P. Barmby, T. Harries, S. Higgins, and J. Suggate, The array representation and primary children's understanding and reasoning in multiplication, Educational Studies in Mathematics, vol.70, issue.3, pp.217-241, 2009.
DOI : 10.1007/s10649-008-9145-1

URL : http://dro.dur.ac.uk/5458/1/5458.pdf

M. T. Battista and D. H. Clements, Students' understanding of three-dimensional rectangular arrays of cubes, Journal for Research in Mathematics Education, vol.27, issue.3, pp.258-292, 1996.

J. S. Bruner, Beyond the information given: Studies in the psychology of knowing, 1974.

E. Carruthers and M. Worthington, Children's mathematics: Making marks, making meaning, 2006.

C. Finesilver, Drawing division: emerging and developing multiplicative structure in lowattaining students' representational strategies (PhD), London. Thematic Working Group, p.24, 2014.

K. L. Fletcher, L. F. Huffman, N. W. Bray, and L. A. Grupe, The use of the microgenetic method with children with disabilities: Discovering competence, Early Education & Development, vol.9, issue.4, p.357, 1998.

T. Harries and P. Barmby, Representing and understanding multiplication, Research in Mathematics Education, vol.9, issue.1, pp.33-45, 2007.
DOI : 10.1080/14794800008520169

A. Izsák, You have to count the squares': Applying knowledge in pieces to learning rectangular area, The Journal of the Learning Sciences, vol.14, issue.3, pp.361-403, 2005.

L. Jacob and J. Mulligan, Using Arrays to Build towards Multiplicative Thinking in the Early Years, Australian Primary Mathematics Classroom, vol.19, issue.1, pp.35-40, 2014.

V. L. Kouba, Children's solution strategies for equivalent set multiplication and division word problems, Journal for Research in Mathematics Education, vol.20, issue.2, pp.147-158, 1989.
DOI : 10.2307/749279

G. Lakoff and R. Nu?n?ez, Where mathematics comes from: How the embodied mind brings mathematics into being, 2000.

G. T. Matney and B. N. Daugherty, Seeing Spots and Developing Multiplicative Sense Making, Mathematics Teaching in the Middle School, vol.19, issue.3, pp.148-155, 2013.

L. Meira, The Microevolution of Mathematical Representations in Children's Activity, Cognition and Instruction, vol.13, issue.2, pp.269-313, 1995.

T. Nunes and P. Bryant, Children doing mathematics, 1996.

J. Piaget, The Child's Conception of Number, 1952.

A. H. Schoenfeld, J. P. Smith, and A. Arcavi, Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain, Advances in instructional psychology, vol.4, pp.55-175, 1993.

C. Voutsina, A micro-developmental approach to studying young children's problem solving behavior in addition, The Journal of Mathematical Behavior, vol.31, issue.3, pp.366-381, 2012.

E. C. Wittmann, Mathematics as the science of patterns-a guideline for developing mathematics education from early childhood to adulthood. Plenary Lecture presented at the International Colloquium 'Mathematical learning from Early Childhood to Adulthood, Mons. Thematic Working Group, p.24, 2005.

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