The article is dedicated to solving extrema problems in teaching mathematics, without using calculus. We present and discuss a wide variety of mathematical extrema tasks where the extrema are obtained and find their solutions without resorting to differential. Particular attention is paid to the role of arithmetic and geometric means inequality in…

This article uses parts of qualitative data from the first author's study that focused on exploring Pirie and Kieren's process of "folding back," revisiting previously held understandings of a concept for its extended understanding in order to solve the problem of enhancing Grade 10 learners' reasoning in geometry. In South Africa,…

This research study examined the ways participants analyzed students' mathematical thinking in a Teaching Mathematics with Technology Massive Open Online Course for Educators. 179 discussion forum posts made by 35 highly engaged participants were analyzed to determine the focus of their attention. If the focus of the post was student thinking, the…

Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…

This paper aimed to investigate secondary school students' representations for solving geometric word problems in different clinical interviewing processes. More specifically, the focus was to understand the changes/developments in students' representations through think-aloud interviews (TAIs) and open-ended prompting interviews (OEPIs). Three…

This research was carried out to investigate the effect of graphing calculator program supported problem solving instruction on mathematical achievement and attitude in transformation geometry subject. The study was carried out with 49 seventh grade students in a middle school in Balikesir province. A pre-test post-test quasi-experimental design…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

There is a great deal of overlap between the set of practices collected under the term "computational thinking" and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the…

In this study, we investigate sixth, seventh, and eighth grade students' achievement in nonlinear (quadratic or cubic) proportional problems regarding length, area, and volume of enlarged figures. In addition, we examine students' solution strategies for the problems and obstacles that prevent students from answering the problems correctly by…

Student problem solving in the context of a dynamic mathematics environment (DME) has previously been investigated primarily through the lens of whether or not the student could complete a problem-solving task. Herein, we investigate what trajectories students employ in the realms of mathematics, technology, and problem solving as they attempt to…

Children's cognitive control and knowledge at school entry predict growth rates in analogical reasoning skill over time; however, the mechanisms by which these factors interact and impact learning are unclear. We propose that inhibitory control is critical for developing both the relational representations necessary to reason and the ability to…

Science, Technology, Engineering, and Mathematics (STEM) education initiatives have placed pressure on teachers to bring technology tools into classroom, including three-dimensional (3D) printing. Yet, little research has examined what specific math skills are required for 3D printing technology. This article describes a follow-up analysis of…

While a wide range of approaches and tools have been used to study children's creativity in school contexts, less emphasis has been placed on revealing students' creativity at university level. The present paper is focused on defining a tool that provides information about mathematical creativity of prospective mathematics teachers in…

A classroom activity for high-school students, aiming at introducing space geometry from plane geometry has been introduced back in 2009 by Mammana, Margarone, Micale, Pennisi and Pluchino (2009a). The activity was based on the use of a Dynamic Geometry System and of the analogy between figures. Several aspects of the activity have been studied in…

The paper deals with searching for synthetic solution supported by the means of dynamic geometry. It consists of two parts. The first one describes how software influences searching for synthetic solutions of geometric problems. The second one describes a small pilot experiment in which students of Faculty of Education solved two more difficult…