Number Sense: The Underpinning Understanding for Early Quantitative Literacy

Abstract

The fundamental meaning of Quantitative Literacy (QL) as the application of quantitative knowledge or reasoning in new/unfamiliar contexts is problematic because how we acquire knowledge, and transfer it to new situations, is not straightforward. This article argues that in the early development of QL, there is a specific corpus of numerical knowledge which learners need to integrate into their thinking, and to which teachers should attend. The paper is a rebuttal to historically prevalent (and simplistic) views that the terrain of early numerical understanding is little more than simple counting devoid of cognitive complexity. Rather, the knowledge upon which early QL develops comprises interdependent dimensions: Number Knowledge, Counting Skills and Principles, Nonverbal Calculation, Number Combinations and Story Problems -summarised as Number Sense. In order to derive the findings for this manuscript, a realist synthesis of recent Education and Psychology literature was conducted. The findings are of use not only when teaching very young children, but also when teaching learners who are experiencing learning difficulties through the absence of prerequisite numerical knowledge. As well, distilling fundamental quantitative knowledge for teachers to integrate into practice, the review emphasises that improved pedagogy is less a function of literal applications of reported interventions, on the grounds of perceived efficacy elsewhere, but based in refinements of teachers' understandings. Because teachers need to adapt instructional sequences to the actual thinking and learning of learners in their charge, they need knowledge that allows them to develop their own theoretical understanding rather than didactic exhortations.

Early Warning Signals from Automaticity Diagnostic Instruments for First- and Second-Semester General Chemistry

“…The evidence contributed by this study bolsters that QL/QR also plays and important role. Students need the ability to do simple calculations (add, subtract, multiply, and divide) with minimal mental effort by having these basics committed to long-term memory for easy retrieval (i.e., the preferred outcome and desirable condition needed for success). , …”

“…Successful implementation of numeracy skills requires habits of mind that include prior knowledge and automaticity of arithmetic. , As Maclellan points out, no argument can be made that using QL/QR is critical in society but the inability to apply QL/QR skills in new situations (such as a chemistry course) is extremely problematic . A quantitatively literate student has the ability to reason and synthesize information, interpret problems, and ask thought-out questions to make informed decisions on how to solve the problem(s) at hand .…”

Pre-Primary School Teachers’ Pedagogical Content Knowledge in Teaching Mathematics: A Review of Literature

“…Pre-primary mathematics education was found to be a helpful content since it is through mathematics that children construct a solid base for school achievement. Numbers and operations come first when delivering the preprimary mathematics content because they prepare a basis for children's prospect of educational achievements in mathematics (Yilmaz, 2017) and it was highlighted that teachers' understanding of the concepts of numbers and operations helps them create the foundation of young children's math understanding (Maclellan, 2012).…”

“…Further, learning to count enables children to develop the language of numbers and leads the children to take a grasp on the meanings of songs they sang before starting school, makes the children know more numbers through counting, and it helps the children know how they can solve the different mathematical equations. However, it was found that teachers still have gaps in teaching numbers and operations (Maclellan, 2012). Thus, teachers need to possess a special kind of knowledge relevant to the level of pre-primary children and also to the mathematics content areas discussed here especially the area of numbers and operations as it helps children to easily understand other mathematics content areas.…”

Primary special school teachers' knowledge and beliefs about supporting learning in numeracy

“…There has been a growing body of research evidence, over the last 30 years, in the area of mathematics teaching connecting effective learning with teachers' knowledge of how children are conceptualising (and misconceptualising) mathematical principles (Ball, Thames and Phelps, 2008;Carpenter, Fennema and Peterson et al, 1988;Greer and Meyen, 2009;Jacobs, Lamb and Philipp, 2010;Maclellan, 2012;Peterson, Fennema and Carpenter et al, 1989;Ryan and Williams, 2007). The recognition of this kind of pedagogical knowledge as relevant for all children connects with inclusive arguments which promote the extension of what is commonly available for all as a means of accommodating difference (Florian and Black-Hawkins, 2011;Hart, Drummond and McIntyre, 2007;Norwich and Nash, 2011;Ylonen and Norwich, 2012).…”