Tensions between constructivist learning theories and objectivist learning theories in online courses implicate a need for a theoretical balance. This article describes organizing and enacting tasks that elicit constructivist learning of mathematics in an online mathematics teacher education course. The results focus on a conceptual framework that…

Over half a century has passed since Bruner suggested his three-stage enactive-iconic-symbolic model of instruction. In more recent research, predominantly in educational psychology, Bruner's model has been reformulated into the theory of instruction known as concreteness fading (CF). In a recent constructivist teaching experiment investigating…

Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

This paper reports on an intervention as part of which direction fields were introduced to students learning ordinary differential equations (ODEs). The intervention was designed and implemented to address issues with students' conceptions of the solutions of ODEs. These were identified by a diagnostic survey and through a review of the…

Teacher knowledge of students' mathematical thinking has been a growing research area in mathematics education. Although researchers have made substantial progress in understanding students' mathematical thinking and created research programs and curricula tailored to the research findings, teacher education programs have, by and large, not been…

This paper describes an empirical study examining action research papers submitted by a group (n = 81) of out-of-field mathematics teachers as part of a professional development programme in Ireland. Utilising document analysis, the papers were qualitatively analysed for evidence of teachers' beliefs and practices with respect to the teaching and…

As the school population becomes increasingly diverse with students of differing ethnic, cultural and linguistic backgrounds, there is a need for more responsive practices that capitalize on the cultural capital that such students bring to the learning process. Current practices especially in mathematics teaching are failing to meet the learning…

This article highlights the main ideas that underlie the differences in potential pragmatic knowledge constructs students experience when solving problems, between the zone of proximal development (ZPD) and the zone of potential construction (ZPC). This qualitative research is based on a phenomenological approach to finding the meaning of things…

It is widely accepted in the mathematics education community that pedagogies oriented toward inquiry are aligned with a constructivist theory of learning, and that these pedagogies effectively support students' learning of mathematics. In order to promote such an orientation, we first separate the idea of inquiry from its conception as a…

The research has shown a model of learning activities that can be used to stimulate reflective abstraction in students. Reflective abstraction as a method of constructing knowledge in the Action-Process-Object-Schema theory, and is expected to occur when students are in learning activities, will be able to encourage students to make the process of…

Research on self-determination theory (SDT) has shown that positive learning outcomes accrue in classrooms that support students' needs for autonomy, competence, and relatedness. Studies on what need supportive teaching entails in practice are, however, scarce. In the present study, we aimed to gain in-depth understanding of typical manifestations…

Constructivism is currently a hotly debated topic, with proponents and opponents equally adamant and emotional with respect to their viewpoints. Many misconceptions exist on both sides of the debate, and misuses of terminology and attribution are rampant. Constructivism is a theory of learning, not a particular approach to instruction and not a…

This research aimed to identify the educational approaches that pre-service elementary mathematics teachers adopt for their first teaching practice (TP) and the reasons for their choices. It was carried out with thirteen pre-service teachers (PTs). These PTs were observed during their first TP in a real school setting, and interviews were…

Low achievement on standardized tests may be attributed to many factors, including teaching methods. Differentiated instruction has been identified as a teaching method using different learning modalities that appeal to varied student interests with individualized instruction. The purpose of this quantitative study was to compare whole-group…

As we move into the 21st century, the needs of our students are more variable than ever. There has been a proliferation of social networking usage in society yet there has been little use of those emerging tools in schools as a means to enhance student learning. It is a common practice in school districts to block social networking sites and…