The purpose of the present study was to portray students' misconceptions and errors while solving conceptually and procedurally oriented tasks involving length, area, and volume measurement. The data were collected from 445 sixth grade students attending public primary schools in Ankara, Türkiye via a test composed of 16 constructed-response…

This article presents research into human mental spatial reasoning with orientation knowledge. In particular, we look at reasoning problems about cardinal directions that possess multiple valid solutions (i.e., are spatially underdetermined), at human preferences for some of these solutions, and at representational and procedural factors that lead…

Previous study has shown that tracing gesture may enhance the worked example-based learning by reducing cognitive load. The present study attempted to replicate the previous results and further explored the individual differences in tracing effect in relation to the learners' working-memory capacity. Specifically, 11- to 13-year-old students…

Some years back, the author found the following problem in a spatial puzzle book: how many ways can you put four blocks together, face to face (with no vertical rotation symmetry)? He gave each student just four blocks and they collectively tried combinations to eventually agree on the answer of 15. He used to think it was a halfway decent task,…

We consider here a number of ideas for the classroom or lecture theatre associated with the mensuration of solids. In particular, the volumes of various tetrahedra are obtained in an indirect manner (by way of prisms and square-based pyramids). This activity develops problem-solving skills, spatial visualization and a from-first-principles…

The move from additive to multiplicative thinking requires significant change in children's comprehension and manipulation of numerical relationships, involves various conceptual components, and can be a slow, multistage process for some. Unit arrays are a key visuospatial representation for supporting learning, but most research focuses on 2D…

This article presents a teaching intervention where programming was used to facilitate preschoolers' learning of mathematics, especially in their development of spatial thinking. In the intervention, the programming was made with a small programmable robot especially designed for young students. The results indicate that the children developed…

Many innovations in organizations result when people discover insightful solutions to problems. Insightful problem-solving was considered by Gestalt psychologists to be associated with productive, as opposed to re-productive, thinking. Productive thinking is characterized by shifts in perspective which allow the problem solver to consider new,…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show…

The present study assessed a short training experiment to improve spatial abilities using two tools based on virtual technologies: one focused on manipulation of specific geometric virtual pieces, and the other consisting of virtual orienteering game. The two tools can help improve spatial abilities required for many engineering problem-solving…

Spatial abilities are used in many aspects of everyday life, thus developing these abilities should be one of the most important goal of Mathematics Education. These abilities should be developed starting with early school years, thus pre-school and primary school teachers have an important role in setting the foundation of these abilities. A…

The central dogma has served as a foundational model for information flow, exchange, and storage in the biological sciences for several decades. Despite its continued importance, however, recent research suggests that novices in the domain possess several misconceptions regarding the aforementioned processes, including those pertaining…

With ongoing concerns about environments that push teachers toward increasingly structured assessments, thus reducing opportunities to observe young learners' mathematical capabilities, the publication of this special issue on formative assessment is especially significant and timely. The articles illustrate how we cannot rely solely on…

The present article describes two studies that examine the impact of teaching students to use gesture to support spatial thinking in the Science, Technology, Engineering, and Mathematics (STEM) discipline of chemistry. In Study 1 we compared the effectiveness of instruction that involved either watching gesture, reproducing gesture, or reading…