Background: This paper compares the effects of two classroom-based technology-enhanced teaching interventions, conducted in two schools in sixth (age 11-12) grade. In one school, the intervention involves the use of a class set of 3D Printing Pens, and in another school the use of dynamic geometry environments, for inquiry-based learning of the…

In this paper we show how we can utilize human-guided machine learning techniques coupled with a learning science practitioner interface (DataShop) to identify potential improvements to existing educational technology. Specifically, we provide an interface for the classification of underlying Knowledge Components (KCs) to better model student…

Planning a mathematics lesson plan is a complex process. Its quality contributes to the effectiveness of mathematics instruction. Given this significance, improving prospective mathematics teachers' lesson planning ability is essential for teacher preparation programs to produce effective teachers. This study examines how a lesson study within a…

In this paper, a teaching path on non-Euclidean geometry focused on the Poincare-disk model, and its connection with art is shown. We consider as artistic contents the Escher's hyperbolic art and some paradoxes on Magriue's work. The mathematical aspects are illustrated thanks to a Dynamic Geometry System (GeoGebra) implemented with a laboratory…

This study focuses on how the combined use of graphic calculators with connectivity software promotes the social construction of mathematical knowledge. Particular emphasis is placed on the aspects related to design, development, implementation, and evaluation of didactic activities that integrate these technologies. We use Didactical Engineering…

This paper reflects on the design of tasks that could take profit from the new features for Automated Reasoning, recently available in the dynamic geometry program GeoGebra. We report on some ongoing experiment, involving initial mathematics teacher students, aiming to develop and evaluate the characteristics of tasks that, with the concurrence of…

This qualitative study aimed at describing student verbal interaction verbally through cognitive activities consisting of procedural, disputational, and exploration in solving geometry problems. This research was in the form of students' verbal interaction activities in group discussion which decribe students' thinking process in detail, both the…

With the aid of longitudinal country-level data from five IEA TIMSS assessments (1995--2011), the current study addresses the issue of the globalisation of curricula and achievement. To explore the hypothesis of global convergence, we study performance in four subdomains of mathematics. Using regression with fixed effects for countries, we…

A growing body of research suggests that interventions promoting students' utility value for a subject can improve their academic outcomes. However, numerous questions remain regarding how much to adapt prior intervention materials to promote utility value in new educational contexts and how implementation constraints of an educational context may…

A growing body of research suggests that interventions promoting students' utility value for a subject can improve their academic outcomes. However, numerous questions remain regarding how much to adapt prior intervention materials to promote utility value in new educational contexts and how implementation constraints of an educational context may…

Two mathematics teachers in a small rural school decided to create a task that would engage seventh graders. The goal of the real-world activity was to help students develop geometric and spatial reasoning and to support their understanding of volume of rectangular prisms. The impetus for the task came from the teachers' desire to engage students…

National Council of Teachers of Mathematics' (NCTM's) "Principles to Actions: Ensuring Mathematical Success for All" outlines eight teaching practices for effective teaching and learning of mathematics (NCTM 2014). One of the teaching practices, "elicit and use evidence of student thinking," states, "Effective teaching of…

The purpose of this paper is to present an analysis of the difficulties faced by students when working with different representations of vectors, planes and their intersections in R[superscript 3]. Duval's theoretical framework on semiotic representations is used to design a set of evaluating activities, and later to analyze student work. The…

We explore the mathematics engagement of a group of mathematics coaches, working in k-12 mathematics education. The incenter of a triangle is used to derive an alternative formula for the area of a triangle inspired by Usiskin, Peressini, Marhisotto, and Stanley (2002).

In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the…