The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is…

This paper discusses a proposal for exploration and verification of numerical and algebraic behavior correspondingly to Generalized Fibonacci model. Thus, it develops a special attention to the class of Fibonacci quaternions and Fibonacci octonions and with this assumption, the work indicates an investigative and epistemological route, with…

The purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK). As part of a larger study, nine current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT)--Mathematics assessment and the Cognitively Activating Instruction in Mathematics…

Differences in definitions of limit and continuity of functions as treated in courses on calculus and in rigorous undergraduate analysis yield contradictory outcomes and unexpected language. There are results about limits in calculus that are false by the definitions of analysis, functions not continuous by one definition and continuous by…

This study investigated the development of the concept of variables in middle grades mathematics textbooks during four eras of mathematics education in the United States. Findings revealed that each of the middle grades mathematics curricula examined used variables, but in varied proportions and levels of complexity. Formal definitions for…

What is mathematical learning disability (MLD)? The reviews in this special issue adopt different approaches to defining the construct of MLD. Collectively, they demonstrate the current status of efforts to establish a consensus definition and the challenges faced in this endeavor. In this commentary, we reflect upon the proposed pathways to…

Compares effects of two models of vocabulary instruction--an integrated graphic organizer/discussion model and a definition-only model--on the mathematical vocabulary use of fourth grade students. Finds, after two weeks of instruction, a larger number of mathematical concepts recorded by the group using the integrated model than the group using…