This article presents several activities suitable for a transition to proofs course. In addition, this article surveys literature in support of active learning in the transition to proofs course and discusses how these activities have been successfully implemented in one such course.

Background: Adults with intellectual disabilities are an at-risk group of developing dementia. In the absence of a cure for dementia, emphasis on treatment is the promotion of Quality of life (QoL). The aim of this review is to identify and describe QoL tools for people with intellectual disabilities and dementia. Method: A systematic review was…

There are known issues in authentic assessment design practices in digital education, which include the lack of freedom-of-choice, lack of focus on the multimodal nature of the digital process, and shortage of effective feedbacks. This study looks to identify an assessment design construct that overcomes these issues. Specifically, this study…

The Adult Autism Quotient (AQ), the Empathy Quotient (EQ) and the Relative's Questionnaire (RQ) were used as part of the Adult Asperger's Assessment (AAA) by a diagnostic service for adults without an intellectual disability with suspected autism spectrum disorder (ASD). This service is part of the National Health Service (NHS) in England. Little…

Given the absence of expertise criteria of academics or lecturers, we sought to explore relevant studies to formulate an informed framework of academic expertise. Academics at higher education institutions are often considered experts. Usually, academic roles comprise teaching, research, and community service. Therefore, academics' expertise…

With the growth of digital media, learners are presented with multiple options to choose from when looking for resources to learn from. Learning that happens during searching for items to learn from is called Search-as-Learning (SaL). Recommender Systems (RS) can aid in SaL by reducing information overload and providing item suggestions. An…

The mathematics curricula of Australia (ACARA, 2019), Scotland, England and America all require an understanding of proof by contradiction. Specifically, proof by contradiction is included as a Geometry topic in Specialist Mathematics (Version 8.4). In Specialist Mathematics, it is expected that students construct proofs in a variety of contexts…

When constructing measurement scales, regular and reversed items are often used (e.g., "I am satisfied with my job"/"I am not satisfied with my job"). Some methodologists recommend excluding reversed items because they are more difficult to understand and therefore engender a second, artificial factor distinct from the…

While numerical bipolar rating scales may evoke positivity bias, little is known about the corresponding bias in verbal bipolar rating scales. The choice of verbalization of the middle category may lead to response bias, particularly if it is not in line with the scale polarity. Unipolar and bipolar seven-category rating scales in which the…

Although critical thinking has been widely accepted as an educational goal for decades, clear evidence for the development of students' critical thinking is sparse. Critical thinking has been conceptualised as skill, knowledge, and disposition respectively in psychology, philosophy and critical theory, but which applies to education is unclear. In…

The argument-based approach is the current framework for validity and validation. One of the criticisms is that understanding and applying this approach to practice are complicated and require abstract thinking. Teachers or school administrators in teaching and learning need support in their validation practice. Due to the abstract structure of…

In order to learn more about student understanding of the structure of proofs, we generated a novel genre of tasks called "Proof Without Claim" (PWC). Our work can be viewed as an extension of Selden and Selden's (1995) construct of "proof framework"; while Selden and Selden discuss how the structure of a proof can be discerned…

Proof validation plays a significant role in students' understanding and learning of mathematical proofs. Recent studies have shown that university students were lacking skills in proof validation and were challenged by the implementation of the appropriate acceptance criteria when validating proofs. Drawing on Habermas' construct and rational…

Tychonov's 1935 solution of the heat equation, exhibiting nontrivial heat fluxes spontaneously appearing along an isolated conducting rod initially held at zero degrees, has intrigued some specialists for almost a century. No doubt those practicing heat engineers who took mathematics seriously were initially relieved to learn that the construction…

PWW style are presented. The difference of evidence is based on various additional auxiliary constructions, which in itself is a "mathematical art" that the student can master as a result of much practice. The PWW are accompanied by GeoGebra applets containing HINT buttons that allow the student to get step-by-step help in completing the…