Abstract
The paper describes one problem solving strategy – the Use of false assumption. The objective of the paper is to show, in accordance with Phylogenesis and Ontogenesis Theory, that it is worthwhile to reiterate the process of development of the concept of a variable and thus provide to pupils one of the ways helping them to eliminate usual difficulties when solving word problems using linear equations, namely construction of the equations. The paper presents the outcomes of a study conducted on three lower secondary schools in the Czech Republic with 147 14–15-year-old pupils. Pupils from the experimental group were, unlike pupils from the control group, taught the strategy the Use of false assumption before being taught the topic Solving word problems. The tool for the study was a test of four problems that was sat by all the involved pupils three weeks after finishing the topic “Solving word problems” and whose results were evaluated statistically. The experiment confirmed the research hypothesis that the introduction of the strategy the Use of false assumption into 8th grade mathematics lessons (14–15-year-old pupils) helps pupils construct equations more successfully when solving word problems.
Highlights
Our paper focuses on the use of a once much used but nowadays overlooked solving strategy – the Use of false assumption (UFA)
Our goal is to introduce this strategy as a suitable propaedeutic to solving word problems using linear equations
A necessary condition for a successful solution of word problems is the construction of an appropriate equation, which corresponds to what Boonen et al (2016: 2) state: ‘That is, word problem solvers have to use a problemmodel strategy in which they translate the problem statement into a qualitative mental representation of the problem situation hidden in the text
Summary
Our paper focuses on the use of a once much used but nowadays overlooked solving strategy – the Use of false assumption (UFA). This strategy is rooted in ancient history (Přibyl, Eisenmann and Gunčaga, 2018). Mathematics education on primary and secondary school levels prepares pupils for solving school problems and shows them possible ways of solving real-life situations. The language of mathematics allows us to describe a problem situation unequivocally and offers us the tools for its solution. Word problems constitute one of the few school mathematics domains which require mathematization of situations described in words and the transformation of a mathematical solution back to the context of the problem.’ (Lewis and Mayer, 1987; Verschaffel, De Corte and Pauwels, 1992) and others show that solving a word problem is difficult
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