National Council of Teachers of Mathematics 2012 Research Presession

Please note: The NCTM conference program is subject to change.

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Wednesday, April 25, 2012: 11:00 AM
Franklin Hall 13 (Philadelphia Marriott Downtown)
Catherine O'Connor , Boston University, Boston, MA
Mary Elizabeth Matthews , Boston University, Boston, MA
Nancy Anderson , Boston University, Boston, MA
When an in vivo classroom study of different instructional methods yields significant results in favor of one condition, the researchers’ next steps are often taken in service of exploring the mechanism for the observed efficacy.  Just as in medicine, education researchers sometimes do not fully understand how their intervention secures its outcomes.

These steps are particularly important when the intervention being studied involves manipulations of teacher and student discourse.  While increasing numbers of researchers have studied talk in mathematics learning, we still do not have a full understanding of why it is sometimes efficacious. A simple mechanism such as number of times a concept or procedure is mentioned might be at work in facilitating student attention and/or memory.  Or the teacher’s encouragement of student discussion of agreements and disagreements might provide extra motivation for students to reason through the material.  These and other factors might be supported or ruled out by close analysis of the actual talk in such studies.

Another reason that discourse analysis of transcripts is needed lies in the pervasive nature of the intervention in such studies. Because studies featuring manipulation of classroom discourse are usually not scripted and take place over several lessons or longer, they often involve improvisational teacher discourse in both the intervention and control classrooms.  The control condition and the intervention condition may contain non-equivalent input beyond that intended by the lesson designer, and this must be sought and ‘controlled’ post-hoc by mining the transcripts.   

Our aim in this paper is to present an analysis of one facet of such a study, in order to serve two purposes.  First, we will report on a rich set of dimensions that can be used to analyse the lessons as mathematical talk, hoping to contribute to others who are interested in the methodological challenges of studying classroom discourse in mathematics.  Second, we will present an analysis of how the classroom talk in the intervention and control classrooms may have contributed to the significantly different results on one question in the posttest.

Our data derive from a tightly controlled three-day study that compares “discourse-intensive instruction”  (DII) with a closely matched NCTM reform instruction, but without talk moves that engage students in discussion (Non-DII). One condition (n=27) featured a teacher experienced in using the techniques and talk moves variously described in the literature as ‘academically productive talk’ or ‘accountable talk.’  The other condition (n=24) had students taught by the same teacher, using exactly the same content, examples, definitions, materials and tasks (e.g. writing down the same definitions in their math notebooks; sorting examples into two categories--integers and non-integers, etc.), however, the instruction did not include use of these talk moves. Instead, the teacher provided direct instruction and asked students for short answers as part of introduction and review. Both 6th grade classes were learning about integers for the first time.  The classes performed the same on the Stanford Diagnostic Mathematics Test given at the beginning of the year (in both computation (t=.60, p=.55) and concepts and applications (t=.02, p=.98) and on the pre-test.

An ANCOVA (pretest used as a covariate) showed a main effect of condition in favor of the Discourse Intensive instruction (F=7.7, p< .008, with a Cohen’s d of 0.83.)  The difference was concentrated in the questions on the post-test that required students to explain their reasoning.  The two classes did not differ at all in their performance on computational items (e.g. 245 + -65 + 60 + -120=?), testing students’ ability to perform the operations of addition and subtraction on series of signed numbers.

In this paper we attempt to understand this result by a detailed study of the classroom discourse in both conditions.  We use as our investigational anchor one post-test question with two parts as our starting point: a) What is the mathematical meaning of the word “opposites”? Give an example.  and  b) What is the sum that results when you add together two opposites? Explain your reasoning.  (Other examples of questions where students performed significantly better in the DII classroom include “When you add any two integers, does it matter which order you add them in? Explain your reasoning and give examples.”  and “Please write a definition of the term ‘integers’.”)  Using complete transcripts from all three days in both classrooms, we pursue all teacher and student utterances that bear on the answer to this two-part question about integer opposites, and seek possible explanations, integrating quantitative and qualitative tools.

For example, one form of quantitative transcript analysis shows that the number of teacher utterances devoted to the topic of integer opposites is actually greater in the Non-DII condition than in the DII condition (39 vs. 28).  This is a counter to the hypothesis that the Non-DII condition caused under-performance because the topic was not covered as extensively by the teacher.  However, the analysis also shows that student utterances related to “opposites” were five times more frequent in the DII condition (73 vs. 14).

If we limit our analysis to the quantitative findings, some might conclude that student talk is a more powerful vehicle for learning than teacher talk.  Yet a microanalysis of the content of the teacher and student utterances in the DII classroom reveals a complex interaction between the type of moves the teacher uses (e.g. “Who can repeat what she just said?”, and “Do you agree or disagree with what she said?”) and how student contributions are taken up and used by others.  We will claim that our quantitative discourse analytic results are not sufficient to explain the contributions to student learning of this instructional approach, but must be elaborated with micro-analysis of the type of teacher moves and the conceptual progress that emerges.

[15 minute round-table sessions will engage participants with additional transcript analysis and comparison of student answers with contents of intervention and control classroom episodes.]

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