This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

This study aims to examine the changes in students' mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in…

This paper discusses the significance of model-based teaching on the topic of ionic and metallic bonding in Year 12 Chemistry in a New Zealand secondary school. Based on the conceptualization of the sub-macro level understanding of the bonding structure and properties of ionic and metallic compounds, models and drawings were used as an effective…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

Introducing new concepts to learners in an order of increasing complexity appears to be beneficial for learning, but typically introduction of concepts does not always adhere to this principle. We examined whether introducing new algebra concepts in a contrasted manner or in an order of increasing complexity instead of a different more typical…

Virtual learning environments can now be enriched not only with visual and auditory information, but also with tactile and kinesthetic feedback. However, the way to successfully integrate haptic feedback on a multimodal learning environment is still unclear. This study aims to provide guidelines on how visuohaptic simulations can be implemented…

In this study I explore the construction of algebraic structure sense through engaging students in task sequences designed to elicit the development of competencies related to this understanding. The primary task-design principle employed in this study is strategic variation, in which certain components of items within task sequences vary while…

The following outlines the rationale and structure of a professional learning initiative that seeks to explore teachers' ways of engaging students more actively in building mathematical connections for themselves. An example of one of the suggested experiences is presented.

This dissertation examines the thesis that implicit learning plays a role in learning about scientific phenomena, and subsequently, in conceptual change. Decades of research in learning science demonstrate that a primary challenge of science education is overcoming prior, naive knowledge of natural phenomena in order to gain scientific…

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

As an important subject in the curriculum, many students find chemistry concepts difficult to learn and understand. Chemical bonding especially is important in understanding the compositions of chemical compounds and related concepts and research has shown that students struggle with this concept. In this theoretical paper based on analysis of…

The distinction between procedural and conceptual learning has long been a topic of discussion in mathematics education and the idea of compression into thinkable concepts that enable the individual make links between them (Tall, 2007). In addition to, the compression to thinkable concept was to be thinking mechanism arising naturally and…

Find out how to use photographic images to support the conceptual development of proportional thinking. This paper provides insight into a sequenced activity that promotes student engagement and makes links to familiar and unfamiliar contexts.

Most children who are older than 6 years of age apply essential counting principles when they enumerate a set of objects. Essential principles include (a) one-to-one correspondence between items and count words, (b) stable order of the count words, and (c) cardinality--that the last number refers to numerosity. We found that the acquisition of a…

This article examines the impact of programming robots on sequencing ability in early childhood. Thirty-four children (ages 4.5-6.5 years) participated in computer programming activities with a developmentally appropriate tool, CHERP, specifically designed to program a robot's behaviors. The children learned to build and program robots over three…