Testing a model for the monitoring of worked-out algebra-problem examples: from behaviours to outcomes on a math task

• Vicente Sanjosé ^[1] ; Carlos B. Gómez-Ferragud ^[1] ; José J. Verdugo-Perona ^[1] ; Joan J. Solaz-Portolés ^[1]
  1. [1] Universitat de València

     Universitat de València

     Valencia, España

     
• Localización: Psicología educativa, ISSN 1135-755X, Vol. 28, Nº. 2, 2022, págs. 141-149
• Idioma: inglés
• DOI: 10.5093/psed2021a25
• Títulos paralelos:
  • La validación de un modelo para el control de la comprensión de problemas de álgebra resueltos: de los comportamientos a los resultados en una tarea de matemáticas
• Enlaces
  • Texto completo (pdf)
• Dialnet Métricas: 1 Cita
• Resumen
  • español

    Este estudio tiene como objetivo probar una extensión de un modelo teórico para el mecanismo de control metacognitivo que sirve para la detección de inconsistencias cuando la información proporcionada incluye símbolos abstractos además de texto natural. Se pidió a 94 postgraduados de especialidades STEM que leyeran un ejemplo resuelto de un problema de álgebra y que informaran sobre cualquier incoherencia, inconsistencia o error detectado en el enunciado o en el procedimiento de resolución. A partir de un modelo teórico se definió un conjunto de índices para describir el comportamiento de los participantes a lo largo de la tarea. Se utilizó el software Read & Answer para registrar online los datos de procesamiento individual y los informes de los participantes. Los resultados confirman las predicciones del modelo. Los índices predicen correctamente los resultados de los participantes en la tarea con gran precisión. Los comportamientos específicos de los alumnos podrían asociarse a los resultados observados de la tarea con suficiente confiabilidad dentro de las limitaciones del estudio. Además se ha comparado el procesamiento del álgebra con el procesamiento del texto natural.

  • English

    This study aimed at testing an extension of a theoretical model for the metacognitive monitoring mechanism implied in the detection of inconsistencies when the information provided includes abstract symbols in addition to plain text. Ninety-four postgraduates of STEM specialities were asked to read a worked-out algebra-problem example and to report any incoherence, inconsistency, or error detected in the statement or in the solving procedure. A set of model-inspired indexes was defined to describe participants’ behaviour along the task. The Read & Answer software was used to record online individual processing data and participants’ reports. Results supported model predictions. Indexes correctly predicted participants’ outcomes in the task with high accuracy. Specific students’ behaviours could be associated to observed task outcomes with sufficient reliability within the limitations of the study. In addition, algebra processing was compared with plain text processing.

• Referencias bibliográficas
  • Andrà, C., Lindström, P., Arzarello, F., Holmqvist, K., Robutti, O., & Sabena, C. (2015). Reading mathematics representations: An eyetracking...
  • Baars, M., Van Gog, T., de Bruin, A., & Paas, F. (2014). Effects of problem solving after worked example study on primary schoolchildren’s...
  • Baars, M., Van Gog, T., de Bruin, A., & Paas, F. (2017). Effects of problem solving after worked example study on secondary school children’s...
  • Baker, L. (2002). Metacognition in comprehension instruction. In C. Collins & S. R. Parris (Eds.), Comprehension instruction: Research-based...
  • Baten, E., Praet, M., & Desoete, A. (2017). The relevance and efficacy of metacognition for instructional design in the domain of mathematics....
  • Boekaerts, M., & Rozendaal, J. S. (2010). Using multiple calibration indices in order to capture the complex picture of what affects students’...
  • Cerdán, R., Gilabert, R., & Vidal-Abarca, E. (2011). Selecting information to answer questions: Strategic individual differences when...
  • Chinn, C. A., & Brewer, W. F. (1993). The role of anomalous data in knowledge acquisition: A theoretical framework and implications for...
  • Cooper, M. (1986). The dependence of multiplicative reversal on equation format. Journal of Mathematical Behaviour, 5(2), 115-120.
  • Cornoldi, C., Carretti, B., Drusi, S., & Tencati, C. (2015). Improving problem solving in primary school students: The effect of a training...
  • Cox, M. T., Alavi, Z., Dannenhauer, D., Eyorokon, V., Muñoz-Avila, H., & Perlis, D. (2016). MIDCA: A metacognitive, integrated dual-cycle...
  • Crippen, K. J., & Earl, B. L. (2004). Considering the efficacy of web-based worked examples in introductory chemistry. Journal of Computers...
  • De Bruin, A. B., Rikers, R. M., & Schmidt, H. G. (2005). Monitoring accuracy and self-regulation when learning to play a chess endgame....
  • Dehaene, S. (2018). The error-related negativity, self-monitoring, and consciousness. Perspectives on Psychological Science, 13(2), 161-165....
  • Desoete, A., & De Craene, B. (2019). Metacognition and mathematics education: An overview. ZDM Mathematics Education. 51(4), 565-575....
  • Docktor, J. L., & Mestre, J. P. (2014). Synthesis of discipline-based education research in physics. Physical Review Special TopicsPhysics...
  • García, T., Cueli, M., Rodríguez, C., Krawec, J., & González-Castro, P. (2015). Conocimiento y habilidades metacognitivas en estudiantes...
  • García, T., Rodríguez, C., González-Castro, P., González-Pienda, J. A., & Torrance, M. (2016). Elementary students’ metacognitive processes...
  • González-Calero, J. A., Arnau, D., & Laserna-Belenguer, B. (2015). Influence of additive and multiplicative structure and direction of...
  • Gómez-Ferragud, C. B., Sanjosé V., & Solaz-Portolés, J. J. (2016). Estudios sobre comprensión y control de la comprensión en resolución...
  • Gómez-Ferragud, C. B., Solaz-Portolés, J. J., & Sanjosé, V. (2013). Analogy construction and success in mathematics and science problemsolving:...
  • Hartman, H. J. (2001). Developing students’ metacognitive knowledge and skills. In H. Hartman (Ed.), Metacognition in learning and instruction...
  • Hyönä, J., Lorch, Jr. , R. F., & Rinck, M. (2003). Eye movement measures to study global text processing. In J. Hyönä, R. Radach, &...
  • Jansen A. R., Marriott K., & Yelland G. W. (2007) Parsing of algebraic expressions by experienced users of mathematics. European Journal...
  • Jupri, A., & Drijvers, P. H. M. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of Mathematics,...
  • Kintsch, W. (1998). Comprehension: a paradigm for cognition. University Press. Koçak, R., & Boyaci, M. (2010). The predictive role of...
  • Lucangeli, D., Penna, M. P., Fastame, M. C., Pedron, M., Porru, A., & Duca, V. (2019). Metacognition and errors: The impact of self-regulatory...
  • Mañá, A., Vidal-Abarca, E., & Salmerón, L. (2017). Effect of delay on search decisions in a task-oriented reading environment. Metacognition...
  • Mason, L., Zaccoletti, S., Carretti, B., Scrimin, S., & Diakidoy, I. A. N. (2019). The role of inhibition in conceptual learning from...
  • McLaren, B. M., van Gog, T., Ganoe, C., Karabinos, M., & Yaron, D. (2016). The efficiency of worked examples compared to erroneous examples,...
  • Mihalca, L., Mengelkamp, C., Schnotz, W., & Paas, F. (2015). Completion problems can reduce the illusions of understanding in a computer-based...
  • Modestou, M., & Gagatsis, A. (2010). Cognitive and metacognitive aspects of proportional reasoning. Mathematical Thinking and Learning,...
  • Morales, J., Lau, H., & Fleming, S. M. (2018). Domain-general and domainspecific patterns of activity supporting metacognition in human...
  • Nelson, L. J., & Fyfe, E. R. (2019). Metacognitive monitoring and help-seeking decisions on mathematical equivalence problems. Metacognition...
  • Nelson, T. O., & Narens, L. (1990). Metamemory: A theoretical framework and new findings. In H. B. Gordon (Ed.), Psychology of learning...
  • Otero, J. (2009). Question generation and anomaly detection in texts. In Handbook of metacognition in education (pp. 59-71). Routledge.
  • Otero, J., Campanario, J. M., & Hopkins, K. D. (1992). The relationship between academic achievement and metacognitive comprehension monitoring...
  • Otero, J., & Graesser, A. C. (2001). PREG: Elements of a model of question asking. Cognition and Instruction, 19(2), 143-175. https://doi.org/10.1207/...
  • Otero, J., Ishiwa, K., & Sanjosé, V. (2008). Readers’ questioning: Some hints for automated question generation. Proceedings of the Workshop...
  • Otero, J., & Kintsch, W. (1992). Failures to detect contradiction in a text: What readers believe versus what they read. Psychological...
  • Özsoy, G., & Ataman, A. (2017). The effect of metacognitive strategy training on mathematical problem-solving achievement. International...
  • Qiu L., Su J., Ni, Y., Bai, Y., Zhang, X., Li, X., & Wang, X. (2018). The neural system of metacognition accompanying decision-making...
  • Rayner, K., Schotter, E. R., Masson M. E. J., Potter M. C., & Treiman R. (2016). So much to read, so little time: How do we read, and...
  • Renkl, A. (2014). Toward an instructionally oriented theory of example-based learning. Cognitive Science, 38(1), 1-37. https://doi.org/10.1111/cogs.12086
  • Rinck, M., Gámez, E., Díaz, J. M., & De Vega, M. (2003). Processing of temporal information: Evidence from eye movements. Memory &...
  • Salmerón, L., Naumann, J., García, V., & Fajardo, I. (2017). Scanning and deep processing of information in hypertext: An eye tracking...
  • Sánchez, E., & García-Rodicio, H. (2013). Using online measures to determine how learners process instructional explanations. Learning...
  • Sanjosé, V., Fernández, J. J., & Vidal-Abarca, E. (2010). Importancia de las destrezas de procesamiento de la información en la comprensión...
  • Sanjosé, V., & Torres, T. (2014). Questions generated on non-textual information: An empirical validation of the obstacle-goal model applied...
  • Schotter, E. R., Tran, R., & Rayner, K. (2014). Don’t believe what you read (only once): Comprehension is supported by regressions during...
  • Seery, M. K. (2013). Harnessing technology in chemistry education. New Directions in the Teaching of Physical Sciences, 9(1), 77-86. https://doi....
  • Sereno, S. C., Rayner, K., & Posner, M. I. (1998). Establishing a timeline of word recognition: Evidence from eye movements and event-related...
  • Smith, A. D., Mestre, J. P., & Ross, B. H. (2010). Eye-gaze patterns as students study worked-out examples in mechanics. Physical Review...
  • Sun, R., Zhang, X., & Mathews, R. (2006). Modeling meta-cognition in a cognitive architecture. Cognitive Systems Research, 7(4), 327-338....
  • Sweller, J. (2006). The worked example effect and human cognition. Learning and Instruction, 16(2), 165-169. https://doi.org/10.1016/j. learninstruc.2006.02.005
  • Throndsen, I. (2011). Self-regulated learning of basic arithmetic skills: A longitudinal study. British Journal of Educational Psychology,...
  • Van der Schoot, M., Reijntjes, A., & van Lieshout, E. C. (2012). How do children deal with inconsistencies in text? An eye fixation and...
  • Van Gog, T., & Rummel, N. (2010). Example-based learning: Integrating cognitive and social-cognitive research perspectives. Educational...
  • Vidal-Abarca, E., & Cerdán, R. (2013). Read & answer: An application to study task-oriented reading situations. Information Design...
  • Vosniadou, S., Pearson, P. D., & Rogers, T. (1988). What causes children’s failures to detect inconsistencies in text? Representation...
  • Wang, M. C., Haertel, G. D., & Walberg, H. J. (1993). Toward a knowledge base for school learning. Review of Educational Research, 63(3),...
  • Yeung, N., & Summerfield, C. (2014). Shared mechanisms for confidence judgements and error detection in human decision making. In S. Fleming...
  • Young, A., & Fry, J. D. (2008). Metacognitive awareness and academic achievement in college students. Journal of the Scholarship of Teaching...