Pupils’ visual representations in standard and problematic problem solving in mathematics: their role in the breach of the didactical contract

Mathematical visualization process of junior high school students in solving a contextual problem based on cognitive style

“…It was based on the finding of [13]. For further research [9], showed that the contextual problem solving, mathematical visualization appeared for understanding the problem with the aim of making it easy to construct his understanding in the form of picture, pattern to help to get solution. Both of the subjects showed the different final result (solution).…”

“…[3] identified that one of abilities in exploring mathematics problem and for giving the meaning of mathematics concept related with the success in solving the problems, namely mathematical visualization. Based on opinions of " particularly, in the context of mathematical problem solving, visualization refers to the understanding of the problem with the construction and/or the use of a diagram or a picture to help obtain a solution" namely in the context of solving mathematics problem., visualization referred in understanding problem by constructing and/or by using diagram or picture to determine the solution [9]. That's why mathematical visualization had to be given more attention and developed in mathematics education and needed further investigation from the beginning in junior high school.…”

Visualization in Mathematics, Reading and Science Education

“…Visual representations constructed by emergent mathematics learners (38 kindergarteners aged 5-6 years and 34 first graders aged 6-7 years) were investigated by Deliyianni et al (2009). Their study was designed to investigate and compare the modes of representations used by the children and to examine the extent to which the children used the rules of the didactic (systematic use of rules and mathematical knowledge) contract.…”

Teachers’ Interpretation of Mathematics Goals in Swedish Preschools

“…According to Deliyianni et al (2009), formal mathematics teaching at early ages can get in the way of children thinking for themselves. When teachers give a more realistic, real-world presentation of problems, problems that need more careful consideration and offer alternative responses, pupils will tend to pay attention to the real meaning of the facts described in the problems (Verschaffel et al 2000).…”