The lesson observation data, including those derived from the SRIs, were extensively analysed in different ways, some of which have been rejected as inappropriate. The key issue to emerge was that when analysed against codes derived from the individual’ preliminary interview, patterns, indicative of unique classroom norms emerged. Importantly, by way of warranting the procedures of the second phase, the six lessons observed for each of Abbie and Beth were randomly selected and indicated that fewer observations would probably suffice for future work.
The most significant outcome, derived from the qualitative analyses, was that although the teachers used the same words, they often meant very different things. For example Beth talked about explaining mathematical concepts, activities and resources to children, yet Abbie only spoke of children explaining to the rest of the class or to her in WCI phases. Discussion was also found to provide differences of opinion. For Beth this was a teacher led, essentially closed, and controlled activity, where she could steer and direct children to specific outcomes. For Abbie discussion was different. Discussion for her could be child led or teacher led, the most important difference was that children were involved and could take the lead. This was an interesting difference and one to which I propose to be alert in the main study. Other pedagogical approaches presented themselves differently in the teachers’ descriptions and observed emphases. Modelling and demonstration were of particular interest and may be of particular interest in the study. Finally, as indicated earlier, different classroom norms emerged from the observation and SRI data which confirmed the importance of its inclusion in the main study.
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The table that follows (table: 4.7), extends over three pages, highlight some of these key characteristics to emerge from this first phase.
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Similarities Notes to inform main study
MI Abbie and Beth
Prior Knowledge Reactivated at the beginning and throughout the lesson
Where is the mathematics emphasised in learning?
PA Abbie and Beth
Enjoyment Seen to emphasise a good attitude through the enjoyment of the subject or the resources
Although both espoused enjoyment in mathematics, the utterances appeared to emphasise either to develop an enjoyment of the subject or the use of interesting resources.
Need to probe more in main study
Discussion Discussion was emphasised Discussion was seen but in varying degrees. Child led or teacher led? Need to probe more in main study
Approach to learning Emphasis made on understanding their class’ attention span and expectations of outcome
Is this something all teachers attend related to belief: Need to probe more in main study
Demonstrating & Modelling
Demonstrating and modelling The data analysis appeared to suggest these were similar, however, there appeared to be differences in the observations of the emphasis e.g. was it demonstrating or modelling, what was the difference between the two approaches? Need to probe more in main study
Vocabulary Vocabulary emphasised The observations revealed differences in when the vocabulary was emphasised – Need to probe more in main study
CN Abbie and Beth
Fun in maths emphasised enjoyment of mathematics and the enjoyment of using a wide range of resources – enjoyment of partaking?
Need to probe more in main study: difference in these two emphases
Attitude Develops positive attitude towards mathematics
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Differences
MI Abbie Beth Need to probe more in main study
Prior Knowledge Reactivated throughout the lesson Reactivated at the beginning of each lesson
Pattern of practice was revealed in the way PK was activated.
Connections explicit connections were made between mathematical topics and real- life experiences
Beth made implicit connections between topics and context
Will this be relevant in main study? Askew et al (1997) believe only effective teachers make explicit connections.
Mathematical reasoning Abbie continuously provided questions and opportunities to think about concepts through whole class discussion
Beth asked conceptual questions to the whole class but expected individuals to think quickly and respond – little observed paired thinking time provided.
Beth used these instances to assess individuals. Teachers have very specific purposes for their emphasis – needs to be deconstructed with other teachers in main study. Is this an individual’s preference?
PA Abbie Beth
Questioning A range of styles of questions asked: open short closed and strings of closed. Probing questions were deliberately pursued with some individuals to assess understanding of concept.
A range of questions asked - focussed on specifically directed questions, often strings of closed questions. Very purposeful and directed often to individuals (differentiated to levels of ability).
This category is well researched, it will be interesting to see if other teachers take very purposeful approaches. Time provided for thinking and discussing ideas drawn from the questions. Or: Quick firing, very deliberate and structured.
Discussion Whole class discussion was observed as a consistent approach in lessons observed. Pace of discussion varied from short and quick to fairly long. Teacher and child led.
Discussion was teacher led through initial questions and individuals answers in response.
Are there further different interpretations of what discussion is?
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Modelling
And/or Demonstration
Abbie modelled games and worked through examples on board with child input.
Beth prompted individual’s participation in worked examples
Are Demonstration and modelling interpreted differently and/or expectations of children’s involvement
Fun and enjoyment Focussed through the use of task to
present the mathematics. Probe through observation and SRI CN
Flexible Pace, discussion and direction, sometimes teacher led sometimes child lead to some degree.
What is Pace?
Need to probe more in main study
Structured Strong structure to direction and
purpose of WCI.
How important is this to the teacher? And how does it influence the emphasis of teaching mathematics?
Need to probe more in main study
Attitude Concerns voiced about the low-baseline
of entry in context
Does this influence the focus of mathematical learning? Need to probe more in main study
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As indicated above, three themes emerged that appeared appropriate for structuring data analysis. These were a teacher’s mathematical intentions (MI), pedagogical approaches (PA) and classroom norms (CN). All evidence indicates that these will facilitate a deep and meaningful analysis, not least because they reflected very well teachers’ emphasis as observed and highlighted in SRI discussions.
In sum, the outcome of this first phase is that the research questions are appropriate and amenable to the data collection approaches used. Despite early difficulties pertaining to the use of pre-determined frameworks, the analytical approaches adopted have proved effective and have yielded the sorts of insights for which I had hoped. Consequently, the second phase will involve four new cases, similar approaches to data collection, although the six lessons will be reduced to three, and adaptations of the revised approaches to analysis. In so doing, I hope to obtain rich data that will be analysed in such depth that a thorough and appropriately novel understanding of how teachers construe the WCI phases of their lessons will emerge.
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