This paper reports the results of an international comparative study conducted in Switzerland and Japan of an elementary school mathematics lesson. The principal aim of the study was to advance understanding of the cultural specificities of a mathematics lesson in its totality using concrete examples of lesson design and implementation and of how…

The purpose of this case study was to discover and describe the components of a "double-dose" math intervention that resulted in increased mathematics achievement for high school Algebra I intervention participants in an effort to inform local decisions regarding program improvements and to provide insight to other educators…

With careful consideration given to task selection, students can construct their own solution strategies to solve complex proportional reasoning tasks while the teacher's instructional goals are still met. Several aspects of the tasks should be considered including their numerical structure, context, difficulty level, and the strategies they are…

The paper reports an investigation into how a group of elementary and middle school teachers collectively attempted to solve and understand a fraction division problem using an area model. Solving the word problem required that teachers determine how many two-thirds fit into three-fourths. The teachers struggled to conceptualise fraction division,…

Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure…

This research analyzed how fractions are taught in the fourth grade of elementary school in Flanders. Analysis centered on the presence of five features of instruction recommended by research on teaching and learning fractions (i.e., multiple solution pathways, linking representations, estimation and justification of the solution, collaboration,…

We consider two complementary aspects of mathematical skills, i.e. "procedural fluency" and "conceptual understanding," from a point of view that is related to modern e-learning environments and computer-based assessment. Pedagogical background of teaching mathematics is discussed, and it is proposed that the traditional book…

This article presents a science, technology, engineering, and mathematics (STEM) activity, building an air cannon, in a mathematics classroom. It describes an investigation grounded in STEM concepts that elementary and middle school teachers carried out to think about ways of implementing STEM activities into their instruction. This particular…

The nature of mathematics teachers' knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness…

This article presents four inquiry-based learning activities developed for a liberal arts math course. The activities cover four topics: the Pythagorean theorem, interest theory, optimization, and the Monty Hall problem. Each activity consists of a dialogue, with a theme and characters related to the topic, and a manipulative, that allow students…

Attending to precision (ATP) is essential in mathematics. This study examined ATP instances through the lens of univocal (functioning to convey information) and dialogic (functioning to generate new meaning) discourse. Analysis of data from five secondary mathematics classrooms focused on whole-class instances of ATP with coding based on the…

This study relates factors in nature of Mathematics and its teaching learning to student difficulties for diverse mathematics tasks. Descriptive survey was done on a sample of 300 high school students in Kerala with a questionnaire on difficulties in learning. Student perception of difficulty on 26 types of tasks, under five heads that students…

Each new version of the GeoGebra dynamic mathematics software goes through updates and innovations. One of these innovations is the GeoGebra 5.0 version. This version aims to facilitate 3D instruction by offering opportunities for students to analyze 3D objects. While scanning the previous studies of GeoGebra 3D, it is seen that they mainly focus…

The aim of this study is to assess learner views with regard to ProbSol learning environment prepared according to problem solving steps for the teaching of "applications related to equations and inequalities". In line with this aim, the study was carried out with 15 volunteered 9th graders who are taught with ProbSol. The study is a…

This paper is, essentially, the transcription of my conference at the conference CIEAEM 63, promoted by the CIEAEM/Commission for the Study and Improvement of Mathematics Teaching, held in Barcelona, Spain, from 24 to 29 July 2011. The main objective of the CIEAEM, since its foundation, in the fifties, has been to analyze the actual conditions and…