This paper presents a model of recurrent multinomial sequences. Though there exists a quite considerable literature on modeling autocorrelation in numerical data and sequences of categorical outcomes, there is currently no systematic method of modeling patterns of recurrence in categorical sequences. This paper develops a means of discovering…

Problem solving is widely regarded as a fundamental feature within the school mathematics curriculum. However, there is considerable disagreement over what exactly problem solving is, and if and how it can be taught. In this article, I define problems as non-routine tasks and propose the explicit teaching of domain-specific problem-solving tactics…

The analysis of sequence data poses a great challenge; existing methods for the comparison of sequences take what theoretical grounding they have from other fields (most importantly, genetics). We argue that set theory provides a way of establishing the relations between sequences that has a natural application to the case in which the sequences…

Music classrooms have incorporated elements of cooperative peer learning for generations. Whether sharing an instrument or composing a song together, peers interact in many meaningful and spontaneous ways. While the principles of peer-assisted learning (PAL) might be familiar to many music teachers, the process and structures of reciprocal peer…

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…

Capturing and measuring instructional patterns by using standardized observation manuals has become increasingly popular in classroom research. While researchers argue that a common vocabulary of teaching is necessary for the field of classroom research to move forward, instructional features vary across classrooms and contexts, which poses…

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.

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…

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 article, the authors explore how the 3C Model can be used to integrate other curriculum areas with mathematics, namely digital technologies. To illustrate the model, they provide a practical example of a teaching sequence. T he 3C Model is designed to create opportunities for applying reasoning and problem-solving skills and learning…

To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with…

Virtual reality (VR) technology is an advanced modern resource commonly integrated into various forms of training. VR training simulations are customizable in that quality-grading parameter settings, physical environment, and user capacity can be modified to personal or professional preference. In this study, VR technology training practices are…

This paper argues for effective sequencing of mathematics content to aid transition from junior (Year 7 to Year 10) to senior mathematics (Year 11 to Year 12) curriculum in Queensland, Australia and provides a tool for sequencing the mathematics content. Planning templates and samples are available to schools; however, it is imperative for…

Academic advising plays an important role in students' decision-making in higher education. Data-driven methods provide useful recommendations to students to help them with degree completion. Several course recommendation models have been proposed in the literature to recommend courses for the next semester. One aspect of the data that has yet to…

The Massachusetts Early College Initiative eases the pathway to postsecondary education for thousands of high school students annually. Early college programs provide strategically-sequenced, real college classes with strong career orientations during students' regular high school day. When fully realized, they also provide enhanced academic and…