Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in…

According to expectancy-value models, two important motivational constructs are task value and self-efficacy expectations. As students work intensively on mathematical problems in the classroom, teachers need the competence to judge whether students value solving the problem and how confident they are that they will succeed. However, not much is…

Topic models are mathematical and statistical models used to analyze textual data. The objective of topic models is to gain information about the latent semantic space of a set of related textual data. The semantic space of a set of textual data contains the relationship between documents and words and how they are used. Topic models are becoming…

In random-effects meta-analysis the between-study variance ([tau][superscript 2]) has a key role in assessing heterogeneity of study-level estimates and combining them to estimate an overall effect. For odds ratios the most common methods suffer from bias in estimating [tau][superscript 2] and the overall effect and produce confidence intervals…

Developing models and using mathematics are two key practices in internationally recognized science education standards such as the Next Generation Science Standards (NGSS, 2013). In this paper, we used a virtual performance-based formative assessment to capture students' competencies at both "developing" and "evaluating"…

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving…

Creativity has been identified as a key characteristic that allows students to adapt smoothly to rapid societal and economic changes in the real world. However, Chinese students appear to perform less well in mathematical problem-solving and problem-posing abilities, which are strongly connected to mathematical creativity. Mathematical modelling…

In 2020, Year 12 students at John Curtin College of the Arts, were required to model COVID-19 data from five different countries in order to find correlations between daily infections and unemployment rates, in order to make future predictions. Work received from students demonstrated how the task successfully provided unique learning…

Quantitative reasoning is defined as reasoning about relationships between items, measurements of objects, and quantities rather than numbers. Both in the transition from arithmetic to algebra and in the problem-solving process, quantitative reasoning is seen as a critical instrument for the development of students' mathematical skills. In the…

As climate change becomes an increasingly important topic for science educators, it is critical to learn how teachers may be able to increase students' knowledge about it. We conducted two consecutive quasi-experimental studies that investigated the role of interest in predicting middle school students' knowledge gains from a unit about how…

In this article we discuss relationships between the cyclic group Z[subscript 12] and Western tonal music that is embedded in a 12-note division of the octave. We then offer several questions inviting students to explore extensions of these relationships to other "n"-note octave divisions. The answers to most questions require only basic…

Here, we present an interdisciplinary educational project intended for high school chemistry that is focused on the establishment of a mathematical model to describe the relationship between conductivity and concentration, while linking chemistry to mathematics with the help of computer software. The project was designed to help high school…

This article reports on the performance of the research funding system of 61 Japanese national universities, specifically the Japanese Grants-in-Aid for Scientific Research (GASR) system. The competitive Japanese research funding system is quantitatively investigated and measured, focusing on the GASR fund and its relationship with the Japanese…

While language aptitude and motivation are considered to be important contributors to second language (L2) attainment, two major gaps in the past research have been (1) a lack of nonlinear models stemming from a naive and tacit assumption that learning outcomes are linearly related to their predictors, and (2) a lack of unified and integrative…

Given the simultaneous rise in time-to-graduation and college GPA, it may be that students reduce their course load to improve their performance. Yet, evidence to date only shows increased course loads "increase" GPA. We provide a mathematical model showing many unobservable factors -- beyond student ability -- can generate a positive…