Report from TWG19 in EMS Magazine

The European Mathematical Society (EMS) Magazine has a column with news from the European Society for Research in Mathematics Education (ERME). In the upcoming issue, this column contains a brief report of the activities from Thematic Working Group 19 (TWG19), on Mathematics Teaching and Teacher Practice(s), which I am leading. In this report, you can read about the focus of our working group—and how it is positioned in the field of research on mathematics teaching—the history of the group, and current efforts in the group. If you are interested in research on mathematics teaching, or in learning more about the work in our group, I recommend reading this brief paper!

Proceedings from CERME 13

The CERME 13 conference was held in Budapest, Hungary, in 2023. Even though the conference was arranged in the summer (July 10–14), the organizers have been able to finish the conference proceedings in record time. The full proceedings are now available at: http://erme.site/cerme-proceedings-series/

As the leader of TWG19, I obviously recommend the papers from that group, but there are many interesting papers to read, and the full proceedings constitute more than 5,000 pages. Happy reading!

Article on mathematics teacher educators' conceptions of MKT

Some articles take longer than others to publish. I have recently published a new article in Journal of Mathematics Teacher Education (Hoover et al., 2023). We started working on this study when I had my sabbatical in Michigan in 2017–2018, so this one has been in the making for a long time. Matt and I spent a lot of time with the initial analyses and work, then Mark came along and took a leader role in the study, and Imani joined the team a bit later. After I moved back to Norway in August 2018, the three of us had weekly Zoom meetings where we worked on analysis and later writing for a long time. Along the way, we developed, presented and published two CERME papers on preliminary parts of this work (Dahlgren et al., 2019, 2022). It is therefore a great pleasure to finally see the finished article in print! You can find the abstract of the article below:

Recent scholarship has explored mathematical demands faced by mathematics teacher educators and ways to support their development, but little attention has been given to the basic question of how mathematics teacher educators think about content knowledge for teaching. Knowing what they think could inform efforts to support them. Our analysis reveals that some think about mathematical knowledge for teaching as an independent, abstracted resource to be taught and learned in relative isolation from teaching, while others think about it as dynamic, situated work. We argue that this key difference matters for how they work with teachers. Further, our analysis reveals that their thinking about both teaching and justice interacts with their thinking about mathematical knowledge for teaching and that their thinking in these other two domains can be a resource for supporting their mathematical development.

Time outs as site for studying MKT

I have recently published a new article entitled, “Teacher time out as a site for studying mathematical knowledge for teaching” with my colleagues Kjersti Wæge and Janne Fauskanger. The article is going to be published in an upcoming special issue of The Journal of Mathematical Behavior, but it is already available online (open access). This article developed from an ICME-paper we presented at the recent ICME 14. In this article, we develop a theoretical argument for why and how “teacher time outs” might be an interesting site for studying mathematical knowledge for teaching. The article draws on illustrative data from the Mastering Ambitious Mathematics teaching (MAM) project. A link to the Norwegian project web site can be found here. Below is the abstract of our article and full reference in APA format. I hope you enjoy reading it just as much as we enjoyed writing it!

The special mathematical knowledge that is needed for teaching has been studied for decades but the methods for studying it have challenges. Some methods, such as measurement and cognitive interviews, are removed from the dynamics of teaching. Other methods, such as observation, are closer to practice but mostly involve an outsider perspective. Moreover, few methods tap into the tacit and often invisible demands that teachers encounter in teaching. This article develops an argument that teacher time outs in rehearsals and enactments might be a productive site for studying mathematical knowledge for teaching. Teacher time outs constitute a site for professional deliberation, which 1) preserves the complexity and gets inside the dynamics of teaching, where 2) tacit and implicit challenges and demands are made explicit, and where 3) insider and outsider perspectives are combined.

Dilemmas of mathematics teaching

A little while ago, Fraser Gobede and I co-authored an article entitled, “Studying dilemmas of mathematics teaching in Southern Africa”. This article was inspired by the works of scholars like Magdalene Lampert and Deborah Ball. Instead of focusing on how well teachers perform, or what knowledge teachers have (or are lacking), these scholars investigate the work of teaching mathematics and its entailments. In the article we focus on the concept of “dilemmas”, which Magdalene Lampert wrote about several decades ago. She considered the teacher as a “dilemma-manager” and aimed at understanding the dilemmas that teachers were faced with in their teaching of mathematics.

In this article, we develop an argument about the promise of focusing on dilemmas of teaching mathematics in the Southern African context, where there tends to be a strong focus on what knowledge teachers are lacking, and many studies have a deficit view of teachers. We suggest that shifting the focus toward identifying and exploring dilemmas of mathematics teaching may provide a more productive approach. Below is the abstract of our article:

Background: Learners in many countries in sub-Saharan Africa are underperforming in important subjects such as mathematics, and research in these contexts tends to focus on the lack of resources, insufficient teacher knowledge or poor quality in teaching as explanatory factors. This study has taken a different approach.

Aim: The study aimed at exploring how analysis of dilemmas that teachers encounter in the work of teaching mathematics may provide a productive approach to studying mathematics teaching in the African context.

Setting: The study was conducted in a rural Malawian Grade 1 classroom, where a teacher was teaching arithmetical notation to young learners.

Methods: A case study approach was applied, and data were gathered through video observations and interviews. Inductive analysis of observation data was applied to identify and unpack dilemmas of mathematics teaching.

Results: Two inherent dilemmas of the complex work of teaching mathematics have been identified and discussed. One dilemma was to decide when and how to present arithmetical notations in different modalities without losing the mathematical meaning. A second dilemma was to decide how to deal with unexpected learner errors while maintaining the planned focus of the lesson.

Conclusion: Considering dilemmas of teaching shifts the emphasis from evaluating the teacher to understanding and developing shared understanding of teaching as professional practice.

Contribution: The suggested shift in focus acknowledges the challenges of the local context without reverting to deficit views, and it contributes to developing a shared professional language.