The final interview

In the interview that was held after the course meetings, five topics and the corresponding questions were highlighted (appendix 8). The data relating to the lists of concepts, the concept map, the final assessment and the numeracy test have been included in the descriptions of the preceding sections; this is not the case for the data relating to the written questionnaire. Anne – like her student peers – filled in the questionnaire (appendix 13) anonymously. The researcher asked her several questions about the difficulty of the course as she had experienced it and her views on (the use of) theory. Anne said the level of difficulty of the course was neutral for her (score 3). She supported that judgement with the argument that while she could understand the content, she found the working method rather difficult. That last point gave rise to some doubts about the yield for herself (A = Anne; O = researcher).

O: Did you find the course easy or hard or somewhere in the middle? Do you still recall where you set the mark [on the five point scale; w.o.]?

A: I think it was in the middle [neutral; w.o.]. It was a bit hard and it was a bit easy… What you had to do exactly, more the way of working, I found hard. The content I found easy to understand. Okay, new things are mentioned, but not so that you had to use a dictionary. Too easy, no, I don’t think so. There were concepts you had to think about longer, like the cognitive network and that type of words. The working method I did find difficult; how it worked, how I had to approach it, what the intention was. O: Was it useful to do?

A: Yes, it was for me. I did hear other reactions, and I started to doubt myself and I asked myself: did I get enough from it. I now find in this kind of interview, that I can explain things and put things into words that I have an image of, something that I never used to think about. I think that’s very important, like the structure of

multiplication, the approach, the materials, I know more about them, I think that’s useful, yes. I also find it enjoyable to talk about it like this, to explain it, to order things for myself. I already found that out in secondary school. It’s also, yes… one of my ways of learning, it’s really part of me. It’s important to know that in teaching, so that you can also use other styles of teaching.

Her answer to the question what she thought of for the word ‘theory’ was: The first thing I think of is a piece of text, books, the literature so to say, that’s what I think of. Then, I also think of umm…, yes, like what kinds of strategies there are. For example, you have a series [of strategies; ed.] that you list, and working them out is then the practice. How the children use them, is practice. The series of strategies, these and these strategies exist, this is the theory.

She felt that theory was mainly ‘covert’ in the course. Theory, with the concept of strategy as its representation, she considers as a means of supporting her own learning and her own practice.

A: (...) it was more covert also, for example in the teaching narratives. Through the reflective notes and the umm… wordlists [concept list; w.o.], you could look up the theory, but initially it was covered up in the teaching narratives about practical situations. And umm… theory was discussed during the lectures. But… we often started with practice and then took things from that.

O: What did you find a remarkable example of theory, something of which you can say, this to me was a real example of the theory of learning to multiply that was discussed in the course.

A: Umm…, the example of the strategies, which strategies there are, and ummm… all the strategies that were mentioned, and the explanations. I thought that was theory, because, well, you don’t use those concepts in the classroom, it’s more background. For myself as well, my own learning question, the structure, yes…, the structure of a learning trajectory, this is theory too.

Anne appears aware of the function of theory (nr. 14).

Working on the basis of a personal learning question was experienced as rather difficult by Anne (and most of her student peers). Though there was a reasonable amount of guidance, perhaps lack of experience in setting a learning path fuelled this uncertainty. Perhaps the information about formulating and elaborating the personal learning question was not fully adequate yet. Apart from that, Anne did understand soon that she should not be too hasty in devising the learning question:

I think that when you are writing down a learning question, you should think: “How am I going to approach this and do I have enough sources and things like that (…).” Your question shouldn’t be too general or too vague. You must be specific and write down exactly what you are looking for, or else your research will be very difficult.

She showed herself aware of the importance of literature as a source for (reflection on) her investigations (nr. 14).

Theory-enriched practical knowledge in mathematics teacher education