This article investigates different meanings associated with contemporary scholarship on the aesthetic dimension of inquiry and experience, and uses them to suggest possibilities for challenging widely held beliefs about the elitist and/or frivolous nature of aesthetic concerns in mathematics education. By relating aesthetics to emerging areas of interest in mathematics education such as affect, embodiment and enculturation, as well as to issues of power and discourse, this article argues for aesthetic awareness as a liberating, and also connective force in mathematics education.

The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view, two phenomena: (1) juxtaposing displacements, and (2) articulating necessary cases. The discussion elaborates on the significance of these phenomena and draws relationships with the perspectives of embodied cognition and intersubjectivity.

Ireland has two official languages—Gaeilge (Irish) and English. Similarly, primary- and second-level education can be mediated through the medium of Gaeilge or through the medium of English. This research is primarily focused on students (Gaeilgeoirí) in the transition from Gaeilge-medium mathematics education to English-medium mathematics education. Language is an essential element of learning, of thinking, of understanding and of communicating and is essential for mathematics learning. The content of mathematics is not taught without language and educational objectives advocate the development of fluency in the mathematics register. The theoretical framework underpinning the research design is Cummins’ (1976). Thresholds Hypothesis. This hypothesis infers that there might be a threshold level of language proficiency that bilingual students must achieve both in order to avoid cognitive deficits and to allow the potential benefits of being bilingual to come to the fore. The findings emerging from this study provide strong support for Cummins’ Thresholds Hypothesis at the key transitions—primary- to second-level and second-level to third-level mathematics education—in Ireland. Some implications and applications for mathematics teaching and learning are presented.

In English-speaking, Western countries, mathematics has traditionally been viewed as a “male domain”, a discipline more suited to males than to females. Recent data from Australian and American students who had been administered two instruments [Leder & Forgasz, in Two new instruments to probe attitudes about gender and mathematics. ERIC, Resources in Education (RIE), ERIC document number: ED463312, 2002] tapping their beliefs about the gendering of mathematics appeared to challenge this traditional, gender-stereotyped view of the discipline. The two instruments were translated into Hebrew and Arabic and administered to large samples of grade 9 students attending Jewish and Arab schools in northern Israel. The aims of this study were to determine if the views of these two culturally different groups of students differed and whether within group gender differences were apparent. The quantitative data alone could not provide explanations for any differences found. However, in conjunction with other sociological data on the differences between the two groups in Israeli society more generally, possible explanations for any differences found were explored. The findings for the Jewish Israeli students were generally consistent with prevailing Western gendered views on mathematics; the Arab Israeli students held different views that appeared to parallel cultural beliefs and the realities of life for this cultural group.

If you are interested in the topic, this article gives a nice overview of the history and theoretical background of the Japanese Lesson Study approach, and there is also a nice list of references to dig into. In the conclusions of the article, they claim:

However, the significant features of Japanese Lesson Study, such as the use of collaborative work, working on common goals, sharing of ideas, team teaching, lesson observation and cooperation among peers seemed to exert similar impacts on all groups of participants. Participants from all glocal programs reported an improvement in their lesson planning, better pedagogical content knowledge and closer collegial relationship as a result of experiencing the Lesson Study process.

Here is the abstract of the article:

Japanese Lesson Study is a model for teacher professional learning that has recently attracted world attention particularly within the mathematics education community. It is a highly structured process of teacher collaboration, observation, reflection and practice. The world focus has been mainly due to the work of American researchers such as Stigler and Hiebert (Am Educ Winter:1–10, 1998; The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. Free Press, New York 1999), Lewis and Tsuchida (Am Educ Winter:14–17; 50–52, 1998) and Fernandez [J Teach Educ 53(5):395–405, 2002]. These researchers have documented Lesson Study from the perspective of their social, cultural and educational contexts. In order to develop a deeper understanding of Lesson Study in a post-modern global world, there is a need to seek views beyond those presented from an American perspective. This paper will provide further additional perspectives from an Australian state view and a Malaysian state district view and a university view. The aim is to develop an understanding of how the different contexts have influenced the structure and implementation of the Japanese Lesson Study model.

The purpose of this study is to analyze the relationship between student behaviors and the growth of mathematical ideas (using the Pirie–Kieren model). This analysis was accomplished through a series of case studies, involving middle school students of varying ability levels, who were investigating a combinatorics problem in after-school problem-solving sessions. The results suggest that certain types of student behaviors appear to be associated with the growth of ideas and emerge in specific patterns. More specifically, as understanding grows, there is a general shift from behaviors such as students questioning each other, explaining and using their own and others’ ideas toward behaviors involving the setting up of hypothetical situations, linking of representations and connecting of contexts. Recognizing that certain types of student behaviors tend to emerge in specific layers of the Pirie–Kieren model can be important in helping us to understand the development of mathematical ideas in children.

Warner focus a lot on the Pirie-Kieren model in her theoretical framework (see the article of Susan Pirie and Thomas Kieren from 1994). The main focus of Warner’s article is to address the following questions:

Are different types of student behaviors associated with the growth of mathematical ideas in specific ways? If so, how?

In her conclusions, Lisa Warner suggests that for the students in her study, “certain types of behaviors appeared to be associated with the growth of mathematical ideas in certain ways”. She also suggests that further research is needed in order to investigate whether these findings correspond with findings in similar studies of other students, different types of tasks, etc.

Cross-national research studies such as the Program for International Student Assessment and the Third International Mathematics and Science Study (TIMSS) have contributed much to our understandings regarding country differences in student achievement in mathematics, especially at the primary (elementary) and lower secondary (middle school) levels. TIMSS, especially, has demonstrated the central role that the concept of opportunity to learn plays in understanding cross-national differences in achievement Schmidt et al., (Why schools matter: A cross-national comparison of curriculum and learning  2001). The curricular expectations of a nation and the actual content exposure that is delivered to students by teachers were found to be among the most salient features of schooling related to academic performance. The other feature that emerges in these studies is the importance of the teacher. The professional competence of the teacher which includes substantive knowledge regarding formal mathematics, mathematics pedagogy and general pedagogy is suggested as being significant—not just in understanding cross-national differences but also in other studies as well (Hill et al. in Am Educ Res J 42(2):371–406, 2005). Mathematics Teaching in the 21st Century (MT21) is a small, six-country study that collected data on future lower secondary teachers in their last year of preparation. One of the findings noted in the first report of that study was that the opportunities future teachers experienced as part of their formal education varied across the six countries (Schmidt et al. in The preparation gap: Teacher education for middle school mathematics in six countries, 2007). This variation in opportunity to learn (OTL) existed in course work related to formal mathematics, mathematics pedagogy and general pedagogy. It appears from these initial results that OTL not only is important in understanding K-12 student learning but it is also likely important in understanding the knowledge base of the teachers who teach them which then has the potential to influence student learning as well. This study using the same MT21 data examines in greater detail the configuration of the educational opportunities future teachers had during their teacher education in some 34 institutions across the six countries.

Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur’s re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance of shared visualizations and problem-posing in learning mathematics, as well as imagination as a cognitive space for learning.