The purpose of this study is to describe how mathematic teacher’s problems occur in the process of pedagogical reasoning from the perspective of a curriculum maker. In order to grasp the structure of the problems, we show the conceptual framework of the curriculum, which has five levels: the intended curriculum, the teacher-intended curriculum, the enacted curriculum, and the teacher-recognized attained curriculum, as well as the attained curriculum. The sample for this study was one single female teacher who was teaching in the sixth grade in elementary school in the Philippines. The observed lesson was finding missing term in proportion. The methods were lesson observation, a researcher-designed short test for students, questionnaire and interview with the teacher. The study determined the teacher’s problems leading to curriculum gaps among five levels of the curriculum. It was revealed that the learning contents in the attained curriculum was less than the teaching contents in the intended curriculum, because of a lack of stressing conceptual understanding in the teacher-intended curriculum. The most important finding is that she did not recognize those curriculum gaps, because learning contents in the teacher-recognized attained curriculum was the same as teaching contents in the teacher-intended curriculum from her view.

Concrete didactical means for learning mathematics, as for instance chips for the number concept, or everyday activities in situations of application as the balance for understanding the algebraic equation, are often seen as an immediate and an effective basis for abstract mathematical knowledge in school mathematics. In this article the specific role of concrete didactical means is analyzed from an epistemological perspective. They are distinguished by two major positions: on the one side they are considered as elements of a real world of things and on the other side they are conceived as elements within a systemic world of mathematical relations. A major consequence of the following epistemological reflections is that the concrete didactical material in the world of things cannot explain per se mathematical knowledge, especially, when the pedagogical tool (i.e. the concrete material) assists in understanding mathematical knowledge, those elements no longer belong to the physical world, but they belong to the world of mathematical relations.

This post-lesson video-stimulated interview study of the creative development of mathematical insight by a Year 6 student—during group activity in class—examines whether scaffolding occurred, and if so, what was its nature? This capable mathematics student who generally disliked school mathematics, became intensely engaged both intellectually and affectively during a problem-solving task in the research period. The task, its implementation, group interactions, and teacher actions all influenced, but did not cause his insight development. Scaffolding actions that differed in nature to those identified by Bruner did occur. This study could inform researchers, teachers, and professional learning providers intending to deepen mathematical understandings and increase student interest in mathematics.

It is important to understand what and how mathematics teachers learn in mathematics professional development (MPD) programs. In this paper, we examined mid-career teachers’ learning in our program wherein participant teachers conducted lesson study and analyzed students’ learning by collecting and discussing multiple sources of data. We approached the issue of teacher learning from the aspect of broadening teachers’ perspectives on teaching and learning in a mathematics lesson. By examining the case of two teachers and focusing on their practical research activity in a lesson on transformations of geometrical figures, we identified four perspectives. These perspectives emerged and developed in different activities and at different periods between the planning of the lesson and the presentation of the final report. The process of growth was further examined using the construct of contextualization. An analysis of two sessions held immediately after the research lesson revealed that the teachers used the four perspectives to recontextualize or decontextualize several classroom situations and that dialogic interaction made it possible for the teachers to form novel interpretations of the behaviors and utterances of students and to reflect on their own instructional actions. This paper thus provides information on features of mid-career teacher learning in a university MPD program that emphasized practical research activity.

To explain the overall research trend in mathematics education in Korea over the last 20 years, this paper presents an analysis of 3044 peer-reviewed papers published in seven domestic professional mathematics education journals. The papers were analyzed in terms of publication year, topic, research method, and target research population. In addition, papers on research conducted in the international context were analyzed. The results of this analysis showed rapid quantitative growth since the late 2000s and a diversity of research topics including learners’ abilities or characteristics, instruction or teaching methods, and curricula or textbooks. The most popular research methods included pedagogical analyses, case studies, and surveys. In terms of the target research population, students were more popular subjects than curricular materials and teachers in both elementary and secondary schools. A majority of the papers on research conducted in the international context were comparative studies dealing with foreign curricula or textbooks. The paper concludes with several implications regarding issues that need to be further considered to promote mathematics education research.

The mathematics education research projects conducted in Singapore found in the database available in the Singapore National Institute of Education are classified according to their nature. A preliminary classification of all these research projects under three types (funded research projects, doctorate thesis and master dissertation), and four categories (Theory Building, Curriculum and Policy, Classroom Teaching and Learning Practice and Teacher Professional Development) is presented. Under funded research projects, the category on classroom teaching and learning practice is the predominant category. Theory building predominates the category of research projects undertaken as part of doctorate and master studies. A glimpse into three exemplars of recent funded mathematics education research projects shows that these projects have first been identified to have addressing Classroom Teaching and Learning Practice of mathematics as their preliminary objective. Delving deeper into the description of the three studies, the three research projects are also tightly linked to Teacher Professional Development, and Curriculum and Policy components. These research projects ended with a wider dissemination to more teachers through teacher professional development and impacting the policy and the curriculum level. As demonstrated by the exemplars, categorizing the projects under the four categories is not sufficient, as these projects tackle issues of mathematics education holistically in addressing the remaining categories.