Skip to main content

Adults’ Conception of Multiplication: Effects of Schooling on Multiplicative Conceptual Field

  • Chapter
  • First Online:
  • 310 Accesses

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

School mathematics is often related to a needing for memorization of a lot of information, times-tables are a paradigmatic example. A large amount of research on arithmetical facts has been implemented within cognitive psychology but rarely it is related to mathematics education research and quantitative methods are always used. In this paper it is presented a pilot study: ten interviews with adults are qualitatively analyzed using constructs from both research fields, showing that times-tables organization in memory could depend on school instruction. Level of instruction of subjects is indicated as an important variable in recalling and in choosing computation strategies, namely in the construction of the concept of multiplication.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Bahrick, H. P., & Hall, L. K. (1991). Lifetime maintenance of high school mathematics content. Journal of Experimental Psychology: General, 120(1), 20–33.

    Article  Google Scholar 

  • Bahrick, H. P., & Phelps, E. (1995). The maintenance of marginal knowledge. In U. Neisser & E. Winograd (Eds.), Remembering reconsidered: Ecological and traditional approaches to the study of memory (pp. 178–192). New York, NY: Cambridge University Press.

    Google Scholar 

  • Butterworth, B., Marchesini, M., & Girelli, L. (2003). Basic multiplication combinations: Passive storage or dynamic reorganization? In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 189–202). Mahwah, NJ: LEA.

    Google Scholar 

  • Byers, V., & Erlwanger, S. (1985). Memory in mathematical understanding. Educational Studies in Mathematics, 16, 259–281.

    Article  Google Scholar 

  • Campbell, J. I. D. (1987). Production, verification, and priming of multiplication facts. Memory & Cognition, 15(4), 349–364.

    Article  Google Scholar 

  • Dagenbach, D., & McCloskey, M. (1992). The organization of arithmetic facts in memory: Evidence from a brain-damaged patient. Brain and Cognition, 20(2), 345–366.

    Article  Google Scholar 

  • Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16, 3–17.

    Article  Google Scholar 

  • Fremont, H. (1967). New mathematics and old dilemmas. The Mathematics Teacher, 60(7), 715–719.

    Google Scholar 

  • García-Orza, J., Damas-López, J., & Matas, A. (2009). “2x3” primes naming “6”: Evidence from masked priming. Attention, Perception, & Psychophysics, 71(3), 471–480.

    Article  Google Scholar 

  • Geary, D. C., Widaman, K. F., & Little, T. D. (1986). Cognitive addition and multiplication: Evidence for a single memory network. Memory & Cognition, 14(6), 478–487.

    Article  Google Scholar 

  • Karsenty, R. (2002). What do adults remember from their high school mathematics? The case of linear functions. Educational Studies in Mathematics, 51(1–2), 117–144.

    Article  Google Scholar 

  • LeFevre, J. A., Lei, Q., Smith-Chant, B. L., & Mullins, D. B. (2001). Multiplication by eye and by ear for Chinese-speaking and English-speaking adults. Canadian Journal of Experimental Psychology, 55(4), 277–284.

    Article  Google Scholar 

  • Lemaire, P., & Fayol, M. (1995). When plausibility judgments supersede fact retrieval: The example of the odd-even effect on product verification. Memory & Cognition, 23(1), 34–48.

    Article  Google Scholar 

  • Mariotti, M. A., & Maffia, A. (2015). Cosa ricordano gli adulti sulle tabelline. Pedagogia più Didattica, 1(1), 21–30.

    Google Scholar 

  • McCloskey, M., Harley, W., & Sokol, S. M. (1991). Models of arithmetic fact retrieval: An evaluation in light of findings from normal and brain-damaged subjects. Journal of Experimental Psychology: Learning, Memory, and Cognition, 17(3), 377–397.

    Google Scholar 

  • Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. New York, NY: Cambridge University Press.

    Google Scholar 

  • Schank, R. C., & Abelson, R. (1977). Scripts, goals, plans, and understanding. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Sherin, B., & Fuson, K. (2005). Multiplication strategies and the appropriation of computational resources. Journal for Research in Mathematics Education, 36(4), 347–395.

    Google Scholar 

  • Siegler, R. S. (1988). Strategy choice procedures and the development of multiplication skills. Journal of Experimental Psychology: General, 117(3), 258–275.

    Article  Google Scholar 

  • Tulving, E. (1972). Episodic and semantic memory. In E. Tulving & W. Dondaldson (Eds.), Organization of memory (pp. 381–403). London, UK: Academic Press.

    Google Scholar 

  • Vergnaud, G. (1983). Multiplicative structures. In L. Landau (Ed.), Acquisition of mathematics concepts and processes (pp. 127–174). London, UK: Academic Press.

    Google Scholar 

  • Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & B. Behr (Eds.), Number concepts and operations in the middle grades (pp. 141–161). Reston, VA: NCTM.

    Google Scholar 

  • Zan, R., & Di Martino, P. (2009). Different profiles of attitude towards mathematics: The case of learned helplessness. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33th Conference of PME (Vol. 5, pp. 417–424). Thessaloniki, Greece: IGPME.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrea Maffia .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Maffia, A., Mariotti, M.A. (2018). Adults’ Conception of Multiplication: Effects of Schooling on Multiplicative Conceptual Field. In: Safford-Ramus, K., Maaß, J., Süss-Stepancik, E. (eds) Contemporary Research in Adult and Lifelong Learning of Mathematics. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-96502-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-96502-4_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96501-7

  • Online ISBN: 978-3-319-96502-4

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics