Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

Problems are part of our lives. It causes stress, tension, emotional instability, and physical strain to us. It is very essential to deal with our problems before they deal with our happiness. Problem solving skill is an irreplaceable life skill and it is cognitive or thinking activity essential to our day-to-day lives. In order to lead a…

The use of the dynamic mathematics software GeoGebra to solve geometric problems on conics and loci from an 18th century textbook will be presented. In particular, examples will be shown of how the use of this program helped the authors to understand the method that our predecessors used to deal with conic sections together with solving loci…

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what…

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This tenth installment of "Explorations in Statistics" explores the analysis of a potential change in some physiological response. As researchers, we often express absolute change as percent change so we can…

Establishing and maintaining key mathematical practices in whole-class discussions, such as justifying claims, representing mathematical objects and making connections between the representations, is crucial to the development of students' mathematical competencies. The aim of this article is to investigate how and why the establishment of key…

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

Both exploration and explicit instruction are thought to benefit learning in many ways, but much less is known about how the two can be combined. We tested the hypothesis that engaging in exploratory activities prior to receiving explicit instruction better prepares children to learn from the instruction. Children (159 second- to fourth-grade…

The article provides a review of recent research on human performance on the traveling salesman problem (TSP) and related combinatorial optimization problems. We discuss what combinatorial optimization problems are, why they are important, and why they may be of interest to cognitive scientists. We next describe the main characteristics of human…

This paper discusses some difficulties in teaching introductory courses to programming, paying particular attention to their mathematical nature. We consider some aspects, which have not been commented in detail in textbooks and often neglected by course outlines and schedules. Some of these are constructing complex conditions, exceeding array…

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

Pattern generalising problems offer a very rich context for exploring relationships among quantities, expressing generality and representing the same relationship in different ways. Selecting appropriate tasks for students to work on in class is by no means a straightforward process, but there are ways to handle it. This article aims to explore…

We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

This study examined how selected school mathematics textbooks in China, Singapore, and USA at the lower secondary grade level represent problem-solving procedures. The analysis of problem-solving procedures was carried out in two layers--general strategies, which adopted Polya's four-stage problem-solving model, and specific strategies, which…