Abstract
Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of “feeling number”, a phrase that we offer in a twofold sense—resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the quantities they represent. First, we distinguish between quantity sense and the relatively vague notion of number sense. Second, we consider the human capacity for quantity sense and place that in the context of related cultural issues, including verbal and symbolic representations of number. Third and more pragmatically, we offer teaching strategies that seem helpful in the development of quantity sense coupled with number sense. Finally, we argue that there is a moral imperative to connect number sense with such a quantity sense that allows students to feel the weight of numbers. It is important that learners develop a feeling for number, which includes a sense of what numbers are and what they can do.
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Notes
There is some evidence that certain species—including primates, dolphins, and, in particular, parrots—can make effective and abstract use of numbers. However, to date, all evidence is based on capacities to master particular aspects of human numeration systems (see Scholtyssek 2006).
We suggest that Whorf’s hypothesis applied to number representation could inspire investigation of the relationships between cultures’ forms of representing large numbers and their practices that relate to relatively large quantities. Such practices may include the accumulation of possessions, structures of governance, and the organization of trade.
In our increasingly multicultural societies, it is becoming more difficult to choose settings that are closely related to the experiences of all the students in any given classroom. Their experiences vary considerably. Thus, we encourage teachers to adapt our strategies or use different strategies with similar characteristics to attend to their particular students’ experiences.
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Wagner, D., Davis, B. Feeling number: grounding number sense in a sense of quantity. Educ Stud Math 74, 39–51 (2010). https://doi.org/10.1007/s10649-009-9226-9
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DOI: https://doi.org/10.1007/s10649-009-9226-9