The Importance, Nature, and Impact of Teacher Questions

Introduction

Teacher questioning has been identified as a critical part of teachers’ work. The act of asking a good question is cognitively demanding, it requires considerable pedagogical content knowledge and it necessitates that teachers know their learners well. A number of research studies have shown that teachers rarely ask ‘higher order’ questions, even though these have been identified as important tools in developing student understanding (Hiebert & Wearne, 1993; Klinzing, Klinzing-Eurich, & Tisher, 1985). Research on the relationships between teacher questions and student learning has produced mixed results, both more generally (Klinzing et al., 1985) and in mathematics (Hiebert & Wearne, 1993). Hiebert and Wearne (1993) argue that questions need to be viewed from within the context of the kind of instruction that is taking place and in relation to the mathematical tasks. In a small comparative study of traditional and “alternative” elementary mathematics classrooms, they show that while teachers in “alternative” classrooms asked a high number of questions requiring recall, they also asked a larger range of questions, and asked more questions requiring explanation and analysis than did teachers in traditional classrooms.

The research that we report on in this paper focuses on teacher questioning in secondary mathematics classrooms. We draw from a larger, ongoing, longitudinal study that follows approximately 1000 students in three schools who experienced different teaching approaches. There are three different mathematics curricula across the three schools, two of which we might characterize as “reform” and one as “traditional”. In two of the schools, students choose between a reform and traditional curriculum. The reform curriculum takes an open-ended, applied mathematical approach in which students work predominantly on long projects that combine and integrate across areas of mathematics. The traditional approach comprises courses of algebra, then geometry, then advanced algebra - taught using traditional methods of demonstration and practice. In the third school, the teachers have created their own curriculum which fits into the traditional algebra-geometry-algebra divisions but which takes a more open, exploratory and conceptual approach to mathematics within these strands. We consider this to be a reform curriculum. In addition to monitoring the students over four years, we are studying one or more focus classes from each approach in each school. In these classes we observe and video lessons, and conduct in-depth interviews with the teacher and selected students. In our paper we will report on our analyses of classroom organization and teacher questions and how these relate to the different curricula, the mathematical tasks within the curricula, the mathematical direction that the lessons take and classroom environment. We will also discuss some methodological issues in analyzing questions.

Findings

One result of our study is the critical role played by the teacher in each approach. We found that crude labels such as ‘‘traditional’’ or ‘‘reform’’, while matching the curriculum approaches used, did little to distinguish effective and ineffective teaching. We thus undertook a closer analysis, both quantitative and qualitative, of the teaching environments. We began with a quantitative analysis of the main activities in each classroom. We classified all the time spent in each class as either being: Teacher Questioning; Teacher Talking; Groupwork; Individual Work; or Student Focus. The categories were mutually exclusive. We coded 6 lessons for each of 6 focus teachers in 30-second intervals and reached an inter-rater reliability of 85 percent. Our first finding that we will report in the paper is that classes taught by different teachers, using the same curriculum, generated very similar categorizations. The amount of teacher questioning and groupwork was higher among the reform curriculum teachers, and the amount of individual work and teacher talking was higher among the traditional teachers. But it was noticeable and significant that some teachers who used the same curriculum approach, but generated very different instructional environments, looked very similar on this broad categorization. Thus this broad categorization of time spent does not seem to capture teaching quality. In some ways this is unsurprising, most people know that teaching quality depends upon the detailed decisions teachers make, but many of the initiatives handed to schools by districts and governments stay at this broad level of detail, as teachers are told to lecture less, engage in group work or have student presentations. Our study reveals that teaching quality is enacted at a finer level of detail.

These results led us to undertake a second, more focused analysis – which involved looking explicitly at all the questions teachers asked, to the whole class and with individuals and groups. “Rich questions” (Wiliam, 1999) or questions that promote mathematical thinking (Watson & Mason, 1998) can come from existing curricula or resource materials for teachers. However the cognitive level of these questions/tasks is often lowered in subsequent interaction (Stein, Grover, & Henningsen, 1996; Stein, Smith, Henningsen, & Silver, 2000). On the other hand, standard mathematical tasks can be opened up for exploration with skilful teacher questioning (Lampert, 2001).
We developed nine categories of teacher questions, through a process of watching the teachers in our study and considering other analyses of questions, particularly those conducted by Hiebert and Wearne (199x) and Driscoll (1999),. Our first sets of videos were coded by different researchers and an inter-rater reliability exercise achieved 90 percent reliability. The remaining of lessons were then coded by Brodie. Table 1 shows the categories we used.

Table 1: Teacher Questions.
Question type Description Examples
1. Gathering information, checking for a method, leading students through a method Wants direct answer, usually wrong or right Rehearse known facts/procedures,Enable students to state facts/procedures[equivalent to closed, lower order questions] What is the value of x in this equation?How would you plot that point?
2. Inserting terminology Once ideas are under discussion, enables correct mathematical language to be used to talk about them What is this called in mathematics?How would we write this correctly mathematically?
3. Probing, getting students to explain their thinking Clarify student thinking Enable student to elaborate their thinking for their own benefit and for the class How did you get 10? Can you explain your idea?
4. Exploring mathematical meanings, relationships Point to underlying mathematical relationships and meanings. Make links between mathematical ideas Where is this x on the diagram? What does probability mean?
5. Linking & Applying Point to relationships among mathematical ideas and mathematics and other areas of study/life In what other situations could you apply this? Where else have we used this?
6. Extending thinking Extends the situation under discussion, where similar ideas may be used Would this work with other numbers?
7. Orienting / Focusing Helps students to focus on key elements or aspects of the situation in order to enable problem-solving What is the problem asking you? What is important about this?
8. Generating Discussion Enables other members of class to contribute, comment on ideas under discussion Is there another opinion about this?What did you say, Justin?
9. Establishing context Talks about issues outside of math in order to enable links to be made with mathematics at later point What is the lottery?How old do you have to be to play the lottery?


A second set of results that we will report are the patterns of questioning across the different approaches. We have found further clear distinctions between traditional and reform teachers. Our findings for the traditional teachers are stark – more than 95 percent of their questions are of type 1. In the case of the reform teachers, between 60 and 75 percent of their questions are of type 1. The teachers using reform approaches are more varied, with some of them asking mainly type 1) and 3) questions and others asking a significant number of type 4) questions, These differences are important in determining the direction and flow of lessons. In our paper we will provide a closer, qualitative analysis of these questions in action. This analysis will both show the importance of the particular questions teachers ask in establishing different instructional environments and the need for teacher learning opportunities that focus on teacher questioning.

We will conclude with some methodological reflections on the importance of capturing teacher differences, and the grain size of analysis that we have found helpful. We will also consider the implications of the questioning differences we recorded – for curriculum policy and for teacher learning.

References

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Driscoll, M. (1999). Fostering Algebraic Thinking. Portsmouth, NH: Heinemann.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393-425.
Klinzing, G., Klinzing-Eurich, G., & Tisher, R. P. (1985). Higher cognitive behaviours in classroom discourse: Congruencies between teachers' questions and pupils' responses. The Australian Journal of Education, 29(1), 63-75.
Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven: Yale University Press.
Stein, M. K., Grover, B. W., & Henningsen, M. A. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455-488.
Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.
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Wiliam, D. (1999). Formative assessment in mathematics, part 1: Rich questioning. Equals: Mathematics and special education needs, 5(2), 15-18.