In the past, my mathematics students have frequently complained at any suggestion that they should communicate ideas through the medium of a written report. This article discusses student responses when they were asked to write a short report for the mayor of a (hypothetical) small town in response to the mayor's plan to eliminate a contagious…

Most mathematicians state mathematics is a field of beauty, creativity, and innovation, yet what is echoed by students is not how mathematics allows students to explore, but rather the ways in which it constrains and does not necessitate creativity. In comparison, many students associate coding with freedom, and the ability to create and express…

Mathematics education often grapples with the challenge of teaching abstract mathematical concepts, particularly those existing in 3D space. Visualizing, manipulating, and comprehending these abstract objects can be a formidable task for learners. While 3D printing technology has found applications in various fields, its utilization in mathematics…

In conversation, "uptake" happens when a speaker builds on the contribution of their interlocutor by, for example, acknowledging, repeating or reformulating what they have said. In education, teachers' uptake of student contributions has been linked to higher student achievement. Yet measuring and improving teachers' uptake at scale is…

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

We propose that by more closely aligning interdisciplinary work in (a) numeracy education for medication dosage calculations and (b) model-driven design for medical devices that are used for delivery of medication we may help address the incident-rate in incorrect medication calculations and delivery, given that such devices commonly require the…

The authors of this article strongly advocate for a change to the current Australian model of primary education in order to, among other things, establish the concrete practicalities of systematic mathematics thinking thereby limiting the "re-teaching" time required of secondary school mathematics teachers; bring a clear focus to the…

The Next Generation Science Standards (NGSS) are composed of three intertwined dimensions--disciplinary core ideas, science and engineering practices, and crosscutting concepts--that provide a foundation for what students should know and be able to do at various grade levels. The eight science practices outlined in the NGSS are critical components…

One of the main tasks in teaching mathematics to elementary students is to form calculating methods and techniques. The efforts of teachers and methodologists are aimed at solving this problem. Educational and psychological research is devoted to it. At the same time school teaching experience demonstrates some difficulties in learning methods of…

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

Mixture factor analysis is examined as a means of flexibly estimating nonnormally distributed continuous latent factors in the presence of both continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood (ML) latent factor modeling. Different results emerge for continuous versus…

In the framework of the Italian National Plan "Lauree Scientifiche" (PLS) in collaboration with secondary schools, we have investigated the mechanical paradox of the double cone. We have calculated the geometric condition for obtaining an upward movement. Based on this result, we have built a mechanical model with a double cone made of aluminum…

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…

Drawing upon research, theory, classroom and personal experiences, this paper focuses on the development of primary-aged children's computational fluency. It emphasises the critical links between number sense and a child's ability to perform mental and written computation. The case of multi-digit multiplication is used to illustrate these…

In this note we develop a framework that makes explicit the inherent dynamic structure of certain mathematical definitions by means of the four facets of context-entity-process-object. These facets and their interrelations are then used to capture and interpret specific aspects of student constructions of the concept of solution to first order…