Structuring versus counting: critical ways of using fingers in subtraction

Abstract

The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126 observations of 4-5-yearolds solving a simple subtraction task, is to discuss different ways of using fingers, with some of the ways appearing more, and others less, powerful. The analysis suggests there is much more complexity to children's finger-related strategies than prior research has indicated. Empirical findings in our study point to the decisive effects of different ways of using fingers, and in particular for either keeping track of counted units or for presenting a structured awareness of number. Three ways of using fingers emerge in the analysis, which are discussed in relation to their rate of success in solving the subtraction task and with attention to why the differences matter for the success rate. Through this discussion we suggest that the complexity of how fingers are used must be considered.

Children’s perception of structures when determining cardinality of sets—results of an eye-tracking study with 5-year-old children

“…The results of Björklund et al (2019) also support these findings. They investigated the use of finger patterns in solving a subtraction task in a study with a total of 126 children aged 4 and 5 years.…”

“…Especially in the number range up to 100 the use of counting strategies is not an efficient strategy for solving arithmetic problems (Gray et al 2000). Björklund et al (2019) also point out that counting unit by unit does not necessarily promote the understanding of a conceptual structure of numbers, that is, of the part-whole relationship. In order to develop other arithmetical strategies, especially the part-whole relationship of numbers is a crucial concept (Resnick 1992;Hunting 2003), and therefore is also an important part in numerical development models (Fritz et al 2013;Baroody et al 2006).…”

Teachers and researchers in collaboration. A possibility to overcome the research‐practice gap?

“…the child points to the thumb (the sixth finger). This is interpreted as experiencing number words describing "the nth" object, thus without cardinal meaning (Björklund, Kullberg, & Runesson Kempe, 2018).…”

“… For example, a child can show six fingers (one hand and the thumb) and when asked “What is six?” the child points to the thumb (the sixth finger). This is interpreted as experiencing number words describing “the nth” object, thus without cardinal meaning (Björklund, Kullberg, & Runesson Kempe, ). …”

Piloting national diagnostic assessment for strategic calculation

“…Structural approaches to working with number (understanding numbers as being constituted as part-part-whole relations rather than individual units) are widely considered important in developing fluent and flexible ways of calculating with number as well as developing conceptual understanding in mathematics (Björklund et al 2019). Mulligan and Mitchelmore (2009) note that "Recent educational research has turned increasing attention to the structural development of young students' mathematical thinking" and that "There is increasing evidence that an awareness of mathematical structure is crucial to mathematical competence among young children" (p. 33).…”