On the origin, characteristics, and usefulness of instrumental and relational understanding

Abstract

In this paper, the aim is to make a theoretical contribution by focusing on the origin, characteristics, and potential values of the concepts of instrumental and relational understanding. Five characteristics are identified to make it easier to operationalise the concepts and use them as an analytical framework. There is also a focus on how the concepts are closely related to two rationales for learning, the instrumental and the social rationale. The potential values of the concepts and their rationales are shown by using them to suggest a revision of the van Hiele framework and to analyse three empirical examples concerning young students’ understanding of triangles and a cylinder.

Teaching Linear Algebra to Engineering Students in Two Different Educational Settings:

“…1b statement 2). This is in accordance with a number of research results focusing on the importance of relational understanding (Herheim, 2023;Hiebert & Lefevre, 1986;Skemp, 1979). For engineering students, the correlation between prior and present performance in mathematics is high (Liebendörfer et al, 2022) and the effect of background experiences on performance, especially when these are of an instrumental type, is described in Zakariya et al (2021).…”

“…Another classical and related distinction is between procedural and conceptual knowledge, given by Hiebert and Lefevre (1986). But there are numerous such pairings (Herheim, 2023). Herheim distinguishes five characteristics of instrumental and relational understanding in order to facilitate for operationalization of the concepts, and thus make them usable in an analytical framework.…”

Multilingual pre-service teacher's knowledge and understanding of analytical geometry content

“…This shows that the PTs were simply using procedures without comprehension and could not make connections between their solutions and the presented problem. They had instrumental understanding, which is a disadvantage for them because of its rigid and context-dependent nature [8]. Attempt A, further confirms this by using the coordinated of Q in the place of P. Sub questions 2.2.3 and 3.4 had the lowest average performance percentages of 15% and 17%, respectively.…”

“…Yet, [8] emphasize that the knowledge that is needed by Mathematics teachers is inclusive of deep content knowledge and knowledge for teaching.…”

Introducing schoolchildren to computational thinking using smartphone apps: A way to encourage enrollment in engineering education

“…They found that children are able to use sequential instructions, but occasionally have difficulty understanding the symbols used in the app and get confused between the left and the right while using the app. Herheim and Severina [16] used ScratchJr to teach computer programming to fourth standard students and found that the app could enhance children's ability of mathematical explanation and justification.…”