This report summarises the research activities and findings from the TLRI-funded project entitled "Visualising Chance: Learning Probability Through Modelling." This exploratory study was a 2-year collaboration among two researchers, two conceptual software developers/interactive graphics experts, three university lecturers/practitioners,…

Many aspects of the geometry of linear statistical models and least squares estimation are well known. Discussions of the geometry may be found in many sources. Some aspects of the geometry relating to the partitioning of variation that can be explained using a little-known theorem of Pappus and have not been discussed previously are the topic of…

I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…

The purpose of this paper is to show an alternative to teach how people can do mathematical modeling of natural sciences such as physics, biology, earth science, meteorology and engineering disciplines like computer science, artificial intelligence, but also social sciences such as economics, psychology, sociology and political science using…

Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…

Lorraine Day and Derek Hurrell provide a convincing argument for using arrays to promote students' understandings of mental computation strategies for multiplication. They also provide a range of different examples that illustrate the benefits of arrays in the primary classroom.

Authentic open-ended problems are increasingly appearing in university classrooms at all levels. Formative feedback that leads to learning and improved student work products is a challenge, particularly in large enrollment courses. This is a case study of one first-year engineering student team's experience with teaching assistant and peer…

When viewed through a lens of embedded cognition, algorithms may enable aspects of the cognitive work of multi-digit multiplication to be "offloaded" to the environmental structure created by an algorithm. This study analyses four multiplication algorithms by viewing different algorithms as enabling cognitive work to be distributed…

Systems biology is frequently taught with an emphasis on mathematical modeling approaches. This focus effectively excludes most biology, biochemistry, and molecular biology students, who are not mathematics majors. The mathematical focus can also present a misleading picture of systems biology, which is a multi-disciplinary pursuit requiring…

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what…

Formative assessment has been identified as a promising intervention to support students' learning. How to successfully implement this means of assessment, however, is still an open issue. This study contributes to the implementation of formative assessment by analyzing the impact of a training measure on teachers' formative feedback practice,…

This article describes a unit in which students investigate total solar eclipses, such as the one coming August 21, from several perspectives. It incorporates mathematical thinking and aligns with the "Next Generation Science Standard." This article refers to physical, virtual, and mathematical modeling. Various models and perspectives…

The pedagogical practice of connecting mathematical content to real world contexts, particularly contexts relevant to students' knowledge and experiences, can positively impact student motivation as well as promote conceptual understanding. However, little is known about how middle school teachers actually make relevant world connections, and more…

This paper describes the design principles and implementation of a novel approach for a K--12 teacher professional development (PD) program. The approach integrates training focused on development of model eliciting activities (MEAs) within authentic engineering design tasks, collaborative 3D model design and fabrication, and inspirational site…

Concurrent enrollment refers to partnerships between postsecondary institutions and schools through which secondary school students can complete a university class taught by a qualifying secondary school teacher at their secondary school. We propose that concurrent enrollment programs are an under-recognized tool for extending the impact of…