Developing the Big Ideas of Number

Abstract

The mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) of primary and elementary teachers at all levels of experience is under scrutiny. This article suggests that content knowledge and the way in which it is linked to effective pedagogies would be greatly enhanced by viewing mathematical content from the perspective of the 'big ideas' of mathematics, especially of number. This would enable teachers to make use of the many connections and links within and between such 'big ideas' and to make them explicit to children. Many teachers view the content they have to teach in terms of what curriculum documents define as being applicable to the particular year level being taught. This article suggests that a broader view of content is needed as well as a greater awareness of how concepts are built in preceding and succeeding year levels. A 'big ideas' focus would also better enable teachers to deal with the demands of what are perceived to be crowded mathematics curricula. The article investigates four 'big ideas' of number -trusting the count, place value, multiplicative thinking, and multiplicative partitioning -and examines the 'microcontent' that contributes to their development.

Designing for learning mathematics through programming: A case study of pupils engaging with place value

“…Place value is a key mathematical concept used to describe "the value assigned to a digit according to its position in a number" [37] and is fundamental to later mathematical attainment [38]. Understanding place value requires learners to integrate three abstract ideas: the quantities and base name (e.g.…”

“…"one hundred and thirty two") [39]. The reduction of place value to these three ideas, a way to read, write and say numbers, hides the underlying complexity of the concept [38,40]. Place value is important for pupils as they develop an understanding of the decimal number system and are able to apply this understanding when performing more sophisticated multi-digit operations or make connections with novel problems [41,42].…”

Manipulatives and Multiplicative Thinking

“…Multiplicative thinking is considered to be one of the 'big ideas' of mathematics (Hurst & Hurrell, 2014;Siemon, Bleckley, & Neal, 2012) and is a complex set of connected mathematical ideas. It has been defined by (Hurst, 2017) with the definition based on earlier work by Siemon et al (2006) and Siemon, Bleckley, & Neal (2012).…”

El pensamiento multiplicativo de niños del pueblo indígena shipibo-konibo de Ucayali: una perspectiva piagetiana

“…En efecto, si bien el uso de algoritmos ayuda a agilizar los cálculos, su uso precoz puede interferir con el desarrollo del pensamiento multiplicativo (SILVA et al, 2015) o ayudar a calcular más rápidamente solo cuando el operador es un cierto número, por ejemplo, el 5 (CAMPBELL; GRAHAM, 1985;LEFEVRE et al, 1996). Enseñar la multiplicación solo como una suma abreviada también produce problemas y puede interferir posteriormente con el desarrollo de nociones tales como razones y proporciones o relaciones algebraicas (HURST;HURRELL, 2014;FERNANDEZ;LLINARES, 2010). Como afirman Clark y Kamii (1996), los niños no deben ser forzados a aprender algoritmos de cálculo y estrategias que no pueden aun hacer ni comprender; diferentes niños muestran diferentes modos de abordar la multiplicación, lo que es una fuente de información importante para el docente acerca de cómo conceptualizan la operación (MABBOTT; BISANZ, 2003;STANIC;KILLION;STEFFE, 1989).…”