24 SES 12, Sense of Belonging, Meaningfulness and Participation
Students’ participating in mathematical discourses in mathematics classroom is today recognized as crucial. Sharing thoughts and justifying reasoning is believed to develop students’ mathematical thinking (Cobb, Boufi, McClain, & Whitenack, 1997; Kieran, Forman, & Sfard, 2001; Lampert, 2001), and mathematics education is seen as especially relevant for fostering 21st century skills, such as critical thinking, problem solving, communication and collaborating (Wagner, 2014). Real problems in work places are often solved in a team drawing on multiple people’s expertise, and depending on the team members’ ability to communicate their thinking to each other. In order to foster such skills, teachers need to be able to orchestra whole class and peer discussions giving opportunity for students to participate in discourse characterized by challenging questions and tasks that help students reflect and build on their thinking (Gravemeijer, Stephan, Julie, Lin, & Ohtani, 2017). Researcher has shown how hard it can be to create classrooms where students actively have the opportunity to talk (Walshaw & Anthony, 2008) and that this requires a change of classroom norms (Yackel & Cobb, 1996) as well as awareness of meta-discursive rules (Sfard, 2001).
In Finnish mathematics classrooms, studies indicate rare and limited opportunities for students to participate in classroom discourse (Author 1 and colleagues, in review; Pehkonen, 2007). The present study examines such opportunities by observing three mathematics teachers’ practices and interviewing them on their rationale behind the instructional choices and asks the following research questions; What kind of opportunites to participate do students have? What is student participation for the teachers? How do teachers perceive student participation?
The applied framework is inspired by the work on meta-discursive rules (Sfard, 2001) and classroom discourse norms (Yackel & Cobb, 1996). Opportunities for student talk is based on the assumption that providing opportunities for students to reflect their own thinking and on the reasoning of others is an important aspect of mathematics discourse (Grouws & Cebulla, 2002; Hiebert & Grouws, 2007). Opportunity for studenttalk is in here analyzed as the quantity and quality of opportunities students have to discuss in whole class or with peers around mathematical content. Opportunity for student talk can be either brief or extended. When brief, students are usually responding to a teacher question in recitation format, often called Initiation-Response-Evaluation/Feedback (IRE or IRF) (Cazden, 1988) or following a Funnel pattern (Wood, 1998), described as teacher leading students to the right answer and thus doing most of the intellectual work. In contrast, extended opportunity for student talk is called a Focusing pattern (Wood, 1998), where a teacher creates situations for students to explain and give reasons to their mathematical ideas.
The data comprise of video observations and interviews collected in 2018. A week’s mathematics lessons were filmed in three 9th grade Swedish-speaking math classrooms from three different schools around Helsinki. Two cameras and two microphones were strategically placed in each classroom. One camera faced the teacher and one on the entire classroom. The teacher wore a microphone and another microphone captured student talk. To enhance the possibility of a variety of perspectives, the teachers were purposefully sampled from a previous study (Author 1 et al., in review) as they at that time had portrayed different instructional patterns of classroom discourse while teaching students with mixed achieving results. This time, they were teaching students on different ability levels: Teacher 1 still taught mixed-achieving students, Teacher 2 taught low-achieving students, while Teacher 3 was responsible for teaching high-achieving students. While videos are often used for systematic coding of classroom activities, we also need complementary qualitative analyses to add insight to the issues of such coding (Snell, 2011) and to address issues such as contextualization (Blikstad-Balas, 2016), in order to comprehend the enacted classroom practices. The Author therefore followed the teachers for one week and conducted interviews at the end of the week to addresses this need to investigate a context from a more complex contextual perspective (Cai, Morris, Hohensee, & Hiebert, 2017). The focus of the semi-structured interviews was on the teachers’ instructional choices and on their perspectives on students’ opportunities to participate in discourse. During observations, the units of analyses were classroom discourse episodes (whole-class or peer activities) on mathematical content lasting more than 5 minutes. Peer activities here means students working in groups or pairs on a common task defined by the teacher. The transcripts from the interviews were analyzed with a focused coding on how teachers perceived student participation and discussions in the classrooms and what their rationale in their instructional choices was for the observed lessons. As the teachers taught students on different achievement levels, they were also asked whether and how that influenced their teaching.
The findings of this study indicate differences of classroom discourse norms (Yackel & Cobb, 1996) in enacted practice, as well as different perspectives of what it means “to participate” among the teachers. Differences in practice were notable in meta-discursive rules (Sfard, 2001) during classroom discourse episodes, were two of the teachers (Teacher 1 and 2) only gave limited opportunity for student participation in line with IRE (Cazden, 1988) and Funneling patterns (Wood, 1998). Teacher 1 expressed value of talking math and gave her students opportunities to engage in group assignments, yet found that her best students learned best individually. Also, student talk was constantly disrupted and monopolized by the teacher’s explanations. Teacher 2 appreciated students answering her questions but did not see much value in her students discussing math and gave no opportunity for them to do so. Teacher 3 valued verbal participation and had clear rules intended to ensure that all students were engaged verbally during group work. Her questioning was in line with a Focusing pattern (Wood, 1998). All teachers expressed how they try to consider and foster student self-confidence and student well-being, and that this sometimes means allowing non-participation. The findings suggest that students’ opportunities to participate were related to views on what it means “to participate”, and to students’ achievements in mathematics, as well as teachers’ concern for student well-being. Knowledge about reasoning behind students’ opportunities to participate in discourse can enrich our understanding of classroom discourse in different contexts. These findings are also relevant for teacher educators and can be used to make teachers aware of their meta-discursive rules and classroom norms and thus evaluate and develop activities where mathematical thinking is developed and expanded, and where student participation is valued and necessary, to closer meet requirements for 21st century skills.
Blikstad-Balas, M. (2016). Key challenges of using video when investigating social practices in education: contextualization, magnification, and representation. International Journal of Research & Method in Education, 1-13. doi:10.1080/1743727X.2016.1181162 Cai, J., Morris, A., Hohensee, C., & Hiebert, J. (2017). Making Classroom Implementation an Integral Part of Research. Journal for Research in Mathematics Education, 48(4), 342-347. doi:10.5951/jresematheduc.48.4.0342 Cazden, C. B. (1988). Classroom discourse : the language of teaching and learning. Portsmouth, NH: Heinemann. Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28(3), 258. doi:10.2307/749781 Gravemeijer, K., Stephan, M., Julie, C., Lin, F.-L., & Ohtani, M. (2017). What Mathematics Education May Prepare Students for the Society of the Future? International Journal of Science and Mathematics Education, 15(Supplement 1), 105-123. doi:10.1007/s10763-017-9814-6 Kieran, C., Forman, E., & Sfard, A. (2001). Guest EditorialLearning discourse:Sociocultural approaches to research inmathematics education. An International Journal, 46(1), 1-12. doi:10.1023/A:1014276102421 Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven: Yale University Press. Pehkonen, L. (2007). To change or not to change Nordic Studies in Mathematics Education, 12(2), 57-76. Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning.(Author abstract). Educational Studies in Mathematics, 46(1 3), 13. Snell, J. (2011). Interrogating video data: systematic quantitative analysis versus micro‐ethnographic analysis. International Journal of Social Research Methodology, 14(3), 253-258. doi:10.1080/13645579.2011.563624 Wagner, T. (2014). The global achievement gap : why even our best schools don't teach the new survival skills our children need--and what we can do about it. In Why even our best schools don't teach the new survival skills our children need- and what we can do about it. Walshaw, M., & Anthony, G. (2008). The Teacher's Role in Classroom Discourse: A Review of Recent Research into Mathematics Classrooms. Review of Educational Research, 78(3), 516-551. doi:10.3102/0034654308320292 Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or Focusing? In H. Steinbring, M. G. B. Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167-178). Reston, Virginia: National Council of Teachers of Mathematics. Yackel, E., & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.
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