The purpose of this article is to illustrate the process and insights gleaned from developing an implementation matrix to convey a concise, yet detailed representation of the project integration steps in a single diagram. The article is based on an explanatory sequential study conducted with 248 teachers exploring how beliefs shaped their use of…

On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of…

Multiple external representations (MERs) are useful for teaching complex content in science education. An open question is whether there is an especially effective way to sequence MERs. On the one hand, the so-called concreteness fading approach suggests starting instruction with more concrete representations and proceeding stepwise to more…

As students with autism spectrum disorder (ASD) participate in the general education setting at greater rates, they are expected to meet rigorous grade-level academic standards. Students with ASD typically struggle with problem solving, higher-ordered thinking, and mathematical reasoning. When students enter middle school, mathematics becomes more…

We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.

The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…

This research integrates context-based learning and modelling. It presents a teaching-learning sequence (TLS) about the dissolution of gases in liquids using carbonated drinks as the context. The impact of the TLS is analysed in a longitudinal short-term study involving two groups of learners aged 13-14 years old (n=53). The results led us to…

This article describes an instructional sequence used with inservice secondary mathematics teachers as part of a graduate course. The instructional sequence focused on designing tasks using Interactive Geometry Software (IGS). This study answers a call for replication studies to investigate the use of an established instructional sequence. Results…

Graphing is a complex and critical skill for behavior analysts. We evaluated the effects of conceptual training modules and feedback checklists on verbal behavior about graphing conventions and adherence to graphing conventions with graduate students in behavior analysis. In Experiment 1, conceptual training increased the accuracy of verbal…

There have been many attempts to address the deficits in traditional teaching methods for decades Multiple studies have been done on the Common Knowledge Construction Model (CKCM) and the results of each study has shown an improvement. The addition of relational conceptual change has added much needed improvement in teaching science. This study,…

Sir Ronald Fisher's venerable experiment "The Lady Tasting Tea" is revisited from a Bayesian perspective. We demonstrate how a similar tasting experiment, conducted in a classroom setting, can familiarize students with several key concepts of Bayesian inference, such as the prior distribution, the posterior distribution, the Bayes…

Although special education teachers are expected to implement evidence-based practices, teachers of students with extensive support needs have reported challenges in identifying and implementing effective practices to meet the unique needs of their students. Systematic instruction has been identified as an evidence-based practice for students with…

International concerns about the educational equity of ethnic minorities have continued to highlight teachers' abilities to be culturally responsive. How do teachers manage cultural diversity through their pedagogical practices in the absence of relevant teacher training? The answer to this question is essential as it may help move our…

In this paper I explain how I usually introduce the Schrödinger equation during the quantum mechanics course. My preferred method is the chronological one. Since the Schrödinger equation belongs to a special case of wave equations I start the course with introducing the wave equation. The Schrödinger equation is derived with the help of the two…

In the context of a professional learning research project we investigated the nature of support offered to classroom teachers and school mathematics leaders to facilitate teachers' implementation of sequences of challenging tasks. End of year questionnaire data were collected from 70 Foundation to Year 2 teachers and ten numeracy leaders who…