paul Brookes.

Connell, M. (2018). A Case Study of Designing an Elementary Math Intervention. IN Schwartz, M. S., & Paré-Blagoev, E. J. (Eds.). Research in mind, brain, and education. New York, NY: Routledge.

Dehaene, S. (2011). The number sense: How the mind creates mathematics. OUP USA.

Dehaene-Lambertz, G., & Spelke, E. S. (2015). The infancy of the human brain. Neuron, 88(1), 93-109.  

Griffin, W. (2005). Fostering the development of whole-number sense: Teaching mathematics in the primary grades. In M. S. Donovan & J. D. Bransford (Eds.), How students learn: Mathematics in the classroom. Committee on how people learn, a targeted report for teachers.  Washington, DC: National Academies Press.