Prospective teachers and cryptography students use programming, statistics and guile to enrich both their courses.

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…

This paper examines current views and definitions of learning transfer as well as their dominant characteristics. An alterior way to view learning transfer as preparation for future learning (PFL) is presented along with its defining features. This paper is divided into five sections: (a) what comprises learning transfer, (b) the conventional…

In the spring of 2020, brick and mortar colleges had to abruptly adapt to the reality of COVID-19 and transition to entirely online environments in a manner of weeks. This required a rapid (< 2 weeks) acquisition of knowledge and flexibility in using technology, most commonly Zoom. Upon completion of the semester, and after debriefing with…

The project team for the National Monitoring Study of Student Achievement (NMSSA) has recently begun writing reports focussed on how insights generated by the study can be used to promote learning and teaching. The reports are written primarily for teachers. This short article introduces the reports with a special emphasis on the mathematics and…

The COVID-19 pandemic is a historic global event that has extended to all parts of society and shaken the core of what we know and how we live. During this pandemic, the work of STEM professionals has taken center stage. Through our close observations of how the events of the pandemic have been unfolding across the globe, we propose an…

Teachers are continually in search of tasks that balance the dual priorities of rigorous thinking and fluency development. These often-competing priorities are emphasized by national-level organizations as well as by state-level standards and assessments. The National Council of Teachers of Mathematics (NCTM) calls for school mathematics…

The pace of development of computer technology and information technology over the last few decades has been unprecedented in the history of technology. Not to mention the impact this has on our daily lives. This requires our children to quickly become familiar with the mindset that is important to be able to use their IT tools effectively in…

The transition to tertiary mathematics requires students to use definitions of mathematical objects instead of intuitions. However, routines of defining and of proving with definitions are difficult to engage in, as they are not familiar to students who come from secondary school mathematics. Defining is highly complex because of its underlying…

A bachelor's degree program in chemistry typically starts with basic concepts in mathematics, physics, and chemistry. Those principles are very important because they pave the ground for future advanced studies and, therefore, one needs to present them in a clear but rigorous way. One example is provided by the mathematical notion of an iterative…

Problem solving follows a cycle of inquiry where the individual iterates between finding possible paths and exploring their likely effectiveness before selecting one as a possible solution. The cycle is enhanced through proximal processes because the number of paths that can be explored in depth are greater when more people work on the same…

Digital culture and creativity are often framed as immaterial (Casemajor, 2015), distinct from traditional media, such as paint and clay, and divorced from the immediate, embodied, and political realities of the arts classroom. 3D printing troubles this distinction, providing a concrete way for students' digitally created artifacts to manifest in,…

Problem solving is perhaps the key characteristic that makes us human. Given the kinds of problems that we face in a competitive economy and society, the new generation of learners is ever more required to have problem-solving abilities. By drawing from the literature on technological pedagogical content knowledge, design thinking, general and…

Informal strategies reflecting the representation of a situation described in an arithmetic word problem mediate students' solving processes. When the informal strategies are inefficient, teaching students to make way for more efficient ways to find the solution is an important educational issue in mathematics. The current paper presents a…

In this paper, we will discuss a type of activity that lets the mathematics classroom become a place where students can learn more than mathematical content. Specifically, students can learn interdisciplinary skills in the area of communication (both verbal and non-verbal) and debate skills that are often taught in communication or English…