To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…

This study aimed to investigate eighth-grade students' mathematical communication competency and mathematical literacy performance in a classroom experiment designed based on the mathematical modeling approach. Accordingly, a teaching experiment methodology was applied. Data were collected from three eighth-grade students through the Mathematical…

We engaged preservice teachers in a redesigned mathematics field experience with a central focus on children's reasoning through teaching experiments and purposeful reflection on practice through Lesson Study. Indicators of effective teaching were examined through analysis of lesson plans and enactment, comparing student teachers who participated…

Over the last forty years of mathematics education research, a coherent body of knowledge has accumulated regarding the teaching of limits. On this basis, it remains a challenge to identify goals and design tasks compatible with ordinary teaching conditions. This paper reports on a teaching experiment carried out in France with year 12 students,…

MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if…

Tallman (2015) argued that pedagogical content knowledge is a form of content knowledge with particular characteristics that endow it with pedagogical utility, and he conjectured that an essential characteristic of a teacher's content knowledge is her conscious awareness of the mental actions and conceptual operations that comprise her…

Help-seeking is a crucial behavior during learning in interactive learning environments (ILEs). Appropriate help-seeking promotes learning, while inappropriate help-seeking prohibits learning. However, many students are unaware of effective help-seeking behaviors. Therefore, research is needed to examine how students seek help in ILEs. Although…

According to the views of social constructivism, learning takes place when individuals engage socially to talk about and act on shared problems or interests. In recent years, this approach has been very popular for the teaching and learning of mathematics in primary and secondary education. On the contrary, in tertiary education, it seems that…

The timing of moves can dramatically affect firm profits and market outcomes. When firms choose output quantities, there is a first-mover advantage, and when firms choose prices, there is a second-mover advantage. Students often find it difficult to understand the differences between these two situations. This classroom experiment simulates each…

Language plays a key role in statistics and, by extension, in statistics education. Enculturating students into the practice of statistics requires preparing them to communicate results of data analysis. Statistical argumentation is one way of providing structure to facilitate discourse in the statistics classroom. In this study, a teaching…

The Riemann sum definition of integration is ubiquitous in college calculus courses. This, however, is not the only possible way to define an integral. Here, we present an alternative mean-based definition of integration. We conjecture that this definition is more accessible to students. In support of this proposition we first present a…

This study used design experiments, specifically micro-cycle teaching experiments (MTE) as a catalyst for practice-based professional development. The MTE incorporated research-based characteristics of effective professional development: it was embedded in the teachers' daily work of planning and enacting lessons, co-constructed with the…

Mobile technologies are quickly becoming tools found in the educational environment. The researchers in this study use a form of mobile learning to support students in learning about angle concepts. Design-based research is used in this study to develop an empirically-substantiated local instruction theory about students' develop of angle and…

This research is an action research which aims to implement contextual teaching and learning (CTL) approach to learn mathematics, focus on the integration subjects. The approach utilizes the use of mathematics manipulative so that students can understand a mathematical concept to construct their own. The method which used in this research are…