Misconceptions in geometry are an essential problem in the understanding of geometric terms by primary and pre-primary aged children. Present research shows some misconceptions in geometry demonstrated in the understanding of circles, squares, triangles and oblongs for children in the last year of kindergarten and pupils in the last year of…

Proportional reasoning involves thinking about parts and wholes (i.e., about fractional quantities). Yet, research on proportional reasoning and fraction learning has proceeded separately. This study assessed proportional reasoning and formal fraction knowledge in 8- to 10-year-olds. Participants (N = 52) saw combinations of cherry juice and water…

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory,…

In an experimental study to explain the effect of structured Building Block Play with LEGO™ bricks on 6-year-old student mathematics achievement and in the areas of logical thinking, divergent thinking, nonverbal reasoning, and mental imagery, students in the experimental group scored significantly higher (p = 0.05) in mathematics achievement and…

In educational settings, continuous assessment of the child's level of understanding is necessary to effectively utilize the principles of scaffolding and to create contexts that can advance the scientific reasoning of the child. In this article, we argue that a child's performance is a dynamic notion that is created by all elements in…

International calls have been made for reasoning-and-proving to permeate school mathematics. It is important that efforts to heed this call are grounded in an understanding of the opportunities to reason-and-prove that already exist, especially in secondary-level geometry where reasoning-and-proving opportunities are prevalent but not thoroughly…

There is substantial variance in the age at which children construct and deploy their first explicit theory of biology. This study tests the hypothesis that this variance is due, at least in part, to individual differences in their executive function (EF) abilities. A group of 79 boys and girls aged 5-7 years (with a mean age of 6½ years) were…

For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

This paper examines the computer game play of an 11-year-old boy. In the course of building a virtual house he developed and used, without assistance, an artefact and an accompanying strategy to ensure that his house was symmetric. We argue that the creation and use of this artefact-strategy is a mathematical abstraction. The discussion…

In this study, we follow students' modeling and covariational reasoning in the context of learning about big data. A three-week unit was designed to allow 12th grade students in a mathematics course to explore big and mid-size data using concepts such as trend and scatter to describe the relationships between variables in multivariate settings.…

In this article, I consider relationships between creativity and ethics, and how they apply in society. I argue that ethical reasoning requires creative thinking at various junctures. I present an 8-step model of ethical reasoning, delineating how creativity can be applied at various steps. Finally, I draw conclusions about how the model can be…

In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…

In two experiments, 2.5-year-old children spontaneously used geometric information from 2D maps to locate objects in a 3D surface layout, without instruction or feedback. Children related maps to their corresponding layouts even though the maps differed from the layouts in size, mobility, orientation, dimensionality, and perspective, and even when…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

Analogies have many advantages for students such as concretizing abstract concepts and enabling motivation. Analogies are frequently used in textbooks. Research shows that the analogies in textbooks are not used based on certain directives and sometimes lead to misconceptions for students. Therefore, analysing the analogies in textbooks on several…