Anne’s work plan

Introduction

As part of the preparation for her special topic, Anne, like all third-year Pabo students, has made a work plan, based on self assessment. This is done on the basis of a number of questions and assignments and should give insight into the knowledge, skills, insights and attitude that have been acquired over the preceding years. For this, a distinction into

Theory-enriched practical knowledge in mathematics teacher education

three areas is made, these areas being domain knowledge, practical skills and educational vision. The intended goal is acquiring an overview of the effort still required within the chosen subject to gain starting level skills as a primary school teacher. The results must lead to a targeted choice for spending the time that is available for study, teaching practice and guidance for – in this case – the specialisation in mathematics.

Domain knowledge

Anne herself says she did not experience primary school arithmetic as particularly difficult. After her secondary school (vwo met wiskunde A; pre-university education with mathematics A), she did find at the start of her Pabo education that much of her primary school arithmetic knowledge was no longer readily at hand. She is now aware that her domain knowledge at that point was mainly formal and that a teacher’s professional domain knowledge also contains students’ informal strategies.

After my VWO (with mathematics A) I did feel far removed from primary school arithmetic. Particularly fractions had faded very badly. I used a lot of formal calculation methods. At Pabo I gradually returned to informal methods. You need them to explain certain calculations to the children. I have regained a lot of my primary school arithmetic.

She points at gaps in her knowledge and puts this self-knowledge into words using appropriate wording:

I am not good at real mental arithmetic. I always need to use paper, to formulate the various steps. Many answers I do not have readily at hand. You could say that I have not yet achieved memorisation.

She uses examples of mental arithmetic strategies to clarify what she thinks is important domain knowledge, and she connects that with the importance of domain-specific pedagogical knowledge in the area of learning trajectories for mental calculation. Where the pedagogics of fractions is concerned, Anne lacks key concepts such as measuring strip and mediating quantity. For example, she cannot immediately give an adequate response to the question regarding a suitable context and model for the problem₃2 + 1₄1 =. At the same time she has apparently enough pedagogical feeling and know-how that she can didacticize a reasonable solution on the spot.

When you place₃2 pizza on top of the pizza that has been divided into twelve slices, you can see that₃2 is the same as₁₂8 . You can do the same for ₄1 . Once the students understand this, you can determine how many twelfth parts ₃2+ 1₄1 are together. Now that I think about it longer, chocolate bars may be even clearer, since they are already divided into 12 parts.

Practical experience

Anne has gained a variety of practical experience in the two previous years of study. She speaks of diagnostic interviews with students who have problems with arithmetic, of research into calculation strategies, of series of lessons, designing themes and more. Anne is positive about the role played by her mentors. Among other things, she gives examples of ideas and educational strategies she has copied from them. That does not mean that she is not critical about her mentors’ action. If she disagrees with her mentor about a problem, she will not refrain from offering her view as an alternative, as for instance in the case of a student in grade 1, who persistently clings to a counting approach for adding and subtracting.

My mentor suggested speed assessment. The child will discover that its method is too slow, and will have to use a faster strategy. I am not too certain that this is the right solution. I think it is too negative an approach. I would like to help him get rid of his counting approach by doing flash games with him. The flashed images of egg boxes, fingers or reckon rack contain the five structure that makes it easy to quickly recognize numbers. By playing these games with him, he can practice counting in groups (...).

View on education

She also shows herself to be a student who can justify her own opinions where her views on education are involved in terms of educational activities and underlying theory.

(...) There was very little room for other strategies. The result was that all children used the strategy that was offered and they were not motivated to find their own solution. The children were also unfamiliar with the various names of the strategies (friends of ten, doubling, etc.). This is where I reach the point where I would act differently from my mentors. I want to give much more room to different strategies. I also want to use the names of the various strategies within teaching.

Anne believes that the realistic approach to mathematics teaching (see section 3.2) fits in her view on education. She finds the attention to meaningful context and the opportunities students get for their own solutions of essential importance. Her experience is that it is not always easy to fit these ideas into existing mathematics education. She is aware that she has a long way to go, but is motivated to take that road.

I still have a lot to learn about planning my time. I often plan too much for one lesson. I do find that it works better when I am teaching a series of lessons. I have only worked with older textbook series myself (Wereld in getallen and Pluspunt). I think the structure of Pluspunt is good. I would like some experience with newer methods. Perhaps realistic mathematics can be included better there. In my next work practice I will come into contact with ‘Wis en Reken.’ I am curious if this method suits my preferences more.

All in all the image appears of a motivated student, who is aware of the development she has undergone in the two preceding years of study as a teacher in training. She is

Theory-enriched practical knowledge in mathematics teacher education

capable of naming knowledge, insights and skills regardless of whether she has gained them and shows the attitude and opinions that are needed to further work on her professional development. She looks upon the continuation of the course as a challenge.

Motivation for the research project

Anne is one of the group of eight students from the IPabo in Alkmaar who are voluntarily taking part in the research project, after they were informed by their teacher educator and the researcher. As well as by her preference for teaching children between the ages of 6 and 8, the group targeted by the course, Anne’s decision is determined by three opportunities the course can offer her. First is the opportunity to learn more about differences between children, a topic that will at a later stage be a key part of her learning question. Second, she sees it as an opportunity to study the developments that can be seen in children of grade 1 as a prelude to the concept of multiplication, which she refers to as ‘awakening multiplication.’ Third, the approach of the course appeals to her: the mixture of cooperative learning and individual study on a specific theme, in this case learning to teach the tables of multiplication. Further, she ‘just wants to learn a lot.’

I also look really forward to working in the classroom, but I feel that I still have a lot to learn. I will just go to work, it is fun to collect all the knowledge that is offered to you.