The role of and connection between systematization and representation when young children work on a combinatorial task

Abstract

This article is about the systematization and representation young children spontaneously use when they are working on a combinatorial task. In this article, documentations from 123 children working on the same task are analysed. The question asked is if there are any connections between the systematizations and representations used in the documentations and how the children solve the task. The results indicate that there are some connections between systematization and representations and that both prepossess children's solutions. In this paper, we provide some possible reasons; however, we also state that more studies are needed to give deeper insights on these issues.

Enhancing young children’s understanding of a combinatorial task by using a duo of digital and physical artefacts

“…However, the latter one is more likely because there are written records where the same combination is repeated Table 4. Categorization of written records cycle 3 based on representation and systematization using Hughes (1986) and English (1996) (Palmér and van Bommel 2018 sequentially. Whichever, based on the results of cycle 3, a duo of artifacts seemed to influence the children's written record regarding both systematization and duplication.…”

“…A total of 35 children used pictographic representations, 71 children used iconic representations, and 8 children used both pictographic Table 3. Categorization of written records in cycle 1&2 based on representation and systematization using Hughes (1986) and English (1996) (Palmér and van Bommel 2018 and iconic representations. Thus, the majority of the children spontaneously used an iconic representation.…”

“…Further, analysis of cycles 1 and 2 indicated a relationship between the number of duplicates and the level of abstraction in the solutions (Palmér and van Bommel 2018).…”

“…The digital version was developed based on an initial design cycle (Palmér and van Bommel 2018) where children seemed to struggle with systematization while working on the tasks using only paper and pencil. The forms of representation and systematization displayed by children directly tackling the paper and pencil version of the task influenced the design of a digital version of the task that would promote exploration of systematization.…”

Young students posing problem-solving tasks: what does posing a similar task imply to students?

“…Lesh and Zawojewski 2007); the students have been involved in problemsolving activities and have simultaneously explored new mathematical content through their involvement in these activities. Several design cycles were implemented and showed positive results regarding students' learning of mathematics (Palmér and van Bommel 2018avan Bommel , 2018bvan Bommel and Palmér 2016), as well as students' feelings towards problem solving (Palmér and van Bommel 2018c). However, as both the Swedish curriculum and research have pointed out possible applications of problem posing at the elementary school level (see e.g., Ellerton et al 2015), we found a need to expand the research project to also include problem posing.…”