interaction process between teacher and students: The labeling of students on the basis of relative characteristics, The

Now another decision rule will be added: every teacher uses a minimum level (L) which consists of the subject matter and final level to be reached. This level is the standard used by teachers to decide how to divide time and attention. Those students who have not reached this minimum level after group instruction will receive individual instruction first. After all students have reached this minimum level, the teacher divides the time and attention left2. To illustrate, in Figure 2 the same minimum levels are added for both students. On the basis of the group instruction both students have reached their minimum level.

The situations of Figure I and 2 are very simplified descriptions of reality, but can easily be elaborated to cover whole groups of students. The time and attention division of the teacher will now be based on a global picture that the teacher has about all his/her students. This situation can be pictured by putting the characteristics of the 'average' student on the vertical axis. The interpretation of Figure 1 becomes now that student 1 profits twice as much from individual instruction as does the 'average' student from the group. The decision the teacher has to make is now: How much time and attention do I give student 1 in relation to the average time and attention I give the other students? This means that point B stands for the average achievement of the whole group, except student 1. Point C remains the optimum, the teacher gives student 1 as much as time as, on average, the other students.

Becoming a problem student

From the forgoing the conclusion can be drawn that the ultimate achievement of a student depends not only on characteristics of his/her own, but also on characteristics of the other students. The definition of a problem student is based on two characteristics of the students. On the one hand, a problem student is a student with achievements beneath the minimum level. In theory this situation exists only when the teacher gives all his/her individual time and attention to this student, but in spite of this, the achievement of this student stays beneath the minimum level. In Figure 2, this achievement is beneath the horizontal L-line and/or to the left of the vertical L-line. In practice, the teacher will not give all his/her time and attention to such a student. After concluding that the student will not reach the minimum level, the teacher will devote his/her time and attention to other students, while achievements beneath the minimum level give no benefit to him/her. Only group instruction will be given to such students. With respect to Figure 2, this means that such students no longer form part of the division process. However, the minimum achievement level is not absolute. The well-known `Posthumus effect' (Posthumus, 1947) states that the minimum level is based on the `average level' of the group. So, in a group with a high average achievement level the minimum level will be higher than in a group with a lower average level. So, it is not the absolute achievements of a student which determine the labeling "problematic", but rather the relative achievements. This leads to the first hypothesis of this paper: