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…

Different types of reasoning, such as intuitive, inductive, and deductive, are used in the generalization of figural patterns, as an important part of patterns in school mathematics. It is difficult to demarcate the constructive patterns where the regularity observed in the first few sentences is generalizable to the other sentences and each…

This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…

The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

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)…

An important approach for developing children's algebraic thinking involves introducing them to generalized arithmetic at the time they are learning arithmetic. Our aim in this study was to investigate children's attention to and expression of generality with the subtraction-compensation property, as evidence of a type of algebraic thinking known…

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…

It is known that teacher noticing skills improve through different interventions such as video clubs, lesson study, and short-term professional development programs. However, it is not known whether this improvement is permanent and whether teachers can transfer their noticing skills into the classroom. It is extremely important to provide an…