Cognitive and metacognitive processes involved in arithmetic problem solving: the software "Solving Arithmetic Problems"
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Jan 1, 2010
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Abstract
This paper examines recent literature about mathematical problem solving and describes a multimedia software program called “Risolvere problemi aritmetici”, which deals with arithmetical problem solving. The software was developed for primary school children and also for children with difficulties in arithmetical problem solving. “Risolvere problemi aritmetici” contains both a test module and a training module. The test module consists of a set of arithmetical problems ordered according to difficulty level. The training module comprises a series of activities centred on arithmetical problem comprehension, representation, categorization and planning. It also features specific activities dedicated to the training of memory abilities involved in problem solving. The training module has a metacognitive orientation, since the learner is guided through the system by two “schoolmates” who stimulate metacognitive skills through questions about the activities.
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References
Baddeley A.D. (1986). Working memory, London: Oxford University Press.
Baddeley A.D. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology, 49 (A), pp. 5-28.
Chi M.T.H., Feltovich P.J., Glaser R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, pp. 121-152.
D’Amico A., Passolunghi M.C., La Porta R., (2009). Risolvere problemi aritmetici (CD-ROM). Test e training su comprensione, rappresentazione, categorizzazione, pianificazione e memoria. Erickson, Trento.
De Candia C., Cibinel N., Lucangeli D. (2009) Risolvere problemi in 6 mosse. Trento: Erickson.
Greeno J.G., Riley M.S. (1987). Processes and Development of Understanding. In R.E. Weinert, R.H. Kluwe (a cura di). Metacognition, Motivation and Understanding. Hillsdale N.J.: Lawrence Erlbaum Associates, pp. 289-313.
Hegarty M., Mayer R.E., Monk C.A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of educational psychology, 87 (1), pp. 18-32.
Hegarty M., Kozhevnikov M., (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), pp. 684-689.
Lucangeli D., Cornoldi C. (1995). Metacognizione e matematica. In O. Albanese, P.A. Doudin, D. Martin (a cura di). Metacognizione ed educazione. Milano: Franco Angeli.
Lucangeli D., Tressoldi P., Cendron M. (1998a). Cognitive and metacognitive abilities involved in the solution of mathematical word problems: validation of a comprehensive model. Contemporary educational psychology, 23, pp. 257-275.
Lucangeli D., Tressoldi P.E., Cendron M. (1998b). SPM. Test di abilità di soluzione dei problemi matematici. Trento: Erickson.
Mayer R.E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, Vol. 26, pp. 49-63.
Montague M. (1992). The Effects of Cognitive and Metacognitive Strategy Instruction on the Mathematical Problem Solving of Middle School Students with Learning Disabilities. Journal of Learning Disabilities, 25(4), pp. 230-248.
Passolunghi M.C., Lonciari I., Cornoldi C. (1994). Abilità di pianificazione nella risoluzione di problemi aritmetici di tipo verbale. Atti del Congresso nazionale Airipa su Problemi di attenzione e comportamento nei disturbi di apprendimento, Ferrara.
Passolunghi M.C., Lonciari I., Cornoldi C. (1996). Abilità di pianificazione, comprensione, metacognizione e risoluzione di problemi aritmetici di tipo verbale. Età Evolutiva, 54, pp. 36-48.
Passolunghi M.C., Pazzaglia F. (2004). Individual differences in memory updating in relation to arithmetic problem solving. Learning and Individual Difference, 14, pp. 219-230.
Passolunghi M.C., Bizzarro M. (2005). Risolvere Problemi Aritmetici. Attività su comprensione, rappresentazione, memoria e updating. Trento: Erickson.
Riley M.S., Greeno J.G., Heller J.J. (1983). Developments of children’s problem-solving ability in arithmetic. In H.P. Ginsburg (a cura di). The development of mathematical thinking, New York: Academic Press.
Riley M.S., Greeno J.G (1988). Developmental analysis of understanding language about quantities and of solving problems. Cognition and Instruction, 5(1), pp. 49-101.
Swanson H.L., Beebe-Frankenberger M. (2004). The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties. Journal of Educational Psychology, 96 (3), pp. 471-491.
Swanson H.L., Cooney J. B., Brock S. (1993). The influence of working memory and classification ability on children’s word problem solution. Journal of Experimental Child Psychology. 55(3), pp. 374-395.
Thorndyke E.L. (1898). Animal intelligence: an experimental study of the associative process in animals. Psychological Review Monographs Supplement, 2(8).
Baddeley A.D. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology, 49 (A), pp. 5-28.
Chi M.T.H., Feltovich P.J., Glaser R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, pp. 121-152.
D’Amico A., Passolunghi M.C., La Porta R., (2009). Risolvere problemi aritmetici (CD-ROM). Test e training su comprensione, rappresentazione, categorizzazione, pianificazione e memoria. Erickson, Trento.
De Candia C., Cibinel N., Lucangeli D. (2009) Risolvere problemi in 6 mosse. Trento: Erickson.
Greeno J.G., Riley M.S. (1987). Processes and Development of Understanding. In R.E. Weinert, R.H. Kluwe (a cura di). Metacognition, Motivation and Understanding. Hillsdale N.J.: Lawrence Erlbaum Associates, pp. 289-313.
Hegarty M., Mayer R.E., Monk C.A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of educational psychology, 87 (1), pp. 18-32.
Hegarty M., Kozhevnikov M., (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), pp. 684-689.
Lucangeli D., Cornoldi C. (1995). Metacognizione e matematica. In O. Albanese, P.A. Doudin, D. Martin (a cura di). Metacognizione ed educazione. Milano: Franco Angeli.
Lucangeli D., Tressoldi P., Cendron M. (1998a). Cognitive and metacognitive abilities involved in the solution of mathematical word problems: validation of a comprehensive model. Contemporary educational psychology, 23, pp. 257-275.
Lucangeli D., Tressoldi P.E., Cendron M. (1998b). SPM. Test di abilità di soluzione dei problemi matematici. Trento: Erickson.
Mayer R.E. (1998). Cognitive, metacognitive, and motivational aspects of problem solving. Instructional Science, Vol. 26, pp. 49-63.
Montague M. (1992). The Effects of Cognitive and Metacognitive Strategy Instruction on the Mathematical Problem Solving of Middle School Students with Learning Disabilities. Journal of Learning Disabilities, 25(4), pp. 230-248.
Passolunghi M.C., Lonciari I., Cornoldi C. (1994). Abilità di pianificazione nella risoluzione di problemi aritmetici di tipo verbale. Atti del Congresso nazionale Airipa su Problemi di attenzione e comportamento nei disturbi di apprendimento, Ferrara.
Passolunghi M.C., Lonciari I., Cornoldi C. (1996). Abilità di pianificazione, comprensione, metacognizione e risoluzione di problemi aritmetici di tipo verbale. Età Evolutiva, 54, pp. 36-48.
Passolunghi M.C., Pazzaglia F. (2004). Individual differences in memory updating in relation to arithmetic problem solving. Learning and Individual Difference, 14, pp. 219-230.
Passolunghi M.C., Bizzarro M. (2005). Risolvere Problemi Aritmetici. Attività su comprensione, rappresentazione, memoria e updating. Trento: Erickson.
Riley M.S., Greeno J.G., Heller J.J. (1983). Developments of children’s problem-solving ability in arithmetic. In H.P. Ginsburg (a cura di). The development of mathematical thinking, New York: Academic Press.
Riley M.S., Greeno J.G (1988). Developmental analysis of understanding language about quantities and of solving problems. Cognition and Instruction, 5(1), pp. 49-101.
Swanson H.L., Beebe-Frankenberger M. (2004). The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties. Journal of Educational Psychology, 96 (3), pp. 471-491.
Swanson H.L., Cooney J. B., Brock S. (1993). The influence of working memory and classification ability on children’s word problem solution. Journal of Experimental Child Psychology. 55(3), pp. 374-395.
Thorndyke E.L. (1898). Animal intelligence: an experimental study of the associative process in animals. Psychological Review Monographs Supplement, 2(8).