In search of an exemplary mathematics lesson in Hong Kong

Ida Ah Chee Mok has written an article that was published in ZDM on Thursday. The article is entitled In search of an exemplary mathematics lesson in Hong Kong: an algebra lesson on factorization of polynomials. The theoretical perspectives for this article are mathematical enculturation and the theory of learning through variation (variation theory). The study which is described in the article is part of the Learner’s Perspective Study (LPS). This study

(…) has engaged researchers in the investigation of mathematics classrooms of teachers in Australia, China, the Czech Republic, Germany, Israel, Japan, Korea, the Philippines, Singapore, South Africa, Sweden and the USA.

Here is the article abstract:

The author here describes an exemplary grade-8 algebra lesson in Hong Kong, taken from the data of the learners’ perspective study. The analysis presents a juxtaposition of the researcher’s analysis of the lesson with the teacher and students’ perspectives of the lesson. The researcher’s perspective applies the theory of variation for which the main concern of learning is the discernment of the key aspects of the object of learning and that the description of variations delineates the potential of the learning space. Some persistent features were illustrated, namely, the teacher talk was a major input in teaching; the technique of variation was used in the design of the mathematical problems and the dimensions of variation created in the class interaction provided a potential learning environment; the teacher taking seriously the student factor into account in his philosophy and practice. From the standpoint of enculturation, the teacher’s influence as an enculturator is intentional, significant and influential.

Pursuing excellence

Rongjin Huang and Yeping Li have written an article called Pursuing excellence in mathematics classroom instruction through exemplary lesson development in China: a case study. The article was published online in ZDM on Friday. To me, this article is interesting for a few reasons:

  • It has a focus on teaching mathematics
  • It has a focus on how to develop exemplary lessons
  • It has a focus on learning from “master teachers”
  • It provides a nice insight into chinese mathematics teaching

Several aspects in this study remind me of the Lesson Study approach and theories related to Mathematical Knowledge for Teaching (MKT), both of which are among my main research interests. Here is an abstract of their article:

In this article, we aim to examine the features of mathematics classroom instruction excellence valued in China. The popular approach to pursuing mathematics classroom instruction excellence through exemplary lesson development is also investigated to demonstrate the nature of teaching culture that has been advocated and nurtured in China. Features of an exemplary lesson are analyzed in detail, and the practicing teacher’s experience through participating in the development of the exemplary lesson is examined as well. Finally, the implications of developing exemplary lessons for pursuing excellence in mathematics classroom instruction as a culturally valued approach in China are also discussed.

Preservice teachers’ subject matter knowledge of mathematics

Ramakrishnan Menon has written an article entitled Preservice teachers’ subject matter knowledge of mathematics. The article has been published in International Journal for Mathematics Teaching and Learning. Here is the abstract of the article:

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their solution, b) classify them as easy, of medium difficulty, or difficult, explaining the rationale for their classification, and c) explain how they would teach/help children to solve them. Responses were classified under three categories of subject matter knowledge, namely traditional, pedagogical, and reflective. Implications of these categories to effective math teaching are then discussed.

Using graphing software in algebra teaching

Kenneth Ruthven, Rosemary Deaney and Sara Hennesy have written an article that was published online in Educational Studies in Mathematics on Saturday. It is entitled: Using graphing software to teach about algebraic forms: a study of technology-supported practice in secondary-school mathematics. Besides having a focus on the use of graphing software, the article also discusses issues related to classroom teaching practice, teacher knowledge and teacher thinking. Here is the abstract of their article:

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater depth through case study of two teachers each teaching two lessons of this type. The practitioner model developed in earlier research (Ruthven & Hennessy, Educational Studies in Mathematics 49(1):47–88, 2002; Micromath 19(2):20–24, 2003) provided a framework for synthesising teacher thinking about the contribution of graphing software. Further analysis highlighted the crucial part played by teacher prestructuring and shaping of technology-and-task-mediated student activity in realising the ideals of the practitioner model. Although teachers consider graphing software very accessible, successful classroom use still depends on their inducting students into using it for mathematical purposes, providing suitably prestructured lesson tasks, prompting strategic use of the software by students and supporting mathematical interpretation of the results. Accordingly, this study has illustrated how, in the course of appropriating the technology, teachers adapt their classroom practice and develop their craft knowledge: particularly by establishing a coherent resource system that effectively incorporates the software; by adapting activity formats to exploit new interactive possibilities; by extending curriculum scripts to provide for proactive structuring and responsive shaping of activity; and by reworking lesson agendas to take advantage of the new time economy.

Working for learning

Pat Drake has written an article that was recently published online in Journal of Mathematics Teacher Education. The article is entitled Working for learning: teaching assistants developing mathematics for teaching. Here is the abstract of the article:

This article derives from a case study of 10 secondary school teaching assistants (TAs) who did not have conventional pre-qualifications in mathematics but who undertook an honours degree in mathematics education studies at a Higher Education Institution in England whilst continuing to work as TAs in school. Work-based learning was thus undertaken in parallel with advancement through the hierarchical undergraduate mathematics curriculum. Lave and Wenger’s work on communities of practice is used as a framework to explore the TAs’ learning of mathematics alongside their professional work in schools. This case illustrates how and where institution-based undergraduate teaching relates to work in school, and where it does not, thus signalling the importance of the TAs’ informal learning strategies in bringing together these experiences.