Educational Studies in Mathematics

, Volume 89, Issue 3, pp 307–336 | Cite as

Schoolteacher trainees’ difficulties about the concepts of attribute and measurement

Article
First Online:

Abstract

“Attribute” and “measurement” are two fundamental concepts in mathematics and physics. Teaching these concepts is essential even in elementary school, but numerous studies have pointed out pupils’ difficulties with them. These studies emphasized that pupils must learn about attributes before being taught how to measure these attributes, which can be done through activities involving comparing and sorting. In France, as in numerous English-speaking countries, official teaching instructions for the elementary-school years (Grades 1 to 5) recommend this approach. We consider that to be able to teach attributes, teachers themselves must master and differentiate the concepts of attribute and measurement. Indeed, these concepts are part of any teacher’s subject matter knowledge, especially of what Ball called “specialized content knowledge”, which is needed to effectively teach both attributes and measurement. In this study, we analyze the level of mastery of these concepts among French teacher trainees. Our findings suggest that future teachers do not clearly differentiate these concepts, and that the concept of attribute is the less well understood. We highlight that an erroneous understanding of attribute is extremely prevalent: almost half of our participants think of attribute as a vague, imprecise notion. Finally, we discuss the possible causes of this misconception and its implications for teaching.

Keywords

Elementary school Experimental sciences Mathematics Measurement Attribute Teacher trainees Teachers’ knowledge Conceptions 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgment

This work was funded by the French Ministry of Research.

References

  1. Allie, S., Buffler, A., Kaunda, L., Campbell, B., & Lubben, F. (1998). First-year physics students’ perceptions of the quality of experimental measurements. International Journal of Science Education, 20(4), 447–459.CrossRefGoogle Scholar
  2. Alonzo, A., Kobarg, M., & Seidel, T. (2012). Pedagogical Content Knowledge as reflected in teacher-student interactions: Analysis of two video cases. Journal of Research in Science Teaching, 49(10), 1211–1239.Google Scholar
  3. Ball, D.L. (2003). What mathematical knowledge is needed for teaching mathematics? Retrieved from http://www2.ed.gov/rschstat/research/progs/mathscience/ball.html
  4. Ball, D. L., & Forzani, F. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497–415.CrossRefGoogle Scholar
  5. Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching, who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 14–22, 43–46.Google Scholar
  6. Ball, D. L., Thames, M., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59, 389–407.CrossRefGoogle Scholar
  7. Barrett, J. E., Sarama, J., Clements, D. H., Cullen, C., McCool, J., Witkowski-Rumsey, C., et al. (2012). Evaluating and improving a learning trajectory for linear measurement in elementary grades 2 and 3: a longitudinal study. Mathematical Thinking and Learning, 14(1), 28–54.CrossRefGoogle Scholar
  8. Boulton-Lewis, G. M., Wilss, L. A., & Mutch, S. L. (1996). An analysis of young children’s strategies and use of devices of length measurement. Journal of Mathematical Behavior, 15, 329–347.CrossRefGoogle Scholar
  9. Brousseau, G., & Brousseau, N. (1991–1992). Le poids d’un récipient, étude des problèmes de mesurage en CM [The weight of a bowl, study of measurement problems in grades 4 and 5]. Grand N, 50, 65–87.Google Scholar
  10. Bureau International des Poids et Mesures. (2008). JCGM-VIM [International vocabulary of metrology—basic and general concepts and associated terms]. Retrieved from http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
  11. Carnap, R. (1973). Les fondements philosophiques de la physique [Philosophical foundations of physics]. Paris: Armand Colin.Google Scholar
  12. Chambris, C. (2007). Petite histoire des rapports entre grandeurs et numérique dans les programmes de l’école primaire [Short story of relationships between attributes and numbers in Standards for elementary school]. Repères IREM, 69, 5–31.Google Scholar
  13. Clements, D. H., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics: standards for early childhood mathematics education (pp. 299–320). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  14. Cross, D. (2010). Action conjointe et connaissances professionnelles [Joint action and professional knowledge]. Éducation & Didactique, 4(3), 39–60.Google Scholar
  15. De Broglie, L. (1955). La physique [Physics]. Tome II: Société Nouvelle de l'Encyclopédie Française.Google Scholar
  16. Devichi, C. & Chatillon, J.F. (1993). Task representation and performance in length seriation tasks. Proceedings of the 5th European Conference for Research on learning and Instruction (pp. 167–168). Université d’Aix-Marseille, France.Google Scholar
  17. Dienes, Z.P. & Golding, EW. (1970). Les premiers pas en mathématiques; exploration de l’espace et pratique de la mesure [The first steps in mathematics; exploration of space and practice of measurement]. 5° édition, Paris: OCDL.Google Scholar
  18. Douady, R., & Perrin-Glorian, M. J. (1989). Un processus d'apprentissage du concept d'aire de surface plane [A learning process for the concept of area of plane surfaces]. Educational Studies in Mathematics, 20, 387–424.CrossRefGoogle Scholar
  19. Evangelinos, D., Psillos, D., & Valassiades, O. (2002). An investigation of teaching and learning about measurement data and their treatment in the introductory physics laboratory. In D. Psillos & H. Niederer (Eds.), Teaching and learning in the science laboratory (pp. 179–190). Dordrecht: Kluwer Academic.Google Scholar
  20. Favrat, J.-F., & Munier, V. (2007). Evolution de l’enseignement des grandeurs à l’école élémentaire depuis 1945 [Evolution of the teaching of attributes in elementary school since 1945]. Repères IREM, 68, 51–75.Google Scholar
  21. Flandé, Y. (2003). Tests d’hypothèses et mesure au CM1 [test of hypothesis and measure in grade 4]. Grand N, 71, 91–104.Google Scholar
  22. Friedelmeyer, J. P. (2001). Grandeurs et nombres, l’histoire édifiante d’un couple fécond [Quantities and numbers, edifying story of a fruitful couple]. Repères IREM, 44, 5–31.Google Scholar
  23. Gonella, L. (1984). La notion de mesure [The notion of measure]. Revue Philosophique de la France et de l’étranger, 174(2), 149–187.Google Scholar
  24. Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.CrossRefGoogle Scholar
  25. Journeaux, R., Séré, M. G., & Winther, J. (1995). La mesure en terminale scientifique [Measure in grade 12]. Bulletin d’Union des Physiciens, 779(1), 1925–1945.Google Scholar
  26. Kaplan, A. (1964). The conduct of inquiry: Methodology for behavioral science. New York: Thomas Y. Crowell.Google Scholar
  27. Kelvin, W. (1883). From lecture to the Institution of Civil Engineers, London (3 May 1883), ‘Electrical Units of Measurement’, Popular Lectures and Addresses (1889), 1, 80–81.Google Scholar
  28. Kospentaris, G., Spyrou, P., & Lappas, D. (2011). Exploring students’ strategies in area conservation geometrical tasks. Educational Studies in Mathematics, 77, 105–127.CrossRefGoogle Scholar
  29. Lebesgue, H. (1975). La mesure des grandeurs [Measurement of attributes]. Paris: Librairie scientifique et technique.Google Scholar
  30. Lehrer, R. (2003). Developing understanding of measurement. In J. Kipatrick, W. G. Martin, & D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 197–192). Reston: National Council of Teachers of Mathematics.Google Scholar
  31. Ligozat, F. (2008). Un point de vue de didactique comparée sur la classe de mathématiques. Etude de l'action conjointe du professeur et des élèves à propos de l'enseignement / apprentissage de la mesure des grandeurs dans des classes françaises et suisses romandes [A point of view of comparative didactics on the class of mathematics. Study of the joint action of the professor and the pupils about the teaching/learning of the measurement of attributes in French and French-speaking Swiss classes]. (Unpublished doctoral dissertation).  University of Genève and Aix-Marseille 1, Genève, Suisse.Google Scholar
  32. Lippmann, R. (2005). Teaching the concepts of measurement: an example of a concept-based laboratory course. American Journal of Physics, 73(8), 771–777.CrossRefGoogle Scholar
  33. Lubben, F., Campbell, B., Buffler, A., & Allie, S. (2001). Point and set reasoning in practical science measurement by entering university freshmen. Science Education, 85, 311–327.CrossRefGoogle Scholar
  34. Lubben, F., & Millar, R. (1996). Children’s ideas about the reliability of experimental data. International Journal of Science Education, 18(8), 955–968.CrossRefGoogle Scholar
  35. Macdonald, A. (2011). Young children’s representations of their developing measurement understandings. In J. Clark, B. Kissane, J. Mousley, T. Spencer, & S. Thornton (Eds.), Proceedings of the 34th annual conference of the Mathematics Education Research Group of Australasia and the Australian Association of Mathematics Teachers (pp. 482–490). Adelaide, Australia: MERGA and AAMT.Google Scholar
  36. Maisch, C., Ney, M., & Balacheff, N. (2008). Quelle est l’influence du contexte sur les raisonnements d’étudiants sur la mesure en physique ? [What is the influence of the context on students’ reasoning about measurement in Physics?]. ASTER, 47, 43–70.Google Scholar
  37. Ministère de l’Éducation nationale (France). (1970). Circulaire du 2 janvier 1970 concernant le programme de mathématiques à l’école élémentaire, Bulletin officiel de l’éducation nationale [Note about mathematics Standards for elementary school, Official bulletin of French National Education, 2 January 1970], 5, 349–385.Google Scholar
  38. Ministère de l’Education Nationale (France). (2007). Mise en œuvre du socle commun de connaissances et de compétences. Programmes d'enseignement de l'école primaire, Bulletin officiel de l’éducation nationale [Common basis of knowledge. Standards for elementary school, Official bulletin of French National Education]. hors-série n° 5 April 12.Google Scholar
  39. Ministère de l’Education Nationale (France). (2002). Horaires et programmes d’enseignement de l’école primaire, Bulletin officiel de l’éducation nationale [Working time and standards for elementary school, Official bulletin of French national education]. hors série n°1 February 14.Google Scholar
  40. Ministère de l'Education Nationale (France). (2003). Documents d’accompagnement des programmes de 2002, grandeurs et mesures à l’école élémentaire [In addition to Standards 2002, quantities and measurements in elementary school]. Paris: direction de l’enseignement scolaire.Google Scholar
  41. Munier, V., & Passelaigue, D. (2012). Réflexions sur l’articulation entre didactique et épistémologie dans le domaine des grandeurs et mesures dans l’enseignement primaire et secondaire [Reflections on the links between physics education and epistemology in the field of attributes and measurement in primary and secondary school]. Tréma, 38, 107–147.Google Scholar
  42. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.Google Scholar
  43. Passelaigue, D. (2011). Grandeurs et mesures à l’école élémentaire. Des activités de comparaison a la construction des concepts : le cas de la masse en CE1 [Attributes and measurement at elementary school. From comparison activities to concepts: example of the attribute of mass]. (Unpublished doctoral dissertation). University of Montpellier 2, Montpellier, France.Google Scholar
  44. Perrin-Glorian, M. J. (2002). Problèmes didactiques liés à l'enseignement des grandeurs. Le cas des aires [Difficulties in the teaching of attributes. Example about areas]. In J. L. Dorier (Ed.), Actes de la 11ème école d'été de didactique des mathématiques, Corps, 2001 (pp. 299–315). Grenoble: La Pensée sauvage.Google Scholar
  45. Petrosino, A. J., Lehrer, R., & Schauble, L. (2003). Structuring error and experimental variation as distribution in the fourth grade. Mathematical Thinking and Learning, 5(2&3), 131–156.CrossRefGoogle Scholar
  46. Piaget, J., & Inhelder, B. (1968). Le développement des quantités physiques chez l'enfant [Understanding of physical quantities by children]. Neuchatel et Paris: Delachaux et Niestlé.Google Scholar
  47. Pressiat, A. (2009). Les grandeurs dans les mathématiques et dans leur enseignement [Attributes in mathematics and in mathematics education]. Conférence pour l’Association des Professeurs de Mathématique de l’Enseignement Public, 483. Besançon. Retrieved from www.apmep.asso.fr
  48. Rey-Debove, J., & Rey, A. (1996). Le petit Robert—Dictionnaire alphabétique et analogique de la langue française [Alphabetical dictionary and thesaurus of the French language]. Paris: Le Robert.Google Scholar
  49. Rouche, N. (1994). Qu’est-ce qu’une grandeur ? Analyse d’un seuil épistémologique [What is an attribute?]. Repères IREM, 15, 25–26.Google Scholar
  50. Rouche, N. (2006). Nombres, grandeurs, proportions [Numbers, attributes, proportions]. Paris: Ellipses.Google Scholar
  51. Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: learning trajectories for young children. New York: Routledge.Google Scholar
  52. Séré, M. G. (1992). Le déterminisme et le hasard dans la tête des élèves ou de l’utilité d’un traitement statistique des séries de mesures [Determinism and chance for pupils: about the interest of statistical treatment of series of data]. Bulletin d’Union des Physiciens, 740, 87–96.Google Scholar
  53. Séré, M. G., Journeaux, R., & Larcher, C. (1993). Learning the statistical analysis of measurement errors. International Journal of Science Education, 15(4), 427–438.CrossRefGoogle Scholar
  54. Séré, M. G., Journeaux, R., & Winther, J. (1998). Enquête sur la pratique des enseignants de lycée dans le domaine des incertitudes [Study about the high school teachers’ practices in the field of uncertainties]. Bulletin d’Union des Physiciens, 801, 247–254.Google Scholar
  55. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.Google Scholar
  56. Shulman, L. S. (1987). Knowledge and teaching foundations of the new reform. Harvard Educational Revue, 57(1), 1–22.CrossRefGoogle Scholar
  57. Thomas, D. (2006). A general inductive approach for analyzing qualitative evaluation data. American Journal of Evaluation, 27(2), 237–246.CrossRefGoogle Scholar
  58. Volkwyn, T. S., Allie, S., Buffler, A., & Lubben, A. (2008). Impact of a conventional introductory laboratory course on the understanding of measurement. Physical Review Special Topics Physics Education Research, 4, 1–10.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.LIRDEF (EA 3749), Université de Montpellier et Université Paul Valéry de MontpellierMontpellier cedex 5France

Personalised recommendations