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Unicidad de la representación

4. Cuantización de Fock de perturbaciones cosmológicas sobre un fondo

4.2. Criterios de unicidad para la cuantización de Fock

4.2.3. Unicidad de la representación

With regard to the interaction in L1 classrooms, one known example is interactive whole class teaching that was introduced in the nineties as the National Numeracy

Strategies (NNS) and National Literacy Strategies (NLS) in the UK (Mroz et al., 2000; English et al., 2002; Hardman et al., 2003; Smith et al., 2004; Myhill, 2006). It aimed to promote learning through dialogue and discussion (Smith et al., 2004) for both the primary sector and the first three years of secondary education. The basic principle underlying this strategy is that talk is important for students’ development and that whole class teaching is not a lecturing drill but ‘an active teaching model encouraging a two-way process’ (Smith et al., 2004: 396). Similarly, learning is not meant as the addition of new information to existing knowledge – it is constructing a model of the world (Barnes, 2008). This construction can take place through interaction and the basic idea of the NLS and NNS is to enhance overall student learning through interaction.

Another idea proposed by Jones and Tanner (2002) with regard to the teaching of mathematics through whole class teaching is that for effective teaching and learning

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of mathematics, teachers could use higher order questioning, which requires pupils to think, explain and discuss their own ideas. This process should allow students to have control of their own learning by initiating ideas and promoting their thinking (Mroz et al., 2000). It has been found that when children are able to talk about their understanding they are able to increase their knowledge and improve understanding (Johnson and Johnson, 1990, cited in Hardman et al., 2003). Later, in the last section of this chapter I am going to discuss the similarity of dialogic discourse and dialogic teaching to the ideas expressed in this paragraph. Further, Hardman et al. (2003) explain how the teaching-learning should be in interactive whole class teaching. They state:

One of the most important ways of working on this understanding is through talk, particularly where pupils are given the opportunity to assume greater control over their own learning by initiating ideas and responses which consequently promote articulate thinking. (p. 212) The basic structure of interactive whole class teaching is one whole class section, one group work section and then a plenary section (Hardman et al., 2003), but this does not need to be rigid. For example, in the early stages of the literacy strategy, the following structure is recommended for whole class teaching: 15 minutes of text level work; 15 minutes of sentence or word level work; group work for 20 minutes and plenary for 10 minutes (ibid).

Criticism of interactive whole class teaching

Those who have investigated this approach claim that teachers who practise this approach have no understanding of the underlying principle or how it should be practised in the classroom in order to bring desirable results. That is, teachers are ill informed of this process and they have not been given practical advice on what interactive whole class teaching is and how it should be used in the classroom (Hardman et al., 2003; Smith et al., 2004). Moreover, the strategy gave teachers

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contradictory ideas with regard to whole class interactive teaching (English et al., 2002) because most of the teachers assumed that a higher level of interaction occurs in the form of teachers’ questions and students’ answers. As a result, teachers’ general understanding of interactive whole class teaching is to use questions as much as possible.

This situation has led to further problems. One is that the majority of the questions used by the teachers are either closed or factual questions which did not help students to be involved actively in interaction in the classroom, and therefore the practical value of this approach in terms of the ‘linguistic and cognitive demands made on pupils has become a question’ (Mroz et al., 2000: 387). Further, interaction, which has become a ‘byword for effective teaching, both within the profession and in documentation related to teaching’ (Burns and Myhill, 2004: 47) has been measured based on the number of questions raised in the classroom (ibid). But Burns and Myhill argue that using questions as a measure of interactivity is unsuitable as it ignores the value of interactivity available in statements made by teachers, for example. In addition, they warn of the negative effect of more questioning in classrooms. They claim that the more questions the teachers ask the more passive and silent students become.

The resulting outcome of this approach in the classroom is teacher dominance. In other words teachers control knowledge in an ‘inflexible authoritative manner’ (Burns and Myhill, 2004: 47) and there is little constructive meaning making available from the students. Observations of interactive whole class teaching, therefore, have revealed that teaching tends to be teacher centred with teachers retaining control over the direction and pace of the lesson and the lines of knowledge (Mroz, et al., 2000).

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Further, after the introduction of whole class interactive teaching, the reality of the outcome may be traditional whole class teaching.

This brief review indicates that the NLS and NNS did not bring desirable results. Even though there were interactions between teachers and students those interactions followed the teacher dominated IRF (Initiation – Response – Follow-up) pattern. The pattern of interaction is discussed in detail in chapter 5. In this IRF pattern the teacher controls the discourse, leaving no self initiative for students. Therefore, students, despite their involvement in interaction, are not active. Having reviewed whole class interactive teaching at school, now I turn my attention to interaction in tertiary level L1 and L2 content classes.