We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

"Inclusive Practices in Today's Schools" provides readers with a firm grounding in critical special education concepts, an understanding of the professionals who support students with special needs, knowledge of the procedures that should be followed to ensure that students with special needs rights are upheld and a wealth of…

Transform mathematics instruction with the comprehensive mathematical competencies (CMC) framework--a research-based model that integrates seven essential competencies: conceptual and procedural integration, problem solving, logical reasoning, communication, tool use, pattern recognition, and student engagement. Through practical classroom…

In this article, the author presents a teaching prompt--Write-it-Out--to instruct readers who seemingly guess at words with no or limited use of grapheme-phonemic correspondences to recontextualize word-solving into writing. Through the nature of this prompt, slowing down the pace of solving words on the run with writing also reciprocally builds…

Mathematical problem solving is a complex cognitive activity, which poses difficulties for students with and without disabilities in inclusive learning environments. With a variety of functions, Learning Management Systems (LMSs) have the potential to enhance personalized learning to meet the diverse needs of all students. This paper provides…

In this work, we study several closely related problems involving chains, conveyor belts, and rockets, which are described and solved without the application of infinitesimal calculus, or even the concept of mathematical limit. On one hand, the novelty lies not in the problems themselves, but in the method used for their solution, which brings…

The mathematical modeling process is also a powerful way to teach students the meaning of data. In mathematical modeling, students are collecting data to answer a question. Data collection is the means to an end and not the end in itself. The author was looking for an engaging way to introduce his third-grade mathematics class to the skill of…

In this paper it is demonstrated how the free, and easily downloadable, software package called SMath Studio can be used to set up a model of alpha-particle scattering. The basic physics of the motion of an alpha-particle in the nuclear coulomb field is used to produce a simple stepwise computer algorithm which, in conjunction with a novel set of…

The empirical data in this study are from a series of two lessons on measurement implemented in seven classes with 119 six-year-old students in Sweden. Both problem solving and problem posing were shown to be important in early mathematics when students in this study worked on one problem-solving task and one problem-posing task on measurement. As…

The authors wondered if there was a way to support their reluctant Grades 4, 5, and 6 students in contributing their starting points and strategies and advancing their collective knowledge. They wanted to ensure that the students had the space to develop and take ownership of the strategies they produced through a visual representation of ideas…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

A bachelor's degree program in chemistry typically starts with basic concepts in mathematics, physics, and chemistry. Those principles are very important because they pave the ground for future advanced studies and, therefore, one needs to present them in a clear but rigorous way. One example is provided by the mathematical notion of an iterative…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

Here, we present an interdisciplinary educational project intended for high school chemistry that is focused on the establishment of a mathematical model to describe the relationship between conductivity and concentration, while linking chemistry to mathematics with the help of computer software. The project was designed to help high school…

In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts.…