Two interesting articles on teachers’ knowledge

In the recent issue of Journal for Research in Mathematics Education, two interesting articles about teachers’ mathematical knowledge for teaching are published. One of these articles, “The nature and predictors of elementary teachers’ mathematical knowledge for teaching“, was written by Heather C. Hill. Here is the abstract of her article:

This article explores elementary school teachers’ mathematical knowledge for teaching and the relationship between such knowledge and teacher characteristics. There were few substantively significant relationships between mathematical knowledge for teaching and teacher characteristics, including leadership activities and self-reported college-level mathematics preparation. Implications for current policies aimed at improving teacher quality are addressed.

The other article was written by Courtney A. Bell, Suzanne Wilson, Traci Higgins and D. Betsy McCoach, and this article is entitled “Measuring the effects of professional development on teacher knowledge: the case of developing mathematical ideas“. The abstract of their article can be found below:

This study examines the impact of a nationally disseminated professional development program, Developing Mathematical Ideas (DMI), on teachers’ specialized knowledge for teaching mathematics and illustrates how such research could be conducted. This study adds to our understanding of the ways in which professional development program features, facilitators, and issues of scale interact in the development of teachers’ mathematical knowledge for teaching. Study limitations and challenges are discussed.

Proof constructions and evaluations

Andreas J. Stylianides and Gabriel J. Stylianides have written an article called Proof construction and evaluations. The article was published online in Educational Studies in Mathematics on Friday. Here is a copy of their article abstract:

In this article, we focus on a group of 39 prospective elementary (grades K-6) teachers who had rich experiences with proof, and we examine their ability to construct proofs and evaluate their own constructions. We claim that the combined “construction–evaluation” activity helps illuminate certain aspects of prospective teachers’ and presumably other individuals’ understanding of proof that tend to defy scrutiny when individuals are asked to evaluate given arguments. For example, some prospective teachers in our study provided empirical arguments to mathematical statements, while being aware that their constructions were invalid. Thus, although these constructions considered alone could have been taken as evidence of an empirical conception of proof, the additional consideration of prospective teachers’ evaluations of their own constructions overruled this interpretation and suggested a good understanding of the distinction between proofs and empirical arguments. We offer a possible account of our findings, and we discuss implications for research and instruction.

Exemplary mathematics instruction in Japanese classrooms

Yoshinori Shimizu has written an article that I think will be of great interest to many: Characterizing exemplary mathematics instruction in Japanese classrooms from the learner’s perspective. For more than a decade, researchers have had a focus on teaching practice in East-Asia, and in particular in Japan. Shimizu aims at examining some key characteristics of exemplary mathematics instruction in Japanese eigth-grade classrooms. The article was published online in ZDM on Wednesday. Here is the abstract:

This paper aims to examine key characteristics of exemplary mathematics instruction in Japanese classrooms. The selected findings of large-scale international studies of classroom practices in mathematics are reviewed for discussing the uniqueness of how Japanese teachers structure and deliver their lessons and what Japanese teachers value in their instruction from a teacher’s perspective. Then an analysis of post-lesson video-stimulated interviews with 60 students in three “well-taught” eighth-grade mathematics classrooms in Tokyo is reported to explore the learners’ views on what constitutes a “good” mathematics lesson. The co-constructed nature of quality mathematics instruction that focus on the role of students’ thinking in the classroom is discussed by recasting the characteristics of how lessons are structured and delivered and what experienced teachers tend to value in their instruction from the learner’s perspective. Valuing students’ thinking as necessary elements to be incorporated into the development of a lesson is the key to the approach taken by Japanese teachers to develop and maintain quality mathematics instruction.

Teaching contests

Yeping Li and Jun Li have written an interesting article called Mathematics classroom instruction excellence through the platform of teaching contests. The article was published online in ZDM on Tuesday. Here is a copy of their abstract:

In this study, we aimed to examine features of mathematics classroom instruction excellence identified and valued through teaching contests in the Chinese mainland. By taking a case study approach, we focused on a prize-winning lesson as an exemplary lesson that was awarded the top prize in teaching contests at both the district and the city level. The analyses of the exemplary lesson itself revealed important features on the lesson’s content treatment, students’ engagement, and the use of multiple methods to facilitate students’ learning. These features are consistent with what the contest evaluation committees valued and what seven other mathematics expert teachers focused in their comments. The Chinese teaching culture in identifying and promoting classroom instruction excellence is then discussed in a broader context.

Teaching research groups in China

Yudong Yang has written an interesting article that was recently published online in ZDM. The article has been entitled How a Chinese teacher improved classroom teaching in Teaching Research Group: a case study on Pythagoras theorem teaching in Shanghai. The Teaching Research Group system seems to be somewhat similar to the Japanese Lesson Study approach, and I find this very interesting. Here is the article abstract:

In China, a school-based teaching research system was built since 1952 and Teaching Research Group (TRG) exists in every school. In the paper, a teacher’s three lessons and the changes in each lesson were described, which might show a track of how lessons were continuously developed in TRG. The Mathematical Tasks Framework, The Task Analysis Guide, and Factors Associated with the Maintenance and the Decline of High-level Cognitive Demands developed in the Quantitative Understanding: Amplifying Student Achievement and Reasoning project (Stein and Smith in Math Teach Middle School 3(4):268–275, 1998; Stein et al. in Implementing stardards-based mathematics instruction. Teachers College Press, NY, pp. 1–33, 2000), were employed in this study. Based on the perspective of Mathematical Task Analysis, changes of three lessons were described and the author provided a snapshot for understanding how a Chinese teacher gradually improved his/her lessons in TRG activities.

Good mathematics instruction in South Korea

JeongSuk Pang has written an article called Good mathematics instruction in South Korea. The article has recently been published online in ZDM. Here is the article abstract:

There have been only a few studies of Korean mathematics instruction in international contexts. Given this, this paper describes in detail a sixth grade teacher’s mathematics instruction in order to investigate closely what may be counted as high-quality teaching and learning in Korea. This paper then discusses several key characteristics of good mathematics instruction along with some background information on Korean educational practice. This paper concludes with remarks that good mathematics instruction may be perceived differently with regard to underlying social and cultural norms.

Supervision of mathematics student teachers

Maria Lorelei Fernandez and Evrim Erbilgin have written an article about Examining the supervision of mathematics student teachers through analysis of conference communications. The article was published online in Educational Studies in Mathematics on Tuesday. Here is the abstract of their article:

Student teaching is often a capstone experience in the preparation of mathematics teachers. Thus, it is essential to better understand key aspects of the experience. We conducted a qualitative study of post-lesson conferences led by supervisors (classroom cooperating teachers and a university supervisor) working with mathematics student teachers. Analysis of conference communications revealed differences in the types and content of communications in conferences led by the cooperating teachers and by the university supervisor. Cooperating teachers tended toward evaluative supervision that lacked a focus on the mathematics of the lessons while the university supervisor tended toward educative supervision, guiding student teachers to reflect on and learn from their own classroom experiences including the mathematics of their lessons. Differences are discussed, and suggestions concerning the supervision of student teachers are made along with recommendations for further research.

Mathematical interaction in different social settings

Marcus Nührenbörger and Heinz Steinbring have written an article called Forms of mathematical interaction in different social settings: examples from students’, teachers’ and teacher–students’ communication about mathematics. The article was published on Friday in Journal of Mathematics Teacher Education. This article is related to teachers’ reflection and the construction of mathematical knowledge. Here is the abstract:

The study presented in this article investigates forms of mathematical interaction in different social settings. One major interest is to better understand mathematics teachers’ joint professional discourse while observing and analysing young students mathematical interaction followed by teacher’s intervention. The teachers’ joint professional discourse is about a combined learning and talking between two students before an intervention by their teacher (setting 1) and then it is about the students learning together with the teacher during their mathematical work (setting 2). The joint professional teachers’ discourse constitutes setting 3. This combination of social settings 1 and 2 is taken as an opportunity for mathematics teachers’ professionalisation process when interpreting the students’ mathematical interactions in a more and more professional and sensible way. The epistemological analysis of mathematical sign-systems in communication and interaction in these three settings gives evidence of different types of mathematical talk, which are explained depending on the according social setting. Whereas the interaction between students or between teachers is affected by phases of a process-oriented and investigated talk, the interaction between students and teachers is mainly closed and structured by the ideas of the teacher and by the expectations of the students.

Teachers’ reflective thinking skills

Amanda Jansen and Sandy M. Spitzer have written an article entitled Prospective middle school mathematics teachers’ reflective thinking skills: descriptions of their students’ thinking and interpretations of their teaching. The article was published online in Journal of Mathematics Teacher Education on Friday. Jansen and Spitzer takes the belief “that mathematics teacher educators should foster reflective thinking among prospective teachers” as point of departure, and they ask how teacher educators can help students prepare for this. In their article, which I think is very interesting by the way, they present Lesson study as an approach that can be used in order to learn from practice. Their study is also described as a “modified lesson study experience”.

Here is the article abstract:

In this study, we examined prospective middle school mathematics teachers’ reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers’ descriptions of students’ thinking and frequency of their interpretations about how teaching affected their students’ learning. Thirty-three participants responded to open-ended questionnaires or interviews that elicited reflections on their own teaching practice. Prospective teachers used two forms of nuance when describing their students’ thinking: (1) identifying students’ specific mathematical understandings rather than general claims and (2) differentiating between individual students’ thinking rather than characterizing students as a collective group. Participants who described their students’ thinking with nuance were more likely to interpret their teaching by posing multiple hypotheses with regard to how their instruction affected their students’ learning. Implications for supporting continued growth in reflective thinking skills are discussed in relation to these results.

Teachers’ motivation for fractions

Kristie Jones Newton has written an article that was published in Journal of Mathematics Teacher Education on Wednesday. The article is entitled Instructional practices related to prospective elementary school teachers’ motivation for fractions. Here is Newton’s article abstract:

This study was undertaken in order to better understand prospective elementary school teachers’ motivations for working with fractions before and after taking a course designed to deepen their understanding of mathematics, as well as what instructional practices might be related to any changes detected in their motivations. Eighty-five education students were given a motivation questionnaire at the beginning and end of the semester, and observations were made of the 9 days when fractions were taught. Three levels of teacher data were collected to understand instructional practices. Students’ ratings of the importance and usefulness of fractions (value), self-concept of ability, and anxiety were near the center of the scale at pre-test, with only value in the desired direction. At posttest, value and self-concept of ability increased while anxiety decreased, but these changes differed somewhat by instructor. In particular, reform-oriented practices, such as engaging students in high-level discourse, seemed to be associated with lowered anxiety.