This qualitative study aims to investigate novice undergraduate mathematics students' first encounter with the First Isomorphism Theorem, which is, more often than not, the pinnacle of a typical introductory course in Group Theory. Several studies have reported on the challenges that this mathematical result poses to inexperienced mathematicians,…

The American Association for the Advancement of Science (AAAS) cites evolution as a core concept of biology, yet studies have found that biology students often exhibit low acceptance of evolution. As such, much of evolution education research aims to identify the causes of evolution rejection and develop instructional strategies to increase…

The purpose of this paper is to highlight issues related to students' personal inferences that arise when students verbally explain their justification for calculus statements. We conducted clinical interviews with three undergraduate students who had taken first-semester calculus but had not yet been exposed to formal proof writing activities…

From mathematics education, a great variety of studies have focused on analyzing the presence of digital technology from different points of view. Those who work with proof and argumentation have resisted presenting results with a technological component, due to the idea of formality associated with those terms, which has increased the existing…

Bramlett and Drake (2013) suggest that the ability of teachers to teach proof is crucial for students to learn and develop formal and informal proofs. Teachers need to be involved in the process of proving and have a firm understanding of the critical role of proofs in order to effectively engage their students in proving activities. It is…

This investigation utilized publicly available data from the High School Longitudinal Study 2009 (HSLS:09) by the National Center for Educational Statistics (NCES) to examine any latent structures among variables which may empirically support the validity and reliability of a mathematical sense of belonging (MSB) construct. Using the nationally…

The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

When examinees perceive a test as low stakes, it is logical to assume that some of them will not put out their maximum effort. This condition makes the validity of the test results more complicated. Although many studies have investigated motivational fluctuation across tests during a testing session, only a small number of studies have…

Mathematics majors, including future secondary teachers, should understand the work of pure mathematicians and the crucial role proof plays for the discipline of mathematics. Beyond the textbook proofs seen in most transition-to-proof courses, we conjectured that students might develop a deeper understanding of the discipline of mathematics and…

Teacher candidates bring many beliefs and interpretations of mathematics teaching and learning at the start of their teacher preparation coursework (e.g. methods courses, field experiences, assessment). Well-prepared beginning teachers in many instances requires programs and designed experience to breakdown unproductive beliefs and/or improve…

We report on a research study conducted within a transition-to-proof course for mathematics majors at a large public university. Within the course, students explored famously unproven conjectures and reflected on how their perspectives of mathematics changed through this exploration (if at all). In this report we share students' takeaways from the…

With rising importance of collaborative problem-solving skills (CLPS) for the new information age, the PISA 2015 assessed students' CLPS skills on a large scale. This new attempt to measure CLPS raises an issue of validity. The purpose of this research is to examine evidence for convergent validity of CLPS through investigating the relationships…

Curiosity is one of the 21st century skills and is especially paramount in the digital age. However, curiosity is multifaceted and can be expressed in many ways. Furthermore, assessment of curiosity is often based on self-report or subjective observations. We present work in progress for the development of a digital quantitative assessment game…

This paper presents selected findings from an assessment of university students' moment-by-moment reading of mathematical proof. This method, adapted from an assessment of narrative reading validated by psychologists, yields novel insights into the strategies students use to construct meaning for the equations in a proof text. In particular, we…

The purpose of this study is to develop a valid, reliable, and useful scale to measure high school students' levels of acceptance of mobile technologies in learning mathematics based on the second version of the unified theory of acceptance and use of technology (UTAUT2) model. The study was designed based on a sequential exploratory mixed-method…