EECERA – Using powerful mathematical ideas

I have just been to a very interesting presentation at the EECERA conference. The presentation was held by Bob Perry from Australia, and he talked about “Using powerful mathematical ideas and developmental outcomes to enhance young children’s mathematical learning: An Australian experience”. The project he described had started off as a development study with 7 pre-school teachers in 3 pre-schools in South Australia. The project was so successful, it has now expanded to 350 pre-schools (all pre-schools in the state)! The aim of the project was not to change the teachers’ practice, but rather getting the teachers reflect on their practice and change the way they think about mathematics. (And thereby, they would also change their practice…)

An important practical technique in the project was the use of so-called “learning stories”, which I personally found very fascinating! These learning stories have three important elements:

  1. Descriptions of what the child/children had done
  2. Evaluation of what the child/children had done
  3. Reflections concerning: What next?

Another important concept was related to what Perry referred to as “powerful mathematical ideas”. These might be mathematisation, connections, argumentation, etc.

Here is the abstract of Perry’s presentation:

Young children can be powerful mathematical learners. This paper reports work done with preschool educators in South Australia in which powerful ideas in mathematics were identified, linked to the Developmental Learning Outcomes in the mandated South Australian curriculum, and celebrated and extended through narrative assessment.. It emphasises the processes involved in building the educators’ confidence and competence in the observation, development, implementation and assessment of meaningful mathematical learning for young children and suggests ways in which this approach can improve the mathematics education of these children without weakening the strongly held traditional principles of sound early childhood practice.
The key construct in this project is a numeracy matrix—a 56-cell table linking the powerful mathematical ideas with the Developmental Learning Outcomes through pedagogical inquiry questions. These questions are designed to ask preschool educators about their practice and how it relates to their children’s mathematics learning. Using this matrix, preschool and first year of school educators have devised and begun to trial a detailed assessment process through which they can access children’s powerful mathematical ideas, show progress as these ideas grow, and answer planning questions for each child as to what would be the most appropriate next instructional step.
The value of the paper is that it illustrates how work undertaken at the preschool level can inform similar work undertaken in the first year of school and it provides educators at both levels with an innovative way for considering the mathematics education of young children in both preschool and school.

EECERA – symposium session

We have just finished the first symposium session at the EECERA conference in Stavanger, and I attended a session with focus on mathematics and natural science. All three presentations focused on mathematics, so I guess they could have taken away the last part of the title.

Elizabeth Dunphy from St. Patrick’s College in Ireland did an excellent job to chair the session, and since I took part in one of the presentations myself, I can say that on behalf of the presenters as well as the audience.

The first presenter, Oliver Thiel from Germany, had an interesting presentation about a research project concerning teachers’ attitudes towards mathematics in early childhood. He had used interviews with children, based on already developed questionaires and scales. One part, for instance, was related to mathematical beliefs, and he had taken some scales developed by Grigutsch, Raatz and Törner as a starting point. Here is the abstract of Oliver’s paper:

Over the past few years the nursery school in Germany is increasingly perceived as an educational establishment instead of a child care centre. This can be seen in establishing curricula for young children, including mathematics as a domain of learning skills. In the past mathematics has not been part of the curriculum for training young children’s teachers. Therefore it is not clear, what actually their understanding is concerning mathematics. Van Oers (2004) has proven that teachers would support the mathematical development of the children only on the basis of their mathematical epistemology. The study reported here investigated teachers’ attitudes towards mathematics. The questions risen are:

  • Do nursery school teachers feel open or reluctant towards mathematics?
  • Is mathematics seen as an abstract system of terms, rules and formulas?
  • Or do the teachers see mathematics reflected in the collection and sequencing of experiences and in problem solving?
  • And what activities are expected to further the development of the child’s mathematical ideas?

A questionnaire has been developed, which included four scales, suggested by Grigutsch, Raatz and Toerner (1998). This form has been filled in by 100 teachers in Germany. For the evaluation of the questionnaires confirmatory factor analysis and structural equation modeling were used.
The most important result of this survey is that the teachers show an ambivalent behavior towards mathematics, but in general they underline the benefit for the daily living. Concerning the activities of children, only those are seen as mathematical experiences, which include numbers and shapes.

The second presentation was held by Janne Fauskanger and myself. You can see our presentation below:

Here is our abstract:

In 2006, Norwegian schools and kindergartens were faced with new curriculum reforms. For the first time in Norway the curriculum for kindergartens has a chapter on mathematics. As these reforms are now being put into action, teachers, schools, kindergartens and local governments are asking for in-service education. Evaluation of the previous curriculum reform in compulsory school indicates that there has been little change in the way teachers teach. Our aim is to investigate and try to identify features of ‘the best’ in-service education. A natural point of departure for such a project is to analyse teachers’ knowledge (MKT;mathematical knowledge for teaching) and beliefs to be able to adjust the in-service education to the participants’ needs. Our project is therefore divided into two parts. In the first part, we are researching teachers’ knowledge and beliefs, and in the second part we plan on using this knowledge to design a working model for in-service education. This presentation will focus on the research regarding teachers’ knowledge, and we would like the discussion to focus on pre-school teachers’ knowledge. The first step in our project will be to participate in the translation, adjustment and use of an American measuring system developed at the University of Michigan. It is important to know more about teachers’ knowledge when planning and evaluating in-service education and the measures would allow professional developers to measure teacher learning rather than just teachers’ level of satisfaction with professional workshops and in-service mathematics education can be improved. What about pre-school teachers’ knowledge?

The third and last presenter was Marc Wantz from Luxembourg, who talked about “Gender differences in mathematical competencies”. Here is the abstract of his paper:

In the present paper we use theories from research on the structure of cognitive abilities to conceive a comprehensive measurement conception of mathematical competencies. Specifically, our measurement conception allows disentangling specific arithmetical knowledge as well as the analysis of gender differences in these competencies. Data were obtained from 151 children who participated in a longitudinal study spanning the age range from kindergarten (5 years olds) to second grade (8 years olds). Our results revealed that gender differences in the competencies under investigation were not distinct concerning their static aspects as well as their developmental dynamics.

His entire presentation can be found on this link.

EECERA – day 1

Yesterday, the 18th annual EECERA conference was opened in Stavanger, Norway. The conference is held at the University of Stavanger, where I work, and I will naturally attend. Although it is a conference for research in early childhood education, there are several presentations with a focus on mathematics. I plan to go to all of them, and I will give you a review of my impressions and notes here. I also plan to follow the conference on twitter, so pay attention there as well!

The programme book for the conference can be found here, and the abstract book here.

Proceedings from ICME-10

It has been four years since ICME-10 was arranged in Copenhagen. For different reasons, the publication of the proceedings has delayed. A while ago, though, the proceedings were finally published. Participants at ICME-10 can order a printed book (for free), but those who did not attend can download the proceedings as a (large!) pdf-document. To read the proceedings from this important conference, click here!

YESS-4, Day 7

At the last day of YESS-4, Ferdinando Arzarello is going to deliver the main lecture. The topic for his talk is “Tools for analyzing learning processes in mathematics“. He starts off with a discussion of problems concerning What, Why, How and Goals:

  • What is necessary to observe in the classroom? (What)
  • Which theoretical frames are suitable to answer the What-problem? (Why)
  • How to observe all that is necessary? and How to interpret the observed data according to the assumed frame? (How)
  • How to improve consequent didactical practices in the classroom? (Goal)

YESS-4, Day 5

At the 5th day of the YERME Summer School, Günter Törner is going to deliver the main lecture. His topic is “theory versus practice”, and you can learn more from the paper that is published on the YESS-4 website.

Törner has published a multitude of papers and books in mathematics (algebra, geometry and discrete mathematics) as well as mathematics education. Several of them are available on his website, so take a look at the links I just gave you!

YESS-4, Day 4

The main lecture today at YESS-4 is held by Laurinda Brown. The theme of her main paper is: “Observing systems – how do we see what we see?”. She aims at discussing issues concerning observations, and she points at the necessity of including discussions of theoretical, methodological and philosophical issues.

For more information, you should read her CERME-4 article and an article from Educational Studies in Mathematics. Both are published on the YESS-4 website.

YESS-4, Day 3

The main lecture at Day 3 of the YERME Summer School is held by Jean-Baptiste Lagrange. His talk will be concerning research about technology in mathematics education. Lagrange is going to look at different technologies with certain theoretical concerns:

  • programming with the reification theories,
  • microworlds with situated cognition,
  • spreadsheets and computer symbolic systems with the instrumental and anthropological approaches,
  • today fast developing web based technologies with the need for new approaches.

You can learn more if you read his ICME-paper or the other paper that is published on the YESS-4 website.

YESS-4, Day 2

The main lecture at day 2 of the YERME Summer School will be held by Guershon Harel from University of California, San Diego. Harel’s talk will address two main issues in mathematics education:

  1. What is the mathematics that we should teach in school?
  2. How should we teach it?

To learn more about these issues, and the contents of Harel’s talk, you should read the articles that are published on the YESS-4 website (part I and part II).

YERME Summer School

This week, the 4th version of YERME Summer School (YESS-4) is organized in Turkey. The venue for the summer school is Karadeniz Technical University in Trabzon, near the Black Sea. KTU is a public research university with 30.000 students. There are about 40 master and PhD-students in mathematics education.

The summer school has a very interesting program, and although I am not able to attend it myself, I will try and cover it in my blog.

YESS-4 features a panel of distinguished experts, who will deliver the main lectures:

  • Prof.Dr. Guershon Harel, University of California (USA)
  • Prof.Dr. Linda Brown, University of Bristol (England)
  • Prof.Dr. Jean-Baptiste Lagrange, IUFM De Reims Paris VII University (France)
  • Prof.Dr. Günter Törner, Universität Duisburg-Essen Standort (Germany)
  • Prof.Dr. Ferdinando Arzarello, Università di Torino (Italy)

These experts will be leading the five working groups throughout the week.

The opening talk will be held this afternoon by Barbara Jaworski.

Links: