This article reports on a pilot study that used concrete materials and TinkerPlots to support a Year 4 student's understanding of the big ideas of variation and expectation when investigating a random chance experiment using spinners.

This paper investigated the intuitive development of the concept of integers among primary school students. In order to reveal if primary school students had an intuitive sense of integers, an assessment consisting of five questions was prepared and applied to a total 100 4th grade students. A variety of integer concepts were utilized in the…

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…

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…

The present study examines the ancient Greek history curriculum and the corresponding textbook as they are implemented in the fourth grade of primary school in an aim to determine whether and to what extent empathy is recognized as a fundamental tool for historical understanding. A close examination of the curriculum revealed that empathy is not…

In 4 studies, the authors examined how intuitions about the relative difficulties of the sciences develop. In Study 1, familiar everyday phenomena in physics, chemistry, biology, psychology, and economics were pretested in adults, so as to be equally difficult to explain. When participants in kindergarten, Grades 2, 4, 6, and 8, and college were…

Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10 to 12 years of age, but can solve parallel problems involving continuous quantities by 6 years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A…

In an attempt to devise a methodology for characterizing children's intuitive theories of drug action, 217 children in Grades 1 to 6 were interviewed about how two substances, alcohol and cocaine, cause behavioral changes in their users. Measures tapped both structure (Piagetian complexity of causal reasoning, coherence, and construction of a…