In the process of problem solving, intuitive thinking leads to findings that go beyond gaps and plays a decisive role in problem solving. Considering that problems often need to be solved in groups rather than by individuals, it is necessary to examine how intuitive thinking expressed by individuals is shared and elaborated among peers in a group…

Children's intuitive understandings of mathematical ideas--both correct, generalizable strategies alongside misconceptions--showcase the complexity of their thinking. However, recognizing children as complex thinkers is one thing but it is another thing altogether to leverage their ideas to plan for and carry out mathematics instruction. The…

Recent studies reveal that children can solve proportional reasoning problems presented with continuous amounts that enable intuitive strategies by around 6 years of age but have difficulties with problems presented with discrete units that tend to elicit explicit count-and-match strategies until at least 10 years of age. The current study tests…

We encounter ratios on a daily basis. They also play an important role as a basic construct of thinking in many areas of school mathematics. For example, a fraction can be interpreted as the ratio of a part to the respective whole. Many children appear to have difficulties with fractions and although the concept of ratios is crucial for this…

Understanding contingency table analysis is a facet of mathematical competence in the domain of data and probability. Previous studies have shown that even young children are able to solve specific contingency table problems, but apply a variety of strategies that are actually invalid. The purpose of this paper is to describe primary school…

In Indonesia, proportion is being taught formally in Grade 5 (10-11 years old). However, the existing learning approach does not support the development of the students' proportional reasoning. The way to teach proportion by giving cross multiplication is not meaningful for the students. They just memorize the procedure without understanding how…

Learning physics often requires overcoming common misconceptions based on naïve interpretations of observations in the everyday world. One proposed way to help learners build appropriate physics intuitions is to expose them to computer simulations in which motion is based on Newtonian principles. In addition, playing video games that require…