Mathematics teachers’ reflections about experienced tasks of teaching

Reidar Mosvold has co-authored a peer-reviewed article together with Marianne Maugesten and Janne Fauskanger, which is about to be published in Acta Didactica Norden. The article is written in Norwegian, but an English abstract follows below, along with citation information.

Teaching requires a special content knowledge as well as pedagogical content knowledge. Whereas many studies have investigated the knowledge teachers have or use in teaching, this study investigates what mathematical tasks of teaching that are in focus when teachers reflect on their own mathematics teaching, and what aspects of the professional knowledge base they draw upon. The second grade teachers in this study reflect on several core tasks of teaching mathematics, but their reflections tend to have an unclear mathematical focus — even when they reflect upon tasks of teaching that require specialized content knowledge. The results from this study also indicate that the language teachers use to reflect on their own mathematics teaching tends to lack precision and rigor.

Link to article:


Maugesten, M., Mosvold , R., & Fauskanger , J. (2021). Matematikklæreres refleksjoner om egne undervisningsutfordringer. Acta Didactica Norden15(1).

Nordic contributions to MKT

In the most recent issue of Nordic Studies in Mathematics Education, I published a review article on mathematical knowledge for teaching with a particular focus on Nordic contributions to this field of research. This article draws upon a literature review of research on mathematical knowledge for teaching from 2006 to 2013 that was lead by my colleague Mark Hoover from the University of Michigan. Since this most recent article is in Norwegian, I will summarize some of the highlights here.

As reported more extensively in an article entitled “Making Progress on Mathematical Knowledge for Teaching” (Hoover, Mosvold, Ball, & Lai, 2016), research in this field of research tend to focus on one of three main areas: 1) the nature and composition of MKT (28.9%), 2) improvement of MKT (42.6%), or 3) contribution of MKT (17.4%). Another 11.1% of the studies focus on what teachers know. From 2006 to 2013, there were only a few Nordic contributions to this research, and these studies were in categories 1 or 2. In my most recent review article (Mosvold, 2017), I suggest how Nordic researchers may contribute to this field of research. For instance, some studies apply variation theory to studies of mathematical knowledge for teaching, and the strong focus on theory is an asset of Nordic research in mathematics education that might be useful. In addition, some Nordic studies provide useful perspectives on the role of teacher educators and mentor teachers in the development of mathematical knowledge for teaching. Below is the English abstract, followed by references to the two mentioned articles:

In recent decades, researchers have shown an increasing interest concerning the mathematical knowledge that is specific to the work of teaching mathematics. In this article, Nordic contributions to this field are discussed in light of international research trends. The discussions draw upon results from a literature review of 190 empirical articles that were published in 2006–2013. In addition, Nordic studies that have been published after this are included in the discussion. Some of the studies focus on the nature and composition of this knowledge, other studies focus on the development of this knowledge, whereas a third group of studies focus on how teachers’ knowledge contributes to student learning and the quality of instruction. Further Nordic research in this field might contribute to strengthening theoretical perspectives and connections to practice.


Hoover, M., Mosvold, R., Ball, D. L., & Lai, Y. (2016). Making progress on mathematical knowledge for teaching. The Mathematics Enthusiast, 13(1–2), 3–34.

Mosvold, R. (2017). Studier av undervisningskunnskap i matematikk: Internasjonale trender og nordiske bidrag. Nordic Studies in Mathematics Education, 22(2), 51–69.

New book on Asian research in mathematics education

A couple of years ago, in 2010, Professor Bharath Sriraman edited “The First Sourcebook on Nordic Research in Mathematics Education” along with five researchers from the Nordic countries. This became a monumental book, and I was happy to contribute with a chapter. Now, professor Sriraman has recently finished what turns out to be an equally monumental piece of work: “The First Sourcebook on Asian Research in Mathematics Education“. This impressive book includes a total of 79 (!) chapters with contributions from mathematics education researchers from China, Korea, Singapore, Malaysia, Japan and India. The publishers suggest that: “the book will serve as a standard reference for mathematics education researchers, policy makers, practitioners and students both in and outside Asia, and complement the Nordic and NCTM perspectives”, and I believe they will be right about this. The chapters cover a wide range of topics in mathematics education, and the book presents comprehensive insights into research from this part of the world—both with a contemporary and historical perspective. Definitely a book to put on the wish list for anyone interested in mathematics education research!  

New special issue of The Mathematics Enthusiast

The Mathematics Enthusiast is an eclectic peer-reviewed journal on mathematics (education). The journal has an open access policy, and all articles are available online for free! Recently, a new issue of the journal was published, and this is a special issue on “The 2010 Banff Workshop on Teachers as Stakeholders in Mathematics Education Research“. This special issues contains ten interesting articles written by prominent mathematics education researchers like Alan Schoenfeld, Konrad Krainer, Kim Beswick and Peter Liljedahl (to mention a few).

The 2010 Banff workshop was chaired by Günther Törner and Bharath Sriraman (see their interesting article to learn more about the background and focus of the workshop!).  A key issue in the discussions at this workshop was “whether or not teachers were viewed as stakeholders in the burgeoning body of reported research” (p. 1). With this as a starting point, six issues were discussed in relation to:

  1. Interest in mathematics education research
  2. Trust/distrust among researchers and teachers
  3. (De)professionalization of teachers
  4. Acceptance of mathematics education researchers
  5. Terminology concerning professional growth of teachers
  6. How the relationship between the two groups can help improve learning and teaching of mathematics

The other articles in the special issue discuss different aspects regarding these issues, and they are all well worth reading – at least so I think 🙂

Why mathematicians read proofs

Juan Pablo Mejia-Ramos and Keith Weber have written a very interesting article that was published in the last issue of Educational Studies in Mathematics (Volume 85, Issue 2, February 2014). The article is entitled: “Why and how mathematicians read proofs: further evidence from a survey study”. I have just had the time to read this article today, and I found it very interesting! Their study builds upon a previous study, where the same authors conducted two small-scale interview studies on why and how mathematicians read proofs (Weber & Mejia-Ramos, 2011). In the previous study, nine research mathematicians were interviewed about their strategies when reading mathematical proofs (in published articles etc.). In their study back then, the authors identified three general strategies. When reading proofs, the research mathematicians:

  • appealed to the authority of other mathematicians who had read the proof
  • read the proof carefully line-by-line
  • applied modular reading of the proof

Based on their results from that study, they designed an internet-based survey that was distributed to 118 practicing mathematicians in the USA. When analyzing the results of this study, Mejia-Ramos and Weber (2014) found that the mathematicians had very much the same strategies as the mathematicians they had previously interviewed. When reading proofs, the mathematicians were not so much focused on checking whether or not the proof was correct – they appealed to the reputation of the author and journal on that – but they were more focused on the insights that could be gained. Oftentimes, the mathematicians would investigate how particular steps in a proof could apply to other examples, and they were also focusing on understanding the more overarching ideas and methods in the proof. For me as a mathematics educator, I find studies like these very interesting. The worlds of research mathematicians and mathematics education researchers often seem to be far away from each other, but they shouldn’t be! I think we as mathematics educators need to have a close relationship with research mathematicians, and I also think we can learn a lot by learning about how research mathematicians think when they approach mathematical problems, proofs, etc.

Mejia-Ramos, J.P. & Weber, K. (2014). Why and how mathematicians read proofs: further evidence from a survey study. Educational Studies in Mathematics, 85(2), 161–173.

Weber, K. & Mejia-Ramos, J.P. (2011). Why and how mathematicians read proofs: an exploratory study. Educational Studies in Mathematics, 76(3), 329–344.

Visions of a new editor-in-chief

I would like to take the opportunity to wish all my readers a happy new year! 2013 is gone now, and a new year with plenty of opportunities lie ahead. For this blog, 2013 was a slow year with little activity. One of my resolutions for 2014 is a revival of the blog, so here we go 🙂

2014 is hardly just begun, but some of the journals I follow have already published their first issue of the year. Educational Studies in Mathematics is one of them, and their Volume 85, Issue 1, January 2014 has been published a while ago. With this issue, Merilyn Goos takes over the responsibility of being editor-in-chief, after Norma Presmeg has finished her term. In her first editorial, she ponders about the past, present and future of the journal, and she reveals some interesting things about the visions of the journal. The journal aims at presenting “new ideas and developments of major importance to those working in the field of mathematical education” (p. 1). This might sound as a rather obvious goal for one of the most prestigious journals in mathematics education. She points at three features of the journal in this connection:

First, in presenting new ideas and developments, the journal is committed to shaping the field of mathematics education in innovative ways. Second, in reflecting a variety of research concerns and methods, it welcomes diverse approaches and does not privilege any particular theories or methodologies. Third, in emphasising high-level articles which are of more than local or national interest, its focus is on quality research that speaks to an international audience (p. 2).

Then she adds a fourth dimension, that I find very interesting: 

Educational Studies in Mathematics, through its editors and reviewers, seeks to mentor both new and established authors towards producing work that is original and significant. I hope that these features of the journal will continue to inspire readers and contributors to advance our field of mathematics education (p. 2).

So, with such encouraging words from the new editor-in-chief of Educational Studies in Mathematics, I encourage all of my readers (including myself!) to sharpen the pencils and start writing new and relevant articles for the advancement of the field 🙂

Thematic issue on Mathematical Knowledge for Teaching

Nordic Studies in Mathematics Education has published a call for papers concerning an upcoming thematic issue on Mathematical Knowledge for Teaching (MKT). I will be one of the guest editors for this issue – along with my colleague, Janne Fauskanger – and I would therefore like to share the call for papers with all of you (see also this editorial – towards the end – for the official version!):

We would hereby like to welcome submissions for an upcoming special issue of Nordic Studies in Mathematics Education (NOMAD). The theme of the special issue is “Mathematical knowledge for teaching – Nordic contributions”, and we encourage potential authors to submit articles that report or discuss Nordic contributions related to research on ‘mathematical knowledge for teaching’ (MKT). Teachers play an important role when it comes to determining the quality of students’ learning, and teachers’ knowledge of content is an important aspect of teacher quality. Building upon the theories of Lee Shulman, Deborah Ball and her colleagues at the University of Michigan have developed a practice-based theory of MKT. MKT can be defined as the mathematical knowledge that is needed to do the work of teaching mathematics, and the MKT framework has been described as one of the most promising efforts to find out what kind of mathematical content knowledge that is needed for high-quality teaching. Based on classroom studies, the researchers at the University of Michigan have developed measures to assess teachers’ MKT, and they have found strong connections between teachers’ level of MKT and their mathematical quality of instruction—as well as to students’ achievements. In the last couple of years, researchers have started to use the MKT measures outside the U.S. as well, and several interesting discussions have emerged. We encourage authors to submit articles related to different aspects of MKT in a Nordic context.

Please note the deadline for submissions: November 30, 2013. We hope for many high-quality submissions! Please visit the journal website to learn more about submitting articles to the journal, and don’t hesitate to contact me if you have any questions 🙂

New book on probabilistic thinking!

Egan Chernoff and Bharath Sriraman have edited a book called “Probabilistic Thinking: Presenting Plural Perspectives”. The book is about to be published in Springer’s series on “Advances in mathematical thinking“; Bharath is editor of this series together with Gabriele Kaiser. Fortunately, I have been given a flyer of the book, in order for the readers of my blog to get a little glimpse of this interesting book before it is published!

International perspectives on problem solving research

A new issue of The Mathematics Enthusiast (previously known as The Montana Mathematics Enthusiast) is just about to be published. Once again, I have been lucky enough to get a sneak preview from the editor, Professor Bharath Sriraman. The coming issue is a special issue that focus on “International Perspectives on Problem Solving Research in Mathematics Education“, and guest editors are Manuel Santos-Trigo and Luis Moreno-Armella (both from Mexico). The issue, which is a double issue, contains 18 articles, so we are talking about a monumental publication of more than 500 pages here!

In the issue, you will find a good mixture of articles from a variety of researchers – including some of the most prominent researchers in the field. So, if you are at all interested in problem solving and research on problem solving, this is definitely an issue to pay close attention to. As you can read in Professor Sriraman’s editorial (see embedded sneak preview), some changes have been made to the journal. One thing: the contents of the journal will be more open than ever, which I find great 🙂

Here is a sneak preview. You will be able to download all the articles from the journal website in just a couple of days, so pay attention to that!

Special issue in Journal für Mathematik-Didaktik

Journal für Mathematik-Didaktik had a special issue on early childhood mathematics teaching and learning in their latest issue. In addition to the editorial by Andrea Peter-Koop and Petra Scherer, the issue included the following articles:

  • Fostering Early Mathematical Competencies in Natural Learning Situations—Foundation and Challenges of a Competence-Oriented Concept of Mathematics
    Education in Kindergarten, by Hedwig Gasteiger 
  • Attitudes of Kindergarten Educators about Math, by Christiane Benz 
  • Non-numerical and Numerical Understanding of the Part-Whole Concept of Children Aged 4 to 8 in Word Problems, by Petra Langhorst, Antje Ehlert, Annemarie
  • Young Children’s Structure Sense, by Miriam M. Lüken 
  • First-Graders’ Development of Calculation Strategies: How Deriving Facts Helps Automatize Facts, by Michael Gaidoschik
  • The “Non-canonical” Solution and the “Improvisation” as Conditions for Early Years Mathematics Learning Processes: The Concept of the “Interactional
    Niche in the Development of Mathematical Thinking“ (NMT), by Götz Krummheuer
Whereas most issues in this journal feature articles in German, this special issue includes articles in English only, which is nice for those who are not German-speaking.