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

• We discussed the role of interactive systems in mental model restructuring.
• We developed a novel interactive web-based tool to help to avoid the reversal error.
• We evaluated both the short-term and relatively long-term effectiveness of the tool.

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.