Reading mathematics at school. Inferential reasoning on the Pythagorean Theorem

Journal title CADMO
Author/s Gabriella Agrusti, Valeria Damiani, Daniele Pasquazi
Publishing Year 2015 Issue 2015/1 Language Italian
Pages 25 P. 61-85 File size 310 KB
DOI 10.3280/CAD2015-001007
DOI is like a bar code for intellectual property: to have more infomation click here

Below, you can see the article first page

If you want to buy this article in PDF format, you can do it, following the instructions to buy download credits

Article preview

FrancoAngeli is member of Publishers International Linking Association, Inc (PILA), a not-for-profit association which run the CrossRef service enabling links to and from online scholarly content.

Reading a mathematical problem can be often challenging for students. To be successful, they need to understand the words, transposing their meaning on an abstract level, to identify the relations stated in the problem and the task requested. Even if the meaning of the words is known, the case can be given that the student cannot grab the global meaning, nor inferring useful implications to solve the problem. This article offers an overview on reading comprehension issues linked to mathematical texts, and then proposes a set of common mistakes made by young readers, emerged in a first exploratory field experience carried out with grade 7 students. Given that learning activities were carried out on the Pythagorean Theorem, specific attention was devoted to the transposition of words into geometrical figures.

Keywords: Reading comprehension, mathematics, Pythagorean Theorem, inferences, lower secondary school.

  1. Alexander, P.A., Jetton, T.L. (2000), “Learning from Text: A Multidimensional and Developmental Perspective”, in M. Kamil, P.D. Pearson, R. Barr, P. Mosenthal (eds), Handbook of Reading Research. Mahwah: Erlbaum, pp. 285-310.
  2. Atzeni, L., Depau, P., Figus, R., Lecca, M.T., Milia, L. (2010), “Valutare la competenza linguistica in ambito scientifico”, in E. Lungarini, Valutare le competenze linguistiche. Milano: FrancoAngeli, pp. pp. 257-276.
  3. Birr Moje, E., Stockdill, D., Kim K., Kim, H. (2011), „The Role of Text in Disciplinary Learning”, In M. Kamil, P.D. Pearson, E.B., Moje, P.P Afflerbach, Handbook of Reading Research. Mahwah: Erlbaum, pp. pp. 453-486.
  4. Burton, L., Morgan, C. (2000), “Mathematicians Writing”, Journal for Research in Mathematics Education, 31, pp. 429-453.
  5. 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.
  6. Cornoldi, C. (1995), Metacognizione e apprendimento. Bologna: il Mulino.
  7. D’Amore B. (2001), “Un contributo al dibattito su concetti e oggetti matematici: la posizione ‘ingenua’ in una teoria ‘realista’ vs il modello ‘antropologico’ in una teoria ‘pragmatica’”, La matematica e la sua didattica, 1, pp. 4-30.
  8. De Beni, R., Pazzaglia, F., Molin A., Zamperlin, C. (2003), Psicologia cognitiva dell’apprendimento. Aspetti teorici e applicazioni. Trento: Erickson.
  9. Ferrari, P.L. (2003), “Costruzione di competenze linguistiche appropriate per la matematica a partire dalla media inferiore”, L’insegnamento della matematica e delle scienze integrate, 26A, 4, pp. 469-496.
  10. Giamblico/Iamblichus (1991), La vita pitagorica (introduzione, traduzione italiana e note di Maurizio Giangiulio). Milano: Biblioteca Universale Rizzoli.
  11. Goldman, S.R. (1997). Learning from text: Reflections on the past and suggestions for the future. Discourse Processes, 23, 357-398.
  12. Heath T.L. (1921), History of Greek Mathematics. Oxford: Clarendon Press.
  13. Hersh, R. (2001), Cos’è davvero la matematica. Milano: Baldini&Castoldi (tit. or. What is mathematics, Really?, 1997).
  14. INVALSI (2012), PIRLS e TIMSS: i risultati degli studenti italiani in matematica, lettura e scienze, (al 30/3/2015).
  15. Lee, C.D., Spratley, A. (2010), Reading in the Disciplines and the Challenges of Adolescent Literacy. New York: Carnegy Corporation of New York.
  16. Lucangeli D., Tressoldi P., Cendron M. (1998), “Cognitive and Metacognitive Abilities involved in the Solution of Mathematical Word Problems: Validation of a Comprehensive Model”, Contemporary Educational Psychology, 23, pp. 257-275.
  17. Mayer, R.E., (1998), “Cognitive, Metacognitive, and Motivational Aspects of Problem Solving”, Instructional Science, 26, pp. 49-63.
  18. Mialaret, G. (1969), L’apprendimento della matematica. Saggio di psico-pedagogia (tit. or. L’apprentissage des mathématiques: essai de psycho-pédagogie. Bruxelles:
  19. C. Dessart, 1967). Morgan, C. (2005), “Words, Definitions and Concepts in Discourses of Mathematics, Teaching and Learning”, Language and Education, 19, pp. 103-117.
  20. Mullis, I.V.S., Martin M.O., Foy P. (2013), “The Impact of Reading Ability on TIMSS Mathematics and Science Achievement at the Fourth Grade: An Analysis by Item Reading Demands”, in M.O Martin, I.V.S. Mullis (eds), TIMSS and PIRLS 2011: Relationships Among Reading, Mathematics, and Science Achievement at the Fourth Grade – Implications for Early Learning. Chestnut Hill: TIMSS & PIRLS International Study Center, Boston College.
  21. 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.
  22. Polmonari, A. (1993), Psicologia dell’adolescenza. Bologna: il Mulino.
  23. Read, J. (2000), Assessing Vocabulary. Cambridge: Cambridge University Press.
  24. Remillard, J.T. (2005), “Examining Key Concepts in Research on Teachers’ Use of Mathematics Curricula”, Review of Educational Research, 75, pp. 211-246.
  25. Russo L. (1998), La rivoluzione dimenticata. Milano: Feltrinelli.
  26. 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, pp. 374-395.
  27. Tarr, J.E., Chavez, O., Reys, R.E., Reys, B.J. (2006), “From the Written to the Enacted Curriculum: The Intermediary Role of Middle School in Mathematics Teachers in shaping Students Opportunity to learn”, School Science and Mathematics, 106, pp. 191-201.
  28. Tornatore, L. (1974), “Capire la matematica”, in L. Tornatore, R. Maragliano. L. Rosaia, L. Piracci, M.A. Belasio, M.B. Palma, A. Carpanelli, G. De Sabbata, S. Calzolani, M. Corda Costa, L. Andreotti, L. Salvadori, G. Picchione, L. Cali, G. Staccioli, Proposte didattiche. Insegnamenti matematici e scientifici. Esperienze di attività extracurriculare. Torino: Loescher, pp. 19-23.
  29. Trinchero, R. (2012), Costruire, valutare, certificare competenze. Proposte di attività per la scuola. Milano: FrancoAngeli.
  30. Verschaffel, L., Greer, B., De Corte E. (2000), Making Sense of Word Problems. The Netherlands: Swets & Zeitlinger.
  31. Usiskin, Z. (1996), “Mathematics as a Language”, in C.E. Portia (ed), Communications in Mathematics, K-12 and Beyond. Reston: National Council of Teachers of Mathematics, pp. 231-243.
  32. Wallace, F.H., Clark K.K. (2005), “Reading Stances in Mathematics: Positioning Students and Texts”, Action in Teacher Education, 27 (2), pp. 68-69.

  • Pat-in-the-Loop: Declarative Knowledge for Controlling Neural Networks Dario Onorati, Pierfrancesco Tommasino, Leonardo Ranaldi, Francesca Fallucchi, Fabio Massimo Zanzotto, in Future Internet /2020 pp.218
    DOI: 10.3390/fi12120218

Gabriella Agrusti, Valeria Damiani, Daniele Pasquazi, Leggere la matematica a scuola. Percorsi inferenziali sul teorema di Pitagora in "CADMO" 1/2015, pp 61-85, DOI: 10.3280/CAD2015-001007