Outlook: Operationalizing the dimensions for video-rating

After disentangling the four dimensions into eight categories (in supply and use perspective each) and showing the importance of this step qualitatively, the next step towards a quantitative video-rating is the operationalization of the eight categories. The aim of the operationalization is to gain scales into which quality can be measured between low and high. In a next step, the underlying assumptions of what constitutes factors that promote learning gains are tested in the video data by relating them to students’ learning gains, as usual in quality of instruction research (Helmke, 2009; Hiebert & Grouws, 2007). Only after this step can we be sure that the “quality scale” really deserves this name by having a measurable statistical connection to the learning gains. Currently, we can only provide an outlook on these steps by briefly presenting our suggestions that are still under construction and further refinement.

As a tool for the operationalization, several basic codings are conducted on the tasks and the video data for determining frequencies. All tasks are categorized as having a lexical, conceptual or procedural focus as well as oral or written discursive demands that are further classified as sequencing (describing, reporting,...) or integrating (explaining, arguing, ...). In the video data, each speaker’s time spent on the different tasks (without time for general organization) is captured and can be summed up to the total time on task. Each speaker’s times spent on richer or less rich discourse practices as well as single-word utterances are coded. Besides the overlapping time measurements, all teacher moves are coded as focusing discursive, lexical, conceptual or procedural aspects. For further investigating the lexical dimension, a simplified version of trace analysis (Prediger & Pohler, 2015) is applied that relates the number of offered lexical means to those students’ take-up. More precisely, we count how many of the written offered formal and meaning-related expressions are taken up by students in their oral utterances. By these basic codings, the quality criteria can be specified as follows:

Operationalizing teachers’ intended activation (supply perspective)

The operationalizations of teachers’ activation refer to time units which are coded several times in the different dimensions:

  • • Criteria for the talk-related activation are operationalized as (TA1) the percentage of all students’ talking time related to the groups’ complete time on task, and (TA2) the percentage of time that the teacher is not speaking in the time on task, which operationalizes the time for oral and written talk in whole group phases as well as in pair work and individual seatwork.
  • • Criteria for the discursive activation are focusing the written or oral production of or contribution to discourse practices. On the written level, discursive activation is operationalized as (DAI) the percentage of time spent on writing tasks requesting discourse practices (including the time of orally reviewing these texts) in the time on task (for the whole lesson). On the oral level, two operationalizations are relevant: (DA2) grasps the percentage of time spent on discursive sequences of students and teacher together in the time on task, whereas (DA3) captures only the students’ percentage of time spent on discursive sequences in the time on task.
  • • Criteria for the conceptual activation are proposed on the levels of tasks, teacher moves, and oral discourse. On the level of tasks, conceptual activation is operationalized (CA1) as the percentage of time spent on tasks with conceptual focus in the time on task. On the level of teacher moves, it is operationalized (CA2) as the percentage of teacher moves with conceptual focus in all teacher moves. On the level of oral discourse, conceptual activation is captured (CA3) as the percentage of all students’ time in sequences with integrating discourse in tlie time on task.
  • • Criteria for the lexical activation are suggested for tasks and for teacher moves: (LAI) operationalizes lexical activation as the percentage of time spent on working on subtasks with lexical focus in the time on task. (LA2) operationalizes it as the percentage of teacher moves with lexical focus in all teacher moves.

Operationalizing students’ participation (use perspective)

In each dimension, students’ participation is operationalized for each student:

  • • Criteria for talk-related participation are operationalized (TP1) as the percentage of individual talking time in the time on task, and (TP2) as the percentage of individual talking time in the talking time of all students.
  • • Criteria for discursive participation are operationalized (DPI) as the percentage of individual time in discursive sequences in the time on task, and (DP2) as the percentage of individual talking time in the time spent on tasks demanding written texts.
  • • Criteria for conceptual participation are operationalized (CPI) as the percentage of individual time in sequences with integrating discourse practices in the time on task, and (CP2) as the percentage of individual talking time in the time spent on tasks with conceptual focus.
  • • Criteria for lexical participation are operationalized (LP1) as the percentage of the picked up terms, and (LP2) as the percentage of individual talking time in the time spent on tasks with lexical focus.

Next steps towards a quantitative video-rating study

First quantitative data point to interesting insights into which aspects of quality interaction correlate with students’ learning gains. For example, activation seems to be more important than the individual use of the supplied learning opportunities. Of course, these first findings must be interpreted carefully. Thus, we are currently working on further refining the operationalized criteria of the four dimensions in the supply and use perspectives as well as applying them to a large data base of video-recorded lessons on the conceptual understanding of fractions in the project MESUT 2.Thereafter, we will study their correlations with students’learning gains in conceptual understanding.

We hope to find statistical connections in the data because this would help to overcome the actual limitation of quantitative research to language issues on the discourse level rather than focusing solely on phenomena at the lexical and syntactical levels.

Furthermore, our results will inform teaching practice by pointing to the components of quality interaction that are especially important for (language) learners’ conceptual understanding of mathematics. For this purpose, we will prepare a video-based professional development which allows the discussion of the different quality dimensions with teachers and sensitize for the subtle differences of the dimensions.

 
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