Manfred Hauben proposes an approach to teaching non-transitive relationships between 'paradoxical' dice using simple statistical graphics. This method usefully supplements traditional approaches of conditional probability calculations and trees, and students are thereby better able to see what is going on and the mechanism of these relationships.

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

Recent findings in music research are increasingly confirming the embodied nature of music cognition. Assuming that a bodily engagement with music may affect the children's musical meaning formation, we investigated how young children's interaction with music, based on verbal description after listening versus body movement description while…

Scientists must interpret and produce visuals in their work. Scientists also use visual information to communicate their findings to the general public. Visual representations are used in science because of the abstract nature of scientific information as many concepts are unable to be seen with the naked eye. The current educational climate…

Previous research has found that different presentations of the same concept can result in different patterns of transfer to isomorphic instances of the same concept. Much of this work has framed these effects in terms of advantages and disadvantages of concreteness or abstractness. We note that mathematics is a richly structured field, with…

Instructors draw on their intentions for student learning in the enactment of curriculum, particularly in the selection and presentation of external representation of scientific phenomena. These representations both create opportunities for students to experience non-experiential biochemical phenomena, such as protein translation, and constrain…

Visualizations and visual models are of substantial importance for science learning (Harrison and Treagust, 2000), and it seems impossible to study chemistry without visualizations. More specifically, the combination of visualizations with text is especially beneficial for learning when dual coding is fostered (Mayer, 2014). However, at the same…

The purpose of this study was to understand how the use of multiple representations (MR), during a sequence of lessons on the saponification reaction, can help students develop their cognitive structures. We examined (i) the effect of the teaching sequence with MR on the development of the students' cognitive structures and (ii) how, according to…

Introduction: Because of the preponderance of visual images, many mathematics texts are wholly or largely inaccessible to students who are blind. This study investigated how much description is sufficient to communicate math content in different types of images. Methods: Representative math textbooks from grades five, eight, and 11, aligned to the…

The importance of practical learning environments for developing preservice teachers' (PSTs') dispositions and skills for teaching mathematics is underscored in a growing body of literature. Hence, teacher preparation programs often include methods courses embedded within K-12 schools. Utilized to a lesser extent; however, are campus-based…

"Evolution" is an area of the curriculum in which children show great interest and enthusiasm to learn more. They also bring considerable prior (though incomplete) knowledge from their informal "life worlds". Most children have encountered the term "evolution" from an early age and tend to define it in terms of…

To succeed in STEM, students need to learn to use visual representations. Most prior research has focused on conceptual knowledge about visual representations that is acquired via verbally mediated forms of learning. However, students also need perceptual fluency: the ability to rapidly and effortlessly translate among representations. Perceptual…

This study investigated the use of digital learning objects in elementary and secondary schools. The specific objectives were: a) to identify the frequency with which learning object are used by teachers, the type of object most frequently used, the teaching strategies that is more frequently adopted, the main reason for the use of learning…

There is a perception amongst some of those learning computer programming that the principles of object-oriented programming (where behaviour is often encapsulated across multiple class files) can be difficult to grasp, especially when taught through a traditional, didactic "talk-and-chalk" method or in a lecture-based environment. We…

The purpose of this guide is to provide brief explanations of practices that can be implemented when working with students in need of intensive intervention in mathematics. Special education instructors, math interventionists, and others working with students who struggle with mathematics may find this guide helpful. Specific topics covered…