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…

In this article, we examine how a sequence of modeling activities supported the development of students' interpretations and reasoning about phenomena with negative average rates of change in different physical phenomena. Research has shown that creating and interpreting models of changing physical phenomena is difficult, even for university level…

Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…

In this article I consider what critical mathematics education could mean for different groups of students. Much discussion and research has addressed students at social risk. My point, however, is that critical mathematics education concerns other groups as well: for example, students in comfortable positions, blind students, elderly students,…

A relevant aim of research in education is to find and study the reasoning lines that students deploy when dealing with problematic situations. This can be done through an analysis of the answers students give to a questionnaire. In this paper, we discuss some methodological aspects involved in the quantitative analysis of a questionnaire by means…

Students tend to see mathematical functions as static, mysterious objects that must be approached according to a set of rules and procedures laid out in mathematics textbooks (Clement 2001). Because learners so rarely experience functions as a meaning-making tool that matters to their understanding of the world, they miss critical opportunities to…

Mathematical modeling, a key strand in mathematics, engages students in rich, authentic, exciting, and culturally relevant problems and connects abstract mathematics to the surrounding world. In this, article, the authors describe a modeling activity that can be used when teaching linear equations. Modeling problems, in general, are typically high…

Finite Mathematics has become an enormously rich and productive area of contemporary mathematical biology. Fortunately, educators have developed educational modules based upon many of the models that have used Finite Mathematics in mathematical biology research. A sufficient variety of computer modules that employ graph theory (phylogenetic trees,…

One hundred four students aged 8 to 16 worked on one Fermi problem involving estimating the number of people that can fit in their school playground. We present a qualitative analysis of the different mathematical models developed by the students. The analysis of the students' written productions is based on the identification of the model of…

The aim of this study is to investigate how an augmented reality mobile math trails program can provide opportunities for students to engage in meaningful mathematical modelling activities. An explorative research design was conducted involving two mathematics teachers and 30 eight grades in Semarang, Indonesia. An Augmented Reality Mobile Math…

Mathematics teachers frequently provide concrete manipulatives to students during instruction; however, the rationale for using certain manipulatives in conjunction with concepts may not be explored. This article focuses on area models that are currently used in classrooms to provide concrete examples of integer and binomial multiplication. The…

The purpose of this study was to introduce a rubric named "Rubric for the Assessment of Modeling Skills" for assessing cognitive modeling skills and explaining the rubric's development process. The dimensions of the rubric are understanding the problem, simplifying, mathematizing, working mathematically, interpreting and validating.…

This study aims to produce a learning trajectory using the mathematical modeling in helping students to understand the concept of algebraic operations. Therefore, the design research was chosen to meet the research aims and to give in formulating and developing local instructional theory in learning algebraic operations. Learning trajectory…

Based on an investigation of research literature on the role of mathematics within the context of STEM education and twenty-first century skills, this explorative study presents and analyses 19 pre-service teachers' lesson proposals for innovative STEM activities in secondary mathematics classrooms. Drawing on a categorisation of twenty-first…

Many engineering subjects rely on the interpretation of symbolic, numeric and graphic representations. Engineering students have challenges pertaining to their mathematical understanding of their actions with a computer algebra system (CAS). We investigated how a mathematical modelling task could mediate varied levels of mathematical…