Chapter 5 The Domain in MIRA: Algebra Word Problems

Chapter 5. The Domain in MIRA: Algebra Word Problems 945.7.3 DiscussionThe study results were in line with research showing that construction of relations is the mostdifficult part of the translation process (Heffernan, 2001). The two weakest students, even afterreceiving hints and items to complete their task, were unable to understand the meaning of relationsand solve the problem. One student commented:“I am still trying to figure out what this means, it is all abstract to me.” (participant 3)This suggests that weaker students found the tool less helpful because it did not provide instructionin the underlying principles of algebra, such as the value of translating a problem into an algebraicexpression, the meaning of variables, etc.In the interview, six participants reported that they benefited to some extent from the Pal Toolas an organizational tool. One participant made the following comment:“It helped me to organize the problem, but then it turned out I wasn’t organizing it theright way.” (participant 3)The same six students reported that the hints were useful to keep them on the right track. Oneparticipant made the following statement during a session when she “pressed” the “Show Hint”button:“I want to be given one just to make sure I am at the right track here.” (participant 1)Nevertheless, bringing parts together into relations was reported by all as confusing and hard.The time spent on the task was not well balanced; some participants spent most of their timeidentifying the elements of the problem and lost view of the necessity of integrating them in theequations.From this study it was clear that in addition to the tool, the MIRA environment should includefacilities to support the conceptual understanding of algebra. A glossary with examples ofexpressions, involving the arithmetical operations and typical expressions, might help students totranslate words into equations.5.8 The Implementation of the PAL ToolWith the insights produced by these results we revised the design of the PAL Tool, which wasimplemented in JAVA.All features of the low-fidelity prototype were implemented, except the “fade out” feature.This feature was a dangerous one: if the student mistakenly crossed out an important part of thetext, she was unlikely to review the decision.As one of the requirements of the PAL tool was to provide input information to the metacognitiveengine about students’ understanding of the problem, we used a technique to check theinformation students’ entered in the tables.We adapted an existing matching algorithm, called The Porter Stemming Algorithm (Porter,1990), that scans students’ answers and tries to determine if they are correct.The algorithm identifies the stem of each word in the student’s answer and checks it against aset of word stems representing the correct answer. To make it more robust we included for each