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

#### Abstract

#### Keywords

#### Full Text:

PDF#### 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.

DOI: https://doi.org/10.26220/rev.1627

View Counter: Abstract | 277 | times, and PDF | 126 | times

**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.

Pasithee | Library & Information Center | University of Patras