Order of operations: On convention and met-before acronyms

Zazkis, Rina; Rouleau, Annette

doi:10.1007/s10649-017-9789-9

Cited by 9 publications

(3 citation statements)

References 20 publications

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“…These individuals may never use a shortcut on "a + b − c" problems, because they believe it would not be permitted by a rule they had learnt. Indeed, we are not the first to identify misinterpretations with BODMAS; during interviews with prospective primary-school teachers, Zakis and Rouleau (2017) found that 55% believed that division should be performed before multiplication. Interestingly, in the United States, where the literal order of multiplication and division is reversed in the acronym PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction), 38% of prospective teachers believed the opposite, that multiplication should precede division (Glidden, 2008).…”

Section: Theoretical Contributionmentioning

confidence: 90%

Investigating the role of attention in the identification of associativity shortcuts using a microgenetic measure of implicit shortcut use

Eaves

Gilmore

Attridge

2020

Quarterly Journal of Experimental Psychology

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Many mathematics problems can be solved in different ways or by using different strategies. Good knowledge of arithmetic principles is important for identifying and using strategies that are more sophisticated. For example, the problem “6 + 38 − 35” can be solved through a shortcut strategy where the subtraction “38 − 35 = 3” is performed before the addition “3 + 6 = 9,” a strategy that is derived from the arithmetic principle of associativity. However, both children and adults make infrequent use of this shortcut and the reasons for this are currently unknown. To uncover these reasons, new sensitive measures of strategy identification and use must first be developed, which was one goal of our research. We built a novel method to detect the time-point when individuals first identify an arithmetic strategy, based on trial-by-trial response time data. Our second goal was to use this measure to investigate the contribution of one particular factor, attention, in the identification of the associativity shortcut. In two studies, we found that manipulating visual attention made no difference to the number of people who identified the shortcut, the trial number on which they first identified it, or their accuracy and response time for solving shortcut problems. We discuss the theoretical and methodological contribution of our findings and argue that the origin of people’s difficulty with associativity shortcuts may lie beyond attention.

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Section: Theoretical Contributionmentioning

confidence: 90%

Investigating the role of attention in the identification of associativity shortcuts using a microgenetic measure of implicit shortcut use

Eaves

Gilmore

Attridge

2020

Quarterly Journal of Experimental Psychology

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“…However, many individuals have a limited or misconceived understanding of operation order (Zazkis & Rouleau, 2018), particularly in the UK, USA, Canada and Australia where acronyms such as BODMAS ('Brackets, Orders, Division, Multiplication, Addition, Subtraction') are used to teach it. This is because the acronym is unclear in specifying that some operations have equal precedence.…”

Section: Domain-specific Skillsmentioning

confidence: 99%

The role of domain-general and domain-specific skills in the identification of arithmetic strategies

2022

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Individuals solve arithmetic problems in different ways and the strategies they choose are indicators of advanced competencies such as adaptivity and flexibility, and predict mathematical achievement. Understanding the factors that encourage or hinder the selection of different strategies is therefore important for helping individuals to succeed in mathematics. Our research contributed to this goal by investigating the skills required for selecting the associativity shortcut-strategy, where problems such as ‘16 + 38 – 35’ are solved by performing the subtraction (38 – 35 = 3) before the addition (3 + 16 = 19). In a well-powered, pre-registered study, adults completed two tasks that involved ‘a + b – c’ problems, and we recorded a) whether and b) when, they identified the shortcut. They also completed tasks that measured domain-specific skills (calculation skill and understanding of the order of operations) and domain-general skills (working memory, inhibition and switching). Of all the measures, inhibition was the most reliable predictor of whether individuals identified the shortcut, and we discuss the roles it may play in selecting efficient arithmetic strategies.

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“…Alternatively, some individuals could have conflicting knowledge: For example, the acronym BODMAS (Brackets, Order, Multiplication, Division, Addition, Subtraction) and the equivalents BIDMAS and PEMDAS are typically introduced around the age of 11 years in the UK and USA to help individuals remember operator precedence. However, the acronyms are often misinterpreted (Glidden, 2008;Zakis & Rouleau, 2017), with some individuals incorrectly ascribing precedence to addition over subtraction.…”

Section: Difficulties Using Associativity Shortcutsmentioning

confidence: 99%

Increasing the use of conceptually-derived strategies in arithmetic: using inversion problems to promote the use of associativity shortcuts

Eaves

Attridge

Gilmore

2019

Learning and Instruction

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Declarations of interest: None ACKNOWLEDGEMENTS: This work was supported by a PhD Studentship from Loughborough University Doctoral college. We would like to thank Jayne Pickering who helped to dual-score the data. C.G. is supported by a Royal Society Dorothy Hodgkin Fellowship. Highlights • Associativity is an arithmetic concept that children and adults struggle to apply • Inversion is a simpler concept that older children and adults easily apply • Solving inversion problems ('a + b-b') increased subsequent associativity use • 'a + b-b' inversion, but not 'a + b-a' inversion, increased associativity use • 'a + b-b' problems may direct attention or validate a 'right-to-left' strategy

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Order of operations: On convention and met-before acronyms

Cited by 9 publications

References 20 publications

Investigating the role of attention in the identification of associativity shortcuts using a microgenetic measure of implicit shortcut use

Investigating the role of attention in the identification of associativity shortcuts using a microgenetic measure of implicit shortcut use

The role of domain-general and domain-specific skills in the identification of arithmetic strategies

Increasing the use of conceptually-derived strategies in arithmetic: using inversion problems to promote the use of associativity shortcuts

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