As we have seen, it can be argued that questions are directly and substantially linked and connected to the Mathematical tasks of teaching (Ball et al., 2008). Questions permeate many of the core practices in teaching, as shown here. Some of these core practices, the mathematical tasks, are quite distinct and on the surface they seem unrelated and remote from one another. Like for instance the Mathematical tasks of;
“Evaluating the plausibility of students’ claims (often quickly)” (Sc) and “Selecting representations for particular purposes” (Rp). By connecting instructional questions so closely to the core mathematical tasks we can quite clearly see that these core tasks are related and have a bearing on each other. In this case we could envision one
representation (Rp) for a specific OL. From this representation (Rp), follows
instructional questions in regard to the topic with consequent learner responses (Sc). As we have seen this would follow the IRE/IRF pattern (Mehan, 1979; Sinclair &
Coulthard, 1975). This is just an example that shows how clearly questions are connected to Mathematical tasks of teaching. We have also seen that they are invaluable as discourse accelerators and for the continuation of the discourse or even discussion. By the same token we find and are reminded of the fact that instructional questions are an integral part of teaching and instruction. This would also indicate that continued work on questions asking in regard to teaching and instruction needs to be taken seriously. If taken this seriously and by showing the close connection to core teaching practices, we might get more teachers to actively work on their use, formulation and volume of questions in connection with the OL. This would aid
teachers in the use and exploitation of the up until now, not yet fully explored and unexhausted resources of questioning that Tienken et al. (2009) was rhetorically scouring for. Professor Savas Dimopuolos of Stanford is famously referred to with the quote “If you formulate your question properly, mathematics gives you the answer”, from the preceding findings this study proposes a different quote; “if you formulate your questions properly, it gives you mathematical answers”.
6.1 The road ahead pedagogical implications for teaching and research
Many of the questions, if not most, that are being asked by teachers during discourse and in particular explanatory talk are unplanned I claim. Expanding on the idea from Zodik and Zaslavsky (2008) which is also referred to by Adler and Ronda (2015) when they found that the selection of examples were not a planned and conscious act by the teachers studied, the claim here is that this most likely is the case with questions as well. The findings here regarding the observed teacher’s questions and drawing upon my own experience as teacher, a pre service teacher and co-teaching in colleagues’
classrooms would strongly indicate this claim. Should this be the case, this could imply that teachers are fully aware of the importance of instructional questioning, but they lack sufficient tools to apply in their approach to questions. It would also suggest that proper routines for concentrating on instructional question-asking in teaching from school-owners perspective is also lacking. Otherwise it might already have been
implemented as a specific goal in the preparation time administered in different schools.
One road ahead that might prove useful is to conduct more research on what type of questions prevail in the context of Norwegian mathematics classrooms. Then to use this information to identify what would be a fruitful path to put more focus on how to ask good ritual and rewarding exploratory questions in the education of teachers. Another aspect that should be researched is how we can work out how to ensure that proper steps are taken to master the art of questioning that Enright and Ball (2013) state is necessary to do. One way that could help in this regard would be to find out the extent of prepared versus ad hoc questions in mathematics classes, the same way that Adler and Ronda (2015) did with examples. As we have seen, research on questions in instruction and teaching has revealed interesting results, e.g. (Di Teodoro et al., 2011;
Enright & Ball, 2013; Tienken et al., 2009) . Thus increased research will help put more focus on one aspect of teaching that should be an area that would greatly benefit from this heightened interest. It might be the one thing all teachers regularly do that would improve teaching quickest? More work and focus on and with instructional questioning in teacher education for instance is something that should not be hard to incorporate at all. Expanded research on the use of instructional questions could prove double advantageous. If we accept what Tienken et al. (2009) wrote, they became more attentive to the questions they used and also what they wanted with their questions.
They in addition focused more on the sheer amount of questions. It is therefore conceivable that this could happen again. Hopefully that would spill over into the education of future teachers. As this study only looks at the questions from one teacher in one Norwegian classroom it would be difficult to generalize about the phrasing of questions or the word use within them from these findings. On the other hand the questions that have been scrutinized here are not atypical in any way nor are the topics in which they occur in any way exceptional. For this reason the questions analyzed are deemed suitable for the purpose of having a conceptual look at question use in
mathematical teaching and instruction. This Master’s thesis is on these grounds a contribution to the ongoing research regarding instructional questioning in teaching.