A challenge for teachers is to incorporate the Standards for Mathematical Practice (CCSSI 2010) throughout their teaching of mathematics so that the Common Core Standards do not revert back to a purely content-driven curriculum. One way to achieve this is through the use of mathematically rich, investigative tasks. These tasks encourage students…

In this article, we present investigative tasks that concern loci, which integrate the use of dynamic geometry software (DGS) with mathematics for proving the obtained figures. Additional conditions were added to the loci: ellipse, parabola and circle, which result in the emergence of new loci, similar in form to the original loci. The…

Pattern generalisation has become an important feature of mathematics classrooms around the globe. Sometimes these activities focus purely on given numerical terms, but the use of pictorial or figural patterns is now becoming part of the standard repertoire for such generalisation exercises. From a pedagogic point of view, the investigation of…

Although mathematical pattern tasks are often found in elementary school curricula and are deemed a building block for algebra, a recent report (National Mathematics Advisory Panel, 2008) suggests the resources devoted to its teaching and assessment need to be rebalanced. We examined whether children's developing proficiency in solving algebraic…

How might investigating mathematical tasks through digital media influence students' learning trajectories, and hence their mathematical thinking? This article reports on elements of an ongoing study that examines how engaging mathematical phenomena through digital pedagogical media might influence understanding. As the students sought…

The purpose of this study was to examine the proportional reasoning skills of Turkish middle school students. It was also aimed at revealing the differences in students' performances in terms of their gender, grade level, and problem types--missing value and numerical comparison. The study was conducted with two sixth and seventh grade classes…

This paper reports on study that investigated the tacit-explicit dimension of the learning of mathematics. The study was carried out in a secondary school and consisted of an episode analysis related to a class discussion about the difference between plane figures and spatial figures. The data analysis was based on integration between some aspects…