This article describes two heuristic strategies for problem solving: the use of false assumption strategy and the use of double false assumption strategy. Both of these strategies have their roots deep in history. In this article, we define these two strategies and illustrate their use in a problem developed by Frances Pellos. The article provides an overview of occurrences of these two strategies in various mathematical and educational texts. The texts show clearly that both of these strategies played a significant (...) role in mathematics education in the past. We present some examples from concrete historical documents, which we use later for the preparation of a teaching experiment. We also present the conclusions of an experiment conducted on three lower secondary schools in the Czech Republic, the goal of which was to test the applicability of the use of false assumption strategy as a propaedeutic to solving word problems using equations. (shrink)

The practice of mathematical word problem is ubiquitous and thought to impact academic achievement. However, the underlying neural mechanisms are still poorly understood. In this study, we investigate how lexical consistency of word problem description is modulated in adults' brain responses during word problem solution. Using functional magnetic resonance imaging methods, we examined compare word problems that included relational statements, such as “A dumpling costs 9 dollars. A wonton is 2 dollars less than a dumpling. How much does a wonton (...) cost?” and manipulated lexical consistency and problem operation. We found a consistency by operation interaction in the widespread fronto-insular-parietal activations, including the anterior insula, dorsoanterior cingulate cortex, middle frontal gyrus, and intraparietal sulcus, such that inconsistent problems engaged stronger activations than consistent problems for addition, whereas the consistency effect was inverse for subtraction. Critically, these results were more salient in the less successful problem solvers than their more successful peers. Our study is the first to demonstrate that lexical consistency effects on arithmetic neural networks are modulated during reading word problem that required distinct arithmetic operations. More broadly, our study has strong potentials to add linkage between neuroscience and education by remediating deficits and enhance instruction design in the school curriculum. (shrink)