Reflection, as a technique in teacher education, was stimulated by Donald Schön, who introduced the term ‘reflective practitioner’ (1983). Schön pointed out that the application of theoretical knowledge takes place much less explicitly than is often assumed. The reflective practitioner - the true expert in the field - is described by Schön as someone who is both engaged in practice and, at the same time, can articulate exactly what (s)he is doing and thinking. The reflective practitioner is someone who is able to draw conclusions from his or her reflections for the benefit of the activities that follow. Schön calls this ‘reflection-in-action’ and, in the same context, speaks of ‘theory-in-action’ and ‘theory-on-action’. This can be understood to mean the theoretical reflections engaged in by educators. With professionals, this involves personally acquired and assimilated knowledge (theory) rather than theory that has been acquired on the level of reproductive knowledge.

The following section was inspired by this idea of the reflective practitioner who, in this case, is a reflective teacher.

The reflective teacher

What kind of person is a reflective teacher? How does she distinguish herself from others? To answer this, let us first try and draw a picture of the reflective teacher we have in mind.

In our opinion, this is someone who is able to:

This is no small feat. In order to arrive at such a level, an educator (or a student) must have a number of important tools at her disposal, for example:
- She must in the first place possess a language in which she can express her reflections. In other words, she must be able to describe her own experiences. This requires a journalistic level of language use; take, for instance, the oral and written narratives from the internship. She must also be able to articulate more profound experiences and thought processes; a knowledge of professional terminology is necessary for this.
- In addition, it is important that she feels challenged to think over what she hears, sees and thinks whether this originates with the children or herself. This is called ‘developing reflection’, meaning that she learns from her own history by involving the (near) future as closely as possible.

The student’s or the educator’s knowledge of the theory will become increasingly apparent in these reflections. It should be clear, however, that one can only learn and teach reflection by doing it regularly. By remaining alert to the reactions of fellow students, educators, mentors and children, a student acquires a wealth of reflection material and also learns to reflect her own thoughts and statements in those of others. In the same way, the reflective educator also has an instrument to help her continue in her own further development.

Developing reflection

The following quote is from a journal written by a beginning teacher, which was included in a report by two American researchers, Gipe and Richards (1992).

"Guess what? 1 have had my eyes opened and I still want to teach. I love it. I guess sometimes we act so involved with just teaching that we don’t stop to think clearly. When I think in this journal I think how much I’ve learned about teaching. I have a lone way to go, but now I know that some teachers and some schools don’t treat kids like real people. The worst part is I don’t think anyone cares."

This teacher clearly shows how much she enjoys teaching. She is aware of this, but does not accept it without criticism. The above quote also reveals that she is aware of the value of reflection. She takes pedagogical and moral considerations into account when determining her standpoints. Since the introduction of a new curriculum for mathematics education, in the nineteen-eighties, the major role played by reflection in education is undisputed. Actual practice reveals, however, that reflection really takes place only on occasion. What should, in fact, occur, is that the student should be confronted by a learning environment in which she is often invited to reflect on an increasingly hicher level. We shall now use a few examples to illustrate these level changes in the (concentric) development of learning to reflect.

A report by a lay person

"I began this (mental arithmetic) lesson by writing 6 x 25 on the board. Many children raised their hands to give the answer. Anouk said she knew it right away and that it was 400. Then I let Debbie give the answer. She said:... I asked the other children if this was correct. Then I told them to do the three rows of problems on the stencil - all in their head. The children worked quietly; they also got the right answers. It was a fun lesson!"

The above report is by Thessa, a first-year student. Although you could entitle her report ‘Reflections on a mental arithmetic lesson’, it actually shows an extremely low level of reflection. Anyone, cognizant or not of the situation, could have written this report. In fact, it is no more than a report by a lay person.

Writing reports in response to experiences with educational material and personal preferences

When given the opportunity to think, speak and write about one’s own (lack of) cleverness in solving mathematical problems, the reports appear to gain some depth. In answer to the question: ‘What did you learn from Discovering Octavania’, Lucienne, a classmate of Thessa’s, answered:

"It was hard for me to picture anything with the numbers. I couldn’t get into the abstraction. Until I started working with the Oct-material. For instance, I couldn’t do anything at first with the problem 111-33. Using the material to picture it helped. Especially the number-line really helped with the additions and subtractions. I also learned not to say ‘but it’s obvious’ when I have to explain something to someone who doesn’t get it. You can explain something by asking yourself how you figured it out yourself. But even better you can figure out what the other person is thinking exactly. You can’t explain something from your own arithmetic past. That’s too long ago."

Lucienne clearly shows that she is aware of the essential role played by the manipulatives in her learning process. She is able to produce a good report, possibly because she applies her personal preferences and can state pedagogical considerations.

Relationships between one’s own thought processes and activities and those of children

Francoise, another first-year student, reacted as follows to the question, ‘what is the connection between how young children learn arithmetic and your own work on the problems from ‘Discovering Octavania’.

"First you have to know the names of the numbers. Then you have to be able to count and so you start to see some structure. You also begin to realize that you’re not really calculating much, but that you just know a lot by heart. With children, you have to be really aware that they do have to calculate everything, just like we have to do with 6 + 7 in Discovering Octavania. Actually, we also worked by using the building blocks, I’m kind of aware of that. But I did find that what we already knew got in the way. When you convert back into your own number system it’s very confusing."

In this critical reflection, Francoise makes the connection between her own thought processes and activities and those of primary school children. The reflection thus acquires a theoretical-pedagogical significance.

Theoretical reflections

Monique, a fourth-year student, is explaining her final project:

"As far as my approach in general is concerned, I prefer a development oriented approach. On the one hand, because I don’t think I’m suited to a pure child oriented approach: I just can’t help asking questions, stimulating reflection, or bringing something up for discussion. On the other hand, I think it’s important for children - especially for immigrant children - to be offered something regularly. In many cases, I don’t think it’s enough just to create a rich environment."

Monique is able to weigh the pros and cons of certain theoretical and pedagogical principles and to arrive at a personal evaluation. Making the reflective report undoubtedly inspired her to do this. She knows how to make the connection between theory and practice and also how to use one thing and another on behalf of a personal standpoint (vision).

Concluding remarks

Every educator would like the students, in the course of their education, to naturally and increasingly be able to reflect on their own thought processes and activities and those of the children. But this is not such a simple matter in daily educational practice. Most students require guidelines and stimulation in order to arrive at good quality, meaningful reactions.