POETIC: Interactive solutions to alleviate the reversal error in student–professor type problems

Abstract

The reversal error-reversing the relationship between two variables in a mathematical word problem-is a long-standing issue in mathematics education, despite its apparent simplicity. In this paper, we describe and study POETIC, an interactive web-based environment we developed to teach users to avoid the reversal error.POETIC uses two types of novel interactive visualization, called the Test-Case and Room-Metaphor approaches. To verify the effectiveness of these approaches, we conducted crowdsourcing-based comparison studies with 200 participants and found that both approaches significantly decreased the frequency of reversal errors for certain types of word problems. Our results show that interactive visualization of equations can reduce the occurrence of the reversal error.

Insights into the reversal error from a study with South African and Spanish prospective primary teachers

“…This tendency has been identified in studies with students who speak English (e.g. Cohen & Kanin, 2005;Fisher et al, 2011;Sung et al, 2014) and those who speak Spanish (González-Calero et al, 2015;González-Calero et al, 2020;Soneira et al, 2018). Our study now extends this result to students who speak isiZulu.…”

“…On the one hand, when first introducing the algebraic language in Spanish schools, the study suggests that teachers need to highlight the meaning of the equal sign as an algebraic equivalence instead of correspondence, and the fact that letters represent quantities instead of being labels for objects. This would be so because these aspects have been proposed as the reasoning underlying the use of the static comparison strategy (Clement, 1982;Cohen & Kanim, 2005;Fisher, 1988;González-Calero et al 2020;Soneira et al, 2018;Sung-Hee et al, 2014). Teachers in Spain need to pay attention to the tendency to keep the structure or the visual display of the sentences in natural language when expressing them as equations, as this would underlie the use of the word order matching strategy (Clement, 1982;Fisher et al, 2011;Landy et al, 2014).…”

“…Clement, 1982;Cohen & Kanim, 2005;Fisher et al, 2011;Martin & Bossok, 2005) considered only items with quantities that had discrete magnitudes. Furthermore, those that use items with continuous variables, namely Landy, Brookes and Smount (2014), MacGregor and Stacey (1993), Sung-Hee et al (2014) and Wollman (1983), do not take into account this continuous character of the magnitude in their analysis. The only exception is the work by Soneira et al (2018), who went further to explore whether the type of magnitude used in setting up the direct proportional relationship between two quantities influenced the rate of the reversal errors in expressing the relationship.…”

“…The reversal error has been identified at different levels of study, among high school students in their initial stage of formal algebra learning (MacGregor & Stacey, 1993), and also among university students (Clement, 1982;Cohen & Kanim, 2005;Fisher, Borchert, & Bassok, 2011;González-Calero, Arnau, & Laserna-Berenguer, 2015;Sung-Hee, Phang, Soo, Kenney, & Uhan, 2014). It is therefore important that research is conducted in this area so as to suggest measures that can be taken in the early stages of algebra learning so as to prevent the error, as well as in the later stages in order to remedy it (Barbieri, Miller-Cotto, & Booth, 2019).…”

SeeMore: A kinetic parallel computer sculpture for educating broad audiences on parallel computation

“…Visualization tools have been used to educate audiences on complex topics in fields as diverse as Mathematics [22] and Nanoscience [29]. Others have used visualization to improve the teaching of various computer science topics.…”