This paper describes Alkaline, a size-reduced version of Kyber, which has recently been announced as a prototype NIST standard for post-quantum public-key cryptography. While not as simple as RSA, I believe that Alkaline can be used in an undergraduate classroom to effectively teach the techniques and principles behind Kyber and post-quantum…

Evidence in South Africa of poor performance on word problems points to particular challenges among learners relating to difficulties with, on the one hand, making sense of mathematical word problems and, on the other, moving beyond inefficient counting based calculation methods. While many studies in mathematics education in South Africa have…

The history of mathematics educational reform is replete with innovations taken up enthusiastically by early adopters without significant transfer to other classrooms. This paper explores the coupling of coding and mathematics education to create the possibility that coding may serve as a Trojan Horse for mathematics education reform. That is,…

This study examines the classroom practice and craft knowledge underpinning one teacher's integration of the use of GeoGebra software into mathematics teaching. The chosen teacher worked in an English secondary school and was professionally well regarded as an accomplished user of digital technology in mathematics teaching. Designed in accordance…

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

The ability to notice important events in a teaching situation and make decisions about these events is a key component of teaching well. Prospective teachers tend to notice more superficial aspects of classroom practice, such as class management. This article examines a video club in which four student teachers utilized the Mathematical Quality…

In this work we explored proof schemes used by 41 middle school students when confronted with four mathematical propositions that demanded verification of accuracy of statements. The students' perception of mathematically complete vs. convincing arguments in different mathematics branches was also elicited. Lastly, we considered whether the…

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers' knowledge identified by Shulman ("1987") refined by Ball et al. ("2008") and extended to include teachers' confidence to use…

The Illinois Board of Higher Education (IBHE) provided Early Childhood Educator Preparation Program Innovation (EPPI) grants to 20 partnerships comprised of two- and four-year institutions to further develop models for early childhood educator preparation and build capacity in key areas of need. Recipients used grant funds to design and implement…

The author has worked for three days on a range of mathematical tasks in order to gain a deeper understanding of the role of notation in mathematics education. The general conclusions were that while mathematical notation can be powerful it can also be obstructive. In this article, the author explores the importance on notation in supporting…

The purpose of this article is to provide a comprehensive review of the published research-based strategies used in content area instruction for students with autism spectrum disorders (ASD). Twenty-eight (N = 28) studies published from 2000-2012 that met the criteria for inclusion were located, reviewed, and synthesized. Findings revealed the…

This paper examines teachers' classroom talk as teachers respond to, interact with and take forward learners' contributions. Teachers' responses to learner contributions provide a useful lens in understanding teachers' hybrid practices as they take up aspects of reform practice. A set of codes for teacher moves is developed to describe teacher…

It is well known that meaningful knowledge of statistics involves more than simple factual or procedural knowledge of statistics. For an intelligent use of statistics, conceptual understanding of the underlying theory is essential. As conceptual understanding is usually defined as the ability to perceive links and connections between important…

Using data from an existing pre-algebra computer-based tutor, we analyzed the covariance of item-types with the goal of describing a more effective way to assign skill labels to item-types. Analyzing covariance is important because it allows us to place the skills in a related network in which we can identify the role each skill plays in learning…

The authors examined the extent to which teacher interventions focused on students' mathematical thinking in naturalistic cooperative-learning mathematics classroom settings. The authors also observed 6 videotapes about the same teaching content using similar curriculum from 2 states. They created 2 instruments for coding the quality of teacher…