The most influential books on geometry are those of Euclid called "Elements". In our century, in addition to classical learning, various interactive software are used in teaching geometry. Among them, we can mention GeoGebra. GeoGebra is an interactive math measurement program that consists of teaching and learning from elementary to…

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 study of students' use of representations is one of the main topics of physics education research and is guided by the overarching field of semiotics. In this paper we compare two semiotic frameworks, one coming from didactics of mathematics and one from physics education research; "the theory of registers of semiotic…

The current research around the Fibonacci's and Lucas' sequence evidences the scientific vigor of both mathematical models that continue to inspire and provide numerous specializations and generalizations, especially from the sixties. One of the current of research and investigations around the Generalized Sequence of Lucas, involves it's…

In this paper, an investment problem is investigated in terms of elementary algebra, recurrence relations, functions, and calculus at high school level. The problem comes down to understanding the behaviour of a function associated with the problem and, in particular, to finding the zero of the function. A wider purpose is not only to formulate…

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood-based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

Recent reform movements have emphasized students making meaning of algebraic relationships; however, research on student thinking and learning often remains disconnected from the design of widely used curricular materials. Although a previous examination of algebra textbooks (Nathan, Long, & Alibali, 2002) demonstrated a preference for a…

Algebraic notation has been bedazzling learners for generations, yet despite research, learned papers, comparative studies, and a great deal of hard work on the part of classroom practitioners the situation remains a stubborn constant. In this article some small-scale research has highlighted some issues that might find a resonance in many…

This report describes the pilot conducted in the final phase of a project, Expanding Audio Access to Mathematics Expressions by Students With Visual Impairments via MathML, to provide easy-to-use tools for authoring and rendering secondary-school algebra-level math expressions in synthesized speech that is useful for students with blindness or low…

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…

Polynomial loglinear models for one-, two-, and higher-way contingency tables have important applications to measurement and assessment. They are essentially regarded as a smoothing technique, which is commonly referred to as loglinear smoothing. A SAS IML (SAS Institute, 2002a) macro was created to implement loglinear smoothing according to…

Problem statement: Although there is agreement on the potential of project based learning (PBL) and virtual manipulatives (VMs), their positive impact depends on how they are used. This study was based on supporting the use of online PBL environments and improving the efficacy of the instructional practices in PBL by combining the potentials of…

North Korea is one of the most closed nations in the world. It is difficult to access information about their education system. North Korea's economic system was reorganized on July 1, 2002, as well as the education system. This change has impacted North Korea's mathematics education. With limited information on North Korean mathematics textbooks,…

Introduction: Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary mathematics, we analyse the understanding of number sentences of a group of elementary students and its evolution when working on solving open and true/false number sentences. Method: We developed a teaching experiment with a group of…