This is a companion to our previous paper in which we give a published example, based primarily on Perry's work, of a graph of ln "y" versus "t" when "y" is an exponential function of "t". This work led us to the idea that Lord Kelvin's (William Thomson's) estimate of the Earth's age was…

This article encourages approaches that develop children's understandings of data representations. In particular, when children develope flexibility in their approaches to data representation and understanding, the same data can be represented in different ways. Flexible and adaptive use of representations is part of mathematics competence which…

Fitness trackers can provide primary students with exciting opportunities to calculate, measure time and distance, graph, make sense of data, and improve their activity levels. This article suggests ways to use fitness trackers in the classroom.

As physics educators, we are constantly looking for ways to improve our practice. There are many different kinds of professional development opportunities that have been shown to help us with this endeavor. We can seek assistance from professionals, like mentor teachers or centers for faculty development, we can attend workshops to learn new…

Data-driven inquiry as a science practice and instructional approach can provide a powerful context for project-based learning (PBL). Students engage in data-driven inquiry when they explore a rich data set and observe patterns, ask questions suggested by the data, and pursue answers about underlying phenomena. Krajcik (2015) describes five…

This paper presents a rule-based task-oriented dialogue system for second language learning and a knowledge extraction method which automatically extracts the training data for Natural Language Understanding (NLU) and dialogue rules for dialogue management from a Dialogue Map (DM). The DM consists of turn-by-turn utterances between the system and…

We create a continuous, nowhere monotone function, which would be more suitable for students. (Contains 3 figures.)

Four rather different scatterplots of two variables X and Y are given, which, after dichotomizing X and Y, result in identical fourfold-tables misleadingly showing no association. (Contains 1 table and 1 figure.)

This article draws on extensive experience working with secondary and tertiary teachers and educators using an applet to display rational polynomials (up to degree 7 in numerator and denominator), as support for the challenge to deduce as much as possible about the graph from the graphs of the numerator and the denominator. Pedagogical and design…

This article advances the prerequisite network as a means to visualize the hidden structure in an academic curriculum. Networks have been used to represent a variety of complex systems ranging from social systems to biochemical pathways and protein interactions. Here, I treat the academic curriculum as a complex system with nodes representing…

When working within a meaningful context quite young students are capable of working with sophisticated data. Year 3 students investigate thermal insulation and the transfer of heat in a STEM inquiry, developing skills in measuring temperature by conducting a statistical investigation, and using a stylised graph to interpret their data.

This paper illustrates an approach for architectural design of a Learning Management System (LMS), which is verifiable against the Learning Technology System Architecture (LTSA) conformance rules. We introduce a new method for software architectural design that extends the Unified Modeling Language (UML) component diagram with the formal…

Throughout the general chemistry lab curriculum, a common shortcoming is the way in which students measure, record, and manipulate quantitative data. From initial measurements with different digital and analog instruments to proper conversions, calculations, and comparisons, students are often expected to be experts before they have been taught…

Why would anyone think of teaching and learning mathematics directly from primary historical sources? We aim to answer this question while sharing our own experiences, and those of our students across several decades. We will first describe the evolution of our motivation for teaching with primary sources, and our current view of the advantages…

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…