Notes from the final plenary session at PME-NA

The final plenary session at PME-NA was “Reexamining some widely promoted ideas: What do we know, and what do we believe?” by Suzanne Wilson and Deborah L. Ball. They started off by talking about urban myths vs. knowledge. After having described these two concepts, they listed seven popular themes in our field that they wanted to discuss in relation to those two terms – urban myths and knowledge.

The first theme they started discussing was teachers’ mathematical knowledge. They started off by presenting some of the main issues in the discussion. Do teachers need college level mathematics courses to be properly prepared for teaching? Knowing the material in depth, knowledge beyond the curriculum, perspectives on mathematics as a discipline are some aspects to it. There also seem to be an unclear relationship between academic study and SCK, PCK. Another perspective is that mathematics needed for teaching is not well-aligned with curriculum for college level mathematics.

SW had some interesting reflections about how PCK was picked up really fast after having been presented by Lee Shulman in 1986, and now it is all about MKT and everyone is talking about, measuring MKT. DB had this notion of “alphabet soups”, which I liked, referring to all these acronyms (MKT, PCK, etc.), and the question was raised: have we done ourselves any good by doing this?

High-quality field experience was the next theme for discussion. A widely promoted idea is that teacher candidates need to spend extensive time in classrooms. In this connection, it is important to bridge the gap between theory and practice. Other points in the discussion are that time is important, but an often neglected issue is detail about the clinical curriculum; there is also an underdeveloped pedagogy for clinical teaching – often left to personal preference. Finally, there is the issue of confounding “practice” as a form of learning with “field” as a setting. DB made a nice parallell to medical training, where students never start working with real patients – they start training o something else.

The next theme was “effective professional development”. A widely promoted idea in this connection is that “one shot” sessions are ineffective for teacher learning. Many believe that it takes time to learn teaching, but then again, important things CAN be learned from one single session. It matters more how it is taken up and used. The problem, SW argued, is not the “one shot”, it is more related to the content and the larger context.

A next, and very much related theme, was the pedagogy of teacher education. Teacher educators’ teaching should, according to a widely promoted idea here, model the pedagogy that they are teaching as teachers. This is, of course, related to the common saying: “we should practice what we preach”. One problem, or issue, that comes in here is that teacher education students ARE NOT K-12 learners. Teaching mathematics is, DB argued, a different subject than teaching the teaching of mathematics – it is not only that the students are different, the subjects are different – so the pedagogy is not necessarily appropriate. Teaching to teach is different from modelling the teaching!

After having discussed these issues, they returned to a discussion of whether or not it is a matter of best practices or urban myths, and whether or not there is a dichotomy between the two. They pointed our attention to the importance of being skeptical about what we think we know.

At the very end of their presentation, DB said that they seem to disagree with themselves on some of this, so I am not sure I have been able to capture everything that was said correctly here either – so, please consider this as my personal (possibly faulty) notes on this 🙂

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My own presentation at PME-NA 2012

Yesterday, I finished my own presentation at PME-NA in Kalamazoo, Michigan. I presented a paper on behalf of my colleague, Janne Fauskanger and myself. The title of our paper (and my presentation) was: “Wrong, but still right” – Teachers reflecting on MKT items. Obviously, I was a little bit nervous before the presentation – positive kind of being nervous, that is – but I ended up enjoying both my own presentation and the following discussion/comments session. If you want to see the slides I made for the presentation, you can download them here. I also made audio recordings of my presentation, so when I get home I plan on embedding the audio and the slides and post them here. So, stay tuned for that if you are interested 🙂

For now, I just want to thank everyone of those who came to my presentation! Thanks a lot for all the positive feedback, the comments and the questions!!!

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Jere Confrey’s plenary at PME-NA

The second plenary at PME-NA was “Articulating a learning sciences foundation for learning trajectories in the CCSS-M” by Jere Confrey. In her presentation, Professor Confrey explained how the learning trajectories were connected with the Common Core State Standards for Mathematics. Having been a member of the National Validation Committee for the Common Core State Standards, she was able to give some more personal (and very interesting) insights into the development of the common core standards. The details are laid out in her paper (see the proceedings). As part of her talk, she also shared some of her own experiences with the math war that appears to be going on (and which Jo Boaler talked about in her plenary yesterday). Having listened to her presentation, however interesting it was, I am happy to be a spectator from another country – both when it comes to the CCSS and the ongoing math wars 🙂

Towards the end of her presentation, she shared some ideas about the importance of unpacking. She argued, and I very much agree, that interpretation of the standards really matters. She also returned to one of her main issues in the development of the standards, where she had argued strongly about defining multiplication as repeated addition.

The last couple of minutes, she shared some very interesting information about the development of a tablet-based curriculum (see the Wireless Generation website). She also argued that this would change research, and we need to mobe on this! Personally, I would have liked to listen to an entire plenary on this, but then again I’m not the one who makes the calls 🙂

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Jo Boaler’s plenary at PME-NA

The 34th annual conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2012) takes place in Kalamazoo, Michigan. The conference started today – Thursday afternoon – with a plenary lecture of Jo Boaler. Boaler is professor of mathematics education at Stanford University, and she is one of the most prominent researchers in our field of research. The topic for her plenary lecture was: “Scaling up innovation: using research to make a difference”.

The two main foci of her talk was on research design and the communication of research results. Our aim is for research to have more impact. A question then is how to conduct research so as to have more impact on practice?

An interesting observation that she made: researchers who are critical about teaching as telling, often do the exact same thing when communicating the results of their research to teachers. We need to translate our research results into “records of practice”, as argued by Ball and Cohen (1999). In her presentation, she showed us a couple of video records. These records were discussed, and she pointed at the potential of such records in order to change practice.

When it comes to communicating research, she her own experiences with talking to politicians, writing books for a broader public, contacting the press etc. Through her experiences from radio interviews etc., she learned about how many people have bad experiences with mathematics.

Towards the end of her talk, she connected these ideas about communicating research with her own experiences from the attacks that had been made on herself and her research over the years (see e.g. this link for more about this). This became a very personal talk in which she not only shared her own bad experiences, but also shared a lot of interesting thoughts about the question she posed in the beginning of her talk: how can we design and communicate our research in order for it to make more impact?

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PME-NA here I come (unless my flights are affected by Sandy…)

Tomorrow morning, I am starting my journey from Stavanger to Kalamazoo, MI. The reason for my travel is, of course, the coming PME-NA conference. This is going to be my second time at PME-NA, and I am looking forward to it. On Saturday (2:45 pm), I am presenting a paper that I co-authored with my colleague, Janne Fauskanger. For more information about my session, see this direct link to the online program. If you are interested in reading our paper (Fauskanger & Mosvold, 2012), you can download it below. If you are going to PME-NA yourself, please feel free to get in touch 🙂

So, now that all is set and I am getting ready for my trip, the only thing I am a little bit worried about is how (or if) the hurricane Sandy is going to affect my trip. Hopefully, I’ll only hear about it in the news!


Fauskanger, J. & Mosvold, R. (2012). “Wrong, but still right” – Teachers reflecting on MKT items. In L.R. Van Zoest, J.J. Lo, & J.L. Kratky (Eds.), Proceedings of the 34th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education: Navigating transitions along continuums (pp. 423-429). Kalamazoo, MI: Western Michigan University.

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Second Life lecture coming up!

This week, I’ll give my first ever lecture in Second Life! It will take place on Wheeler Island, a virtual island owned by the David Wheeler Institute for Research in Mathematics Education at Simon Fraser University (Canada). Below is a poster about the lecture:

If you are interested in attending, please contact Melody Li ( as soon as possible to help setting up an avatar and gain entry to Wheeler Island!

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Teacher knowledge and curriculum standards

The latest issue (volume 44, issue 4) in Journal of Curriculum Studies should be of high interest to researchers in mathematics education. It contains six articles that all focus on different aspects concerning the relationship between teacher knowledge (in particular mathematical knowledge for teaching – MKT) and curriculum standards. The articles are written by researchers who all have a connection with the “MKT group” at the University of Michigan, although some of them are employed at other universities at the moment. Here is a list of the articles in the issue:

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New perspectives on the didactic triangle

A new and very exciting (I know, I say that a lot! But many new publications are exciting to me…) issue of ZDM was resently published. This issue (Volume 44, Number 5) is a special issue on: “New Perspectives on the Didactic Triangle: Teacher-Student-Content”. The issue has been guest edited by my friends and colleagues: Professor Simon Goodchild (University of Agder) and Professor Bharath Sriraman (University of Montana). They also wrote the editorial/first article in this special issue, and it has been entitled: Revisiting the didactic triangle: from the particular to the general. The authors of the other articles in the issue is a great mixture of really big names and some younger researchers (upcoming stars if you want) in our field. Here is a complete list of articles and authors in this issue of ZDM, with direct link to the original articles for your convenience:

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Mathematics teacher education in the public interest

I have recently been told (by my good friend Professor Bharath Sriraman) about a new and interesting book that is about to be published. The title is “Mathematics Teacher Education in the Public Interest: Equity and social justice“, and the book is edited by Laura J. Jacobsen, Jean Mistele and Bharath Sriraman. I have been fortunate enough to get a copy of the table of contents (see below) and the front cover of the book, and it looks promising indeed! 

The issues of equity and social justice in relation to mathematics teacher education are indeed of great importance, and I am personally looking forward to reading this book! And the level of productivity that is shown by my good friend Bharath never ceases to amaze me. Yet another book on my reading list – which continues to grow 🙂

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New issue of IJEC with math related articles

A new issue of International Journal of Early Childhood has recently been published, and it contains two articles that focus on mathematics. The first article, “Mathematically-Relevant Input During Play of a Caregiver With a Visual Impairment and Her Toddler“, was written by Joanne Lee, Donna Kotsopoulos and Caryl-Anne Stordy. It has the following abstract:

This research investigated play between two caregivers, one with a visual impairment, and their 15-month-old daughter. The mother has a visual impairment. We aimed to identify the similarities and differences in mathematically-relevant input by comparing the 30-min naturalistic play session conducted separately between the mother–daughter and the father–daughter dyad. The mother in this research participated in two 5-week community-based early numeracy sessions with her daughter. Results revealed that the toddler engaged in more joint attention with her father who also produced more mathematically-relevant utterances than the mother. Furthermore, the toddler was often not in joint attention with her mother despite many of the mother’s attempts to talk about an object by touching. Implications for engaging in mathematically-relevant input by parents with a visual impairment with their pre-verbal children will be discussed.

The second article, which was more interesting to me personally, is entitled “The Mathematical Competencies of Toddlers Expressed in Their Play and Daily Life Activities in Norwegian Kindergartens“. The article was written by Elin Reikerås, Inger Kristine Løge and Ann-Mari Knivsberg. All of them work at my university, and I find the project they report from very interesting. Here is the abstract of their article:

Research on toddlers’ mathematical knowledge is sparse. Studies on children’s mathematical competencies before school age have mostly focused on older children. Few of the previous studies have included large groups of toddlers, few have been conducted in natural settings, and few have been directed at a broad field of mathematical knowledge. The objective of this study was to investigate which mathematical competencies a large group of toddlers’ in Norwegian kindergartens expressed through play and daily life activities. A total of 1,003 children participated. Their competencies were registered when they were between 30 and 33 months. The assessment material consisted of 36 items, divided into three main areas: number and counting, geometry and problem solving. The information was collected through authentic assessment; the staff in the kindergartens observed the toddlers’ competencies in play and daily life activities. The competencies were registered as mastered, partly mastered or mastering not yet observed. The toddlers showed mathematical competencies in all areas observed. A wide dispersion was found; both for the total score and the subareas’ scores. The largest variance was found in number and counting. Our participants displayed lower levels of competencies in using number words and reciting number sequences than reported from previous studies and higher competencies in puzzle-making and following instructions on spatial words. The results indicate that the assessment material may be a valuable tool for the preschool teachers in identifying the variety of competencies mastered by the children in kindergarten. The need for future research is highlighted and discussed.

Their project–which is called “The learning child”– is a long-term project where they follow more than 1000 children’s development (in mathematics, language, social and motor skills) from the age of 2,5. In this article, they report from the mathematics part of the project. Another reason why the project is of personal interest to me, is that they use my oldest daughter in all presentations of the project 🙂 Below is a snapshot of the official presentation of the project (in Norwegian), where two photos of our daughter is displayed–one from when she was 2,5 and one from this year when she turned 7.

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