Investigation of the relationships among number sense, multiple representation and problem solving skills of sixth grade students related to decimal numbers

Associations made by students between the knowledge and skills they have gained in their courses will contribute to their conceptual knowledge. This study aims at examining the relationships among number sense, multiple representation, and problem-solving skills of 6th grade students related to decimal numbers. Whereas 360 students in six different state schools of a province in Eastern Black Sea Region participated in the quantitative part of the research following the exploratory sequence design 6 of those students determined by the criterion sampling technique were involved in the qualitative part. Quantitative data of the study were collected through "The Number Sense Test On Decimal Numbers", "The Multiple Representation Test On Decimal Numbers", and "The Problem Solving Test On Decimal Numbers", and the qualitative data were collected through semi-structured interviews. The quantitative data obtained in this study were analyzed by a statistic program SPSS 20.0, and content analysis was used to analyze the qualitative data of the research. As a result of the study, it was found that number sense of 6th grade students in decimal numbers fell behind their multiple representation and problem-solving skills. In addition, a positive relationship was seen among their number sense, multiple representation, and problem-solving skills related to decimal numbers. Furthermore, multiple representation and number sense of students in decimal numbers were found to be a significant predictor of their problem-solving skills. Lastly, as the most significant predictor of problem-solving skill, number sense and representation skills could be presented according to the order of importance as follows: recognizing decimal number size, understanding the basic meaning of decimal numbers, transferring from pictorial representation to symbolic representation, transferring from symbolic representation to pictorial representation, being able to use a benchmark appropriately, and transferring from symbolic representation to symbolic representation. Consequently, those six variables together were found to explain the problem-solving skill at a significant level.