Exploring the way rational expressions trigger the use of "mental" brackets by primary school students

• Published in: Educational studies in mathematics Vol. 103; no. 2; pp. 191 - 207
• Main Authors: Papadopoulos, Ioannis, Gunnarsson, Robert
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer 01.02.2020; Springer Netherlands; Springer Nature B.V
• Subjects: Analysis; Arithmetic; Brackets; Comprehension; Education; Elementary School Mathematics; Elementary school students; Elementary Schools; Evaluation; Evaluation of arithmetical expressions; Expressions (Mathematics); Foreign Countries; Mathematics; Mathematics Education; Mathematics Instruction; Mental brackets; Numbers; Numbers, Rational; Order of operations; Psychological aspects; Students; Study and teaching; Symbols (Mathematics); Greece; Sweden; Mental brackets; Brackets; Order of operations; Evaluation of arithmetical expressions
• ISSN: 0013-1954; 1573-0816; 1573-0816
• DOI: 10.1007/s10649-019-09929-z

When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way students evaluate this expression. It also seems that a connection exists between this way of evaluation and an understanding of structure. Both issues are examined in this paper. A number of arithmetical expressions in a rational form were given to primary school students from Greece and Sweden. The collected findings strengthen our hypothesis that this rational form of the arithmetical expressions was of critical importance for the students' decision on how to evaluate these expressions. They temporarily put aside their knowledge about the rules for the order of operations, bastead, the way they evaluated the expressions indicates an implicit use of what we call in this paper "mental" brackets. It is very likely that the use of these "mental" brackets is closely connected with students' structure sense.