Resumen de Online processing while monitoring worked-out examples with embedded errors: defining university student profiles

Vicente Sanjosé López, Carlos B. Gómez Ferragud, Joan Josep Solaz Portolés

• This study explores the process itself of comprehension monitoring of worked-out examples in mathematics. A ‘reversal error’ was embedded in a worked-out example of algebraic nature. Ninety-four engineers in a master’s degree program to become secondary teachers of technology were asked to judge the comprehensibility of the statement and the resolution provided, and to report in writing any incoherence, inconsistency, or error they might detect. The participants’ mental processes throughout the task were operationalized through behavioural variables based on a psychological mechanism proposed for inconsistency detection. The behavioural variables focused on the monitoring of important mathematical processes, the algebraic translation, and the interpretation of the numerical solution of the worked example. The software ‘Read and Answer’ was used to record online data on each participant’s behaviour while monitoring the example, as well as his/her written partial and final reports (the task products). An individual short interview was conducted to increase the reliability of the study. Data from each participant were first analysed. Secondly, data from all the participants were considered together in statistical analyses aimed at relating behavioural variables to task products. Four student monitoring profiles were identified corresponding to different combinations of detection/overlooking the embedded algebraic inconsistency, and detection/overlooking the subsequent inconsistency in the result: ‘competent monitoring’, ‘delayed monitoring’, ‘blocked monitoring’, and ‘poor monitoring’ students. Implications for teaching are discussed.