This article is based on a case study conducted within a newly established Year 7 and Year 8 innovative learning environment (ILE). Drawing on the voices of students and teachers, this article explores ways teachers and students learnt together, collectively moulding a suitable fit for mathematics learning within their ILE. Of interest was how the…

This paper presents the results of research about innovative actions that use Virtual Environments to improve the teaching and learning of Mathematics in Higher Education and the participants were higher education students of Mathematics. The project was carried out in three stages. During the first stage, we assessed theoretical assumptions about…

In this article, we wish to explore the influence of the figure of the drawing on the argumentation of students who are involved in a proof task. It is about analysing the knowledge that students associate with parallelograms and the interactions between students and drawing. Our research is based on both Toulmin's model and Vinner's concept image…

Response to Intervention (RtI) has become a common support system for students; yet, no universal RtI model exists, especially for mathematics and specifically at the secondary level. This article focuses on a specific model for delivering Tier 2 mathematics supports and services at the secondary level: math labs. Evidence--based and…

The paper describes two versions of an inquiry-based activity in geometry, designed as a game between two players. The game is inspired by Hintikka's semantic game, which is a familiar tool in the field of logic to define truth. The activity is designed in a dynamic geometry environment (DGE). The inquiry is initially guided by the game itself and…

Thinking about students in terms of participation instead of "high" or "low" achievers is more than replacing one term with another; it encourages us to shift our focus to student activity as well as barriers to and supports for productive activity. It encourages us to create classroom spaces that draw on student strengths and…

With an increased focus on using social discourse to enhance students' mathematical thinking and reasoning (NCTM 2014, Staples and King 2017), teachers are looking for discussion strategies that encourage middlelevel students to make sense of mathematical concepts. However, structuring these valuable discussions is complex. Teachers must carefully…

This article describes the practices the authors use to promote learning mathematics through social interactions that they cultivate in their classrooms throughout the year. The design of their instruction is guided by two productive discourse practices that they have found to be the most powerful. The first practice involved posing open…

Group size and treatment intensity are understudied topics in mathematics intervention research. This study examined whether the treatment intensity and overall intervention effects of an empirically validated Tier 2 mathematics intervention varied between intervention groups with 2:1 and 5:1 student-teacher ratios. Student practice opportunities…

At the University of Paderborn, the course "Introduction into the culture of mathematics" is required for all first-year students who enter the study program for future mathematics teachers at lower secondary level (grade 5-10). In this inquiry-based transition-to-proof course, we use four different kinds of proofs (the generic proof…

The aim of the present study was to investigate the nature of global argumentation structures of prospective middle school mathematics teachers in a technology enhanced environment. A qualitative case study was conducted with 8 participants from an Elementary Mathematics Education undergraduate program of one of the public universities in Ankara.…

This research aims to see and describe the types of questions posed by prospective teachers in learning concepts, principles, procedures and mathematical facts. The mathematics learning is an activity undertaken by teachers, students and learning environments in learning the mathematical material. The mathematics learning, in this case, is the…

This paper dealt with the design of learning tools, that was the development of learning implementation plan or Rencana Pelaksanaan Pembelajaran (RPP) based on Fun and Easy Math (FEM) approach in the form of a number line model. FEM was an approach in order to teach mathematics effectively to students in a fun and easy way according to the…

In this study, we specify teacher's knowledge and beliefs that influence their enactment of mathematics tasks. The use of tasks in lessons requires teachers to consider students' mathematical thinking and to know how to effectively implement tasks. Among the many aspects of teachers' understanding of students and ability to implement tasks for…

Too often, students are merely consumers of mathematics, without many opportunities to engage in authentic processes of doing mathematics. As a mathematics teacher educator, I decided to provide more opportunities for my prospective teachers (PSTs) to do so. In my mathematics class for elementary education majors, the PSTs worked on two…