Special issue on early childhood mathematics teaching and learning

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 Fritz 
• 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. 

Accommodation practices

Mikyung Kim Wolf, Jenny C. Kao, Nichole M. Rivera and Sandy M. Chang have written an article about "Accommodation Practices for English Language Learners in States’ Mathematics Assessments". This article was recently published in Teachers College Record. Here are their conclusions:

Despite the limitation of the small sample in this study, the findings of the study offer practical implications for policymakers and educators in the use of accommodations for ELL students. The study found considerable variation reported by teachers with regard to the perception of accommodation decision makers, selection criteria, and the types of accommodations allowed in each state’s math assessment. This variation raised serious concerns regarding the adequacy of the accommodation uses and the comparability of accommodated test results across schools. In this paper, we discussed a number of possible reasons for teachers’ reported difficulty in keeping up with state policies: (a) lack of clear guidelines in making accommodation decisions and implementing accommodations in a standardized way, (b) lack of or limited opportunities in receiving information and communicating about accommodations among decision makers and teachers, and (c) limited resources and logistical difficulties. To support an appropriate use of accommodations for teachers, we recommend that states make efforts to provide comprehensive, operationalized guidelines for ELL accommodations, monitor the use of the guidelines, and hold regular professional meetings for ELL and content teachers.

Want to join the community?

Since early 2008, I have used this blog as well as my twitter account to communicate things related to research in mathematics education. I started doing this mostly for myself, because I wanted a place to write about new articles, journal issues, conferences etc. from my field. I did this for myself, because when I wrote about it in my blog (or on twitter), there was a bigger chance that I would remember it. It also forced me to use English frequently, since this is not my mother tongue (it is, however, the main language in which I write most of my own academic publications).

Quite early on, I was surprised to learn that lots of people from all over the world was interested in what I did. So, what I was trying to do (aside from the personal aspects of it), with the blog as well as my twitter account, was obviously appreciated by many. It appeared then, that there was a need for somewhere you can go to learn about new things that happen within such a limited field of research as mathematics education.

The last couple of years, I have spent more and more time doing this on twitter, and less time communicating this on my blog. I don't plan on abandoning neither my blog nor my twitter account, but I have started experimenting with Google+, and I now want to invite you all to join me in a collaborative effort to do what I have been trying to do – but now collaboratively (and presumably better)!

I have created a so-called "community" on Google+, called "Mathematics education research", and I hereby invite you all to join me! My hope is that we can use this as a tool to communicate and discuss new articles, journal issues, etc. in the field of mathematics education research.

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 :-)

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!!!

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 :-)

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?

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!

References: 

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.

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:

[scribd id=108601437 key=key-1905y1zom6b69zjtc55i mode=scroll]

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

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:

• Teacher knowledge, curriculum materials, and quality of instruction: Unpacking a complex relationship, by Charalambos Y. Charalambous & Heather C. Hill
• Teaching (un)Connected Mathematics: Two teachers' enactment of the Pizza problem, by Heather C. Hill & Charalambos Y. Charalambous
• Two negatives don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality, by Charalambos Y. Charalambous, Heather C. Hill & Rebecca N. Mitchell
• Reading between the lines: Teaching linear algebra, by Jennifer M. Lewis & Merrie L. Blunk
• MKT and curriculum materials are only part of the story: Insights from a lesson on fractions, by Laurie Sleep & Samuel L. Eskelson
• Teacher knowledge, curriculum materials, and quality of instruction: Lessons learned and open issues, by Heather C. Hill & Charalambos Y. Charalambous

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:

• Revisiting the didactic triangle: from the particular to the general, by Simon Goodchild and Bharath Sriraman


• Problematizing the didactic triangle, by Alan H. Schoenfeld


• On the instructional triangle and sources of justification for actions in mathematics teaching, by P. Herbst and D. Chazan


• Mathematics teaching development as a human practice: identifying and drawing the threads, by Barbara Jaworski


• The didactical tetrahedron as a heuristic for analysing the incorporation of digital technologies into classroom practice in support of investigative approaches to teaching mathematics, by Kenneth Ruthven


• From the didactical triangle to the socio-didactical tetrahedron: artifacts as fundamental constituents of the didactical situation, by Sebastian Rezat and Rudolf Sträßer


• Kindergarten teachers’ accounts of their developing mathematical practice, by Ingvald Erfjord, Per Sigurd Hundeland and Martin Carlsen


• The mediating role of a teacher’s use of semiotic resources in pupils’ early algebraic reasoning, by Raymond Bjuland


• Mediated action in teachers’ discussions about mathematics tasks, by Claire Vaugelade Berg, Anne Berit Fuglestad, Simon Goodchild and Bharath Sriraman

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 :-)

[scribd id=98278972 key=key-1i0bnc0xou5oi3r13mcb mode=list]

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.

AERA 2012 - afterthoughts

The 2012 Annual Meeting of the American Educational Research Association is history, and I enjoyed it a lot! The conference started off Friday morning, April 13, with a number of interesting sessions. In the afternoon, the opening plenary lecture by Professor Linda T. Smith marked the official opening of the conference. In this session, a particular focus on indigineous education was made. To me, this represented a fairly new and very interesting set of perspectives. A refreshing start of such a huge conference!

I am not going to present a full overview of all the sessions I attended, because there is simply far too much to say about that! Instead, I will share some of my favourite moments from the conference.

I attended quite a few sessions from SIG-Research in Mathematics Education. I particularly enjoyed the one on "Mathematical Teachers' Beliefs and Knowledge". The presentation by Cindy Jong–where she told us about the MECS instrument–was of particular interest to me, but I found all papers and presentations in this session quite interesting.

Another very interesting session for me was the one on "Conceptual and Methodological Issues and Advances in Research on Epistemic Beliefs". After this session, I got the opportunity to meet Barbara Hofer (who is one of the major names in this area of research). Among the papers presented in this session, I was particularly interested in the one that was presented by Krista R. Muis.

Finally, I went to a session where Wolff-Michael Roth was discussant. I must be honest and admit that the reason I went wasn't because I found the focus of the session particularly interesting (somewhat, but not extremely)–I went to see Professor Roth live. He is one of those scholars who has a list of publications that is far beyond my comprehension (makes you wonder if he has more hours in his days than the rest of us...), and from the moment he started talking it was easy to understand that he had a knowledge and overview that was both wide and deep. Impressed!

AERA 2012 coming up soon!

The annual meeting of the American Educational Research Association (AERA) is coming up this week, and I am looking forward to attending this year's meeting! Last (and only!) time I attended the AERA conference was in 2009 in San Diego. This year, the conference is held in Vancouver (Canada), and I am looking forward to a great conference. I am presenting a paper in a symposium session this year. Our symposium session is entitled: Defining and Measuring What Math and Science Teachers Need to Know: Implications for Professional Development and will take place on Sunday morning (April 15), so if you are in Vancouver it would have been nice to see you there :-)

Our symposium session is chaired by Professor Elaine Munthe (also from the University of Stavanger). The discussant in our session is Professor Hilda Borko (Stanford).

If interested, you can read our paper below:

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First Asian Sourcebook in Mathematics Education

Professor Bharath Sriraman has just finished editing an exciting new book that is about to be published by Information Age Publishing. This new book is entitled "The First Asian Sourcebook in Mathematics Education: China, Korea, Singapore, Japan, Malaysia, and India. Below is the cover and table of contents to give you an exclusive first taste of the book!

[scribd id=80807392 key=key-1ju0w8coybk6vzguiz1m mode=list]

Tribute to the Springer Author Academy

Being a researcher in mathematics education (or in any field, I guess) involves a lot of hard work. Some parts of that work are more enjoyable than others, and everyone has their own favorite part. Me, I love to write! Working with text, whether it is a scientific article, a conference paper, book chapter or even a blogpost like this; that's the part of my work I love the most! That doesn't imply, however, that writing is easy, or that I know all there is to know about it. Far from it! I keep learning, and sometimes I discover resources that are more useful than others.

Recently, I have been using the Springer Author Academy quite a lot, and I think it is a great resource for me as a scientific writer! It contains lots of useful information and tips about all aspects of the writing process, from even before the first draft to the final part of the peer review process. Actually, I am working on a conference paper for the 2012 PME-NA conference right now, and some of the tips from the Springer Author Academy have been really useful in the process of structuring my paper :-)

So, if you are also involved with scientific research, and especially the writing of scientific literature, you might be interested in checking this out! And if you have some other useful links to share, I would be happy to know! Just use the comment field below! 

[youtube http://www.youtube.com/watch?v=MsPcVjT7tKo&w=640&h=360]

MKT in Ghana

My colleague Yaa Cole has written an article about her project on adapting and using the MKT instrument in Ghana. This article will appear in a forthcoming special issue in ZDM, and it has now been published online. The title of the article is: "Assessing elemental validity: the transfer and use of mathematical knowledge for teaching measures in Ghana". The articles which are going to appear in the MKT section of the forthcoming special issue have now started to be published, and Dicky Ng's article "Using the MKT measures to reveal Indonesian teachers' mathematical knowledge: challenges and potentials" has also been published online. More articles are coming :-)

Below is a preview of Yaa's article (click to see a larger version!):