A theoretical reflection is more than theory alone. The word 'reflection' indicates the presence of a situation, which is then observed, recognized, pondered and analyzed with the help of one's own experiences and knowledge. In a theoretical reflection, the educator demonstrates how the theory can help one understand the practice. Sometimes the educator is even able to make predictions after observing a phenomenon.

Joric (4;9) is crazy about marbles. She has just brought some marbles home from school and has laid eight of them on the table. She counts the marbles one by one. But they're lying rather close together which makes it difficult for her to synchronize the counting: her finger moves a little more quickly than she counts. At first she counts seven, but then she begins to doubt this. To be quite sure, she counts the marbles once more, but this time in a special way: as she counts, she picks up the marbles one by one and moves them away. Now there is no question in her mind: there are definitely eight of them (Goffree, 1993, p. 1 85).

The observer of Jorie's counting (Buys, 1991) has the following comments:

"It is not clear why she began to doubt her first result - seven. Perhaps she already had some experience with incorrect results due to unsynchronized counting. In any case, she knows how she can be sure. She organizes the synchronized counting perfectly. In this way she demonstrates how important it is to organize arithmetic work."

Here we see an example of an observation followed by a (theoretical) reflection. Without the reflection, this observational report would still have been fascinating, but it would have gives less food for thought in tenns of learning and development processes. Goffree (1993, p. 181) has the following comments about observation:

"It is inconceivable that observation be disconnected from theory. Those who have little theoretical insight will not observe much in educational practice. As a consequence, not much will come of developmental support and stimulation."

The following example of theoretical reflection is taken from a class at an institute for primary teacher education. A group of second-year students is busy solving a problem involving tile setting (Goffree, 1992, p.72).

Groups of students are working in various ways, trying to find out how large a square table can be if the tile setter has 1250 tiles. Graph paper and material are being used, but diagrams and bare problems appear as well. The educator walks around the classroom, offering a hint now and then and taking notes on what he sees. After a quarter of an hour he calls the group together and reviews some of the solutions. With each solution he reflects briefly on what he, himself, has observed: trial and error, systematic activities or notations, help or confusion provided by the materials, how articulating the problem to one another plays a role, unusual solutions (repeated addition instead of repeated subtraction), and more. Lastly, he sums up the essential characteristics of the learning process of acquiring an algorithm.

Both examples show how theoretical reflections can be grounded in theory as well as in practice.

Making theoretical reflections is an essential element of an educator's work. Many things are used by the educator to present knowledge, including, for instance, students' internship experiences, primary school situations and anecdotes, textbook examples and events during a student work group. The educator uses a theoretical reflection to show how theory can illuminate practice. The educator's specific expertise is here especially apparent and distinguishes itself from, for instance, that of a primary school counselor, whose primary experience is that of actual school practice.

The value of a theoretical reflection can mainly be found in the educator's ability to refer back and forth between theory and practice. This interaction between theory and practice adds depth to both components and can lead the student to a higher level. And, no less important: the educator's theoretical reflections provide the students with insight into their own learning and development processes and into those of the children!

Each country has its own set of (famous) examples of theoretical reflections in the literature. In the Netherlands there are for example articles by Freudenthal (1975) with his grandchild Bastiaan. In the US literature the book by John Holt (1965) 'How children fail' is such an example.