Teaching suggestions for the measurement of area in Elementary School. Measurement tools and measurement strategies

KONSTANTINOS ZACHAROS, DIMITRIS CHASSAPIS

Abstract


The present study deals with teaching the concept and measurement of area. 106 subjects of the 6th grade of Greek Elementary School measured the area of different kinds of shapes. The subjects were divided into two groups, an experimental group and a control group. In the experimental group, area evaluation was taught in a way that highlighted the conceptual characteristics of area measurement. The teaching intervention and the use of different measurement tools led to different measurement strategies. Moreover, the experimental group used more successful strategies than the control group.

Keywords


Area Measurement, teaching area measurement, measurement tools, elementary school

References


Anderson, N. & Cuneo, D. (1978). The height + width rule in children’s judgments of quantity. Journal of Experimental Psychology: General, 107(4), 335-378.

Battista, M. (1982). Understanding area and area formulas. Mathematics Teacher, 75(5), 362-368.

Bart, W. M., Yuzawa, M. & Yuzawa, M. (2008). Development of mathematical reasoning among young children: How do children understand area and length? In O. N. Saracho & B. Spodek (eds.), Contemporary Perspectives on Mathematics in Early Childhood Education (Charlotte: Information Age Publishing), 157-185.

Borasi, R. (1994). Capitalising on errors as “springboards for inquiry”: a teaching experiment. Journal for Research in Mathematics Education, 25(2), 166-208.

Boyer, C. (1949). The history of the calculus and its conceptual development (New York: Dover Publications).

Brousseau, G., Davis, R. & Werner, T. (1986). Observing students at work. In B. Christiansen, A. G. Howson & M. Otte (eds) Perspectives on mathematics education (Dordrecht: D. Reidel Publishing Company), 205-241.

Brown, T. (2001). Mathematics Education and Language. Interpreting Hermeneutics and Post-Structuralism (Dordrecht: Kluwer Academic Publishers).

Bunt, L. N. H., Jones, P. S., & Bedient, J. D. (1976). The historical roots of elementary Mathematics. Englewood Cliffs: Prentice Hall.

Chassapis, D. (1999). The mediation of tools in the development of formal mathematical concepts: The compass and the circle as an example. Education Studies in Mathematics, 37(3), 275-293.

Clements, D. H. & Samara, J. (2009). Learning and teaching early Math. The Learning Trajectories Approach (London-New York: Routledge).

Cohen, L., Manion, L. & Morrison, K. (2004). Research methods in Education (London and New York: Routledge Falmer).

Fowler, D. (1987). The Mathematics of Plato’s Academy (Oxford: Clarendon Press).

Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures (Dordrecht: D. Reidel).

Kamii, C. & Kysh, J. (2006). The difficulty of “length x width”: Is a square the unit of measurement? Journal of Mathematical Behavior, 25, 105–115.

Kidman, G. & Cooper, T. J. (1997). Area integration rules for grades 4, 6 and 8 students. In Proceedings of the 21st international Conference for the Psychology of Mathematics Education, Lahti, Finland, 136-143.

Lautrey, J., Mullet, E. & Paques, P. (1989). Judgments of quantity and conservation of quantity: The area of a rectangle. Journal of Experimental Child Psychology, 47, 193-209.

Leon, M. (1982). Extent, multiplying, and proportionality rules in children’s judgments of area. Journal of Experimental Child Psychology, 33, 124-141.

Luria, A. R. (1976). Cognitive development: Its cultural and social foundations (Cambridge, MA: Harvard University Press).

Nitabach, E. & Lehrer, R. (1996). Developing spatial sense through area measurement. Teaching Children Mathematics, 2(8), 473-476.

Nunes, T. & Bryant, P. (1996). Children Doing Mathematics (UK: Blackwell Publishers).

Nunes, T., Light, P. & Mason, J. (1993). Tools for thought: The measurement of length and area. Learning and Instruction, 3, 39-54.

Outhred, L. & Mitchelmore, M. (1996). Children’s intuitive understanding of area measurement. In Proceedings of the 20th international Conference for the Psychology of Mathematics Education, Valencia, Spain, 91-98.

Piaget, J. & Inhelder, B. (1956). The child's conception of space (London: Routledge).

Piaget, J., Inhelder, B. & Szeminska, A. (1960). The child’s conception of geometry (London: Routledge & Kegan Paul).

Resnick, L. B., Pontecorvo, C. & Saljo, R. (1997). Discourse, tools, and reasoning: Essays on situated cognition. In B. Resnick, R. Saljo, C. Pontecorvo & B. Burge (eds) Discourse, tools, and reasoning: Essays on situated cognition (Berlin, Heidelberg, New York: Springer-Verlag), 1-20.

Ryan, J. & Williams, J. (2007). Children’s Mathematics 4-15. Learning from errors and misconceptions (England: Open University Press, The McGraw-Hill Companies).

Silverman, J. & Thompson, P. W. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11, 499–511

Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114 - 145.

Stephan, M. Cobb, P., Gravemeijer, K. & Estes, B. (2001). The role of tools in supporting student’s development of measuring conceptions. In A. A. Cuoco & F. R. Curcio (eds) The roles of representation in school mathematics (Reston, Virginia: National Council of Teachers of Mathematics, 2001 Yearbook), 63-76.

Van de Walle, J. & Lovin, L. H. (2006). Teaching student-centered Mathematics: Grades K-3. (Boston, MA: Allyn and Bacon Pearson Education, Inc).

Vygotsky, L. S. (1978). Mind in society. The development of higher psychological processes (Cambridge, MA: Harvard University Press).

Wagman, H. (1975). Τhe Child’s conception of area measure. In M. Rosskopf (ed.) Children's mathematical concepts: Six Piagetian studies in Mathematics Education (New York: Teachers College, Columbia University), 71-110.

Wheatley, G. & Reynolds, A. (1996). The construction of abstract units in geometric and numeric settings. Educational Studies in Mathematics, 30(1), 67-83.

Zacharos, K. (2006). Prevailing educational practices for area measurement and students’ failure in measuring areas. Journal of Mathematical Behavior, 25, 224–239.

Zacharos, K. Antonopoulos, K. & Ravanis, K. (2011). Activities in mathematics education and teaching interactions. The construction of the measurement of capacity in preschoolers. European Early Childhood Education Research Journal, 19(3), 451-468.


Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

 


 

Re S M ICT E , ISSN: 1792-3999 (electronic), 1791-261X (print)

Laboratory of Didactics of Sciences, Mathematics and ICT, Department of Educational Sciences and Early Childhood Education - University of Patras.

Πασιθέη: Ηλεκτρονικές Επιστημονικές Δημοσιεύσεις Ανοικτής Πρόσβασης, 2008-2012, Βιβλιοθήκη & Κέντρο Πληροφόρησης - Πανεπιστήμιο Πατρών