Arguably, the ability to generalize is an essential characteristic of students who succeed in mathematics and computer science. Teachers should be aware of its presence in their classroom and have tools to encourage its existence. Thus, it is important to examine the successful ways that generalization is taught. This systematic review examined…

In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…

Recommendations for achieving generalized instructional outcomes often overlook the capacity for generative learning for most verbally competent humans. Four children (ages 5-8) participated in this project. In Study 1, we provided decontextualized discrete trial teaching to establish arbitrary relations between colors, pictures of characters, and…

GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

The tradition of studies involving the combinatorial approach to recurring numerical sequences has accumulated a few decades of tradition, and several problems continue to attract the interest of mathematicians in several countries. This work specifically discusses the Fibonacci, Pell, and Jacobsthal sequences, focusing on Mersenne sequences. The…

Teaching an infant manual signs is beneficial as it promotes early communication, improves socialization, and can functionally replace behaviors such as crying and whining. Improving early communication also may reduce the probability of an infant engaging in dangerous behavior, like unsafe climbing. The purpose of this study was to extend…

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

Selecting and remembering the necessary information from rapidly increasing information requires summarization skills. Research on improving students' summarization skills has focused on deletion, generalization, and reconstruction strategies. However, direct teaching of these strategies does not yield successful results. For this reason,…

Quadratics provide a foundational context for making sense of many important algebraic concepts, such as variables and parameters, nonlinear rates of change, and views of function. Yet researchers have highlighted students' difficulties in connecting such concepts. This in-depth qualitative study with two pairs of Year 10 (15 or 16-year-old)…

This work is a segment of an ongoing doctoral research in Brazil. The Leonardo numbers and the Leonardo sequence have gained attention from mathematicians and the academic community. Despite being a relatively new sequence within mathematical literature, its discussion has intensified over the past five years, giving rise to other branches, with…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

This study investigated how three fifth-grade students' understanding of fraction and decimal magnitude evolved over the course of a five-week teaching experiment. Students participated in teaching and learning sessions focused on developing concepts of fraction and decimal magnitude. The following questions guided this study: (1) How do fifth…

Efforts to implement high-quality communication instruction for students with autism spectrum disorder (ASD) and complex communication needs (CCN) may be difficult for some educators with limited time and resources. In this article, we offer guidance on implementing several economic strategies that can be easily embedded into existing classroom…

Further research is needed on strategies to improve employment outcomes for individuals with autism spectrum disorder (ASD). We replicated and extended prior research by examining the acquisition, maintenance, and generalization of discrete-trial training (DTT) performance of adults with ASD who were interested in careers as behavior technicians.…

The aim of this study was to investigate the effectiveness of teaching with graduated guidance on teaching the playing backgammon skill, which is one of the leisure skills, to children with "Autism Spectrum Disorder (ASD)". Three children with ASD participated in this research. A multiple probe design across the participants was used in…