Misconceptions of the order of operations and associativity use

IF 4.7 1区教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH

Learning and Instruction Pub Date : 2025-02-25 DOI:10.1016/j.learninstruc.2024.102074

Joanne Eaves , Nina Attridge , Camilla Gilmore

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引用次数: 0

Abstract

Background

Conceptual knowledge of arithmetic is essential for progressing in mathematics. Associativity is one concept, which permits some problems to be solved in different ways; for example, solving ‘a + b – c’ by ‘b – c’ then ‘+a’ is a ‘shortcut’ strategy derived from associativity. However, individuals struggle to apply associativity and misconceptions of the order of operations may be one factor that is responsible.

Aims

To investigate whether misconceptions of the order of operations hinder associativity shortcut use.

Samples

76 (Study 1) and 130 (Study 2) adults aged 18–60 years participated.

Method

In Study 1, we developed a novel instrument that quantitatively measures how people interpret the order of operations. In Study 2, we conducted a well-powered, pre-registered experiment to investigate whether reminding individuals of the correct order of operations improved a) knowledge of the order of operations and b) associativity shortcut use.

Results

We found that only 16% of adults fully understood the order of operations and almost 50% had specific ‘literal’ and ‘left-to-right’ misconceptions of acronyms used to teach it. Those with misconceptions were less likely to use associativity shortcut. Reminding individuals of the order of operations reduced misconceptions of the order of operations but did not improve associativity shortcut use.

Conclusions

Misconceptions of the order of operations hinder the application of associativity shortcut strategies. Our findings have theoretical impact on the relationship between procedural and conceptual knowledge of arithmetic and have practical benefits for teachers who could use our instrument to identify misconceptions.

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来源期刊

Learning and Instruction Multiple-

CiteScore

11.30

自引率

4.80%

发文量

109

期刊介绍： As an international, multi-disciplinary, peer-refereed journal, Learning and Instruction provides a platform for the publication of the most advanced scientific research in the areas of learning, development, instruction and teaching. The journal welcomes original empirical investigations. The papers may represent a variety of theoretical perspectives and different methodological approaches. They may refer to any age level, from infants to adults and to a diversity of learning and instructional settings, from laboratory experiments to field studies. The major criteria in the review and the selection process concern the significance of the contribution to the area of learning and instruction, and the rigor of the study.