This case study takes its focus on upper secondary school students’ work in small groups with a problem related to the derivative. The analysis aims to identify factors that promote or hinder an individual’s participation in and development of the mathematical communication in the classroom. The theoretical basis of the study is Anna Sfard’s commognitive framework, where learning mathematics is seen as participating in a mathematical discourse.
For more than a decade, reports about Swedish students’ decreasing levels of school mathematical knowledge have been put forward. Research points to various factors behind this development. The prevailing educational culture, where students largely work individually from the textbook, is seen as one explanation for the deterioration in the results, and that teaching does not give students the opportunity to develop all the required competencies in the curriculum. To achieve this, both research and the new Swedish curriculum from 2011 emphasize the importance of student communication in mathematics. In this perspective, there is a need to highlight the differences in student participation in the communication of mathematics in the classroom, particularly in the context of small group learning, and how this is assumed to influence students’ opportunities for learning.
The focus of the research is directed towards the participants’ contributions to the group’s mathematical discourse, i.e. when they communicate about mathematical objects or processes, and how these affect students’ opportunities and participation in the communication. Focus is also directed to the communication that involves participants in the group, what the students are doing and how they evaluate each other’s way to participate in the mathematical discourse in the classroom. This type of communication is in the framework referred to as subjectifying, and is assumed to affect the individual’s mathematical learning.
Data collection methods used are interviews, audio and video recordings, as well as “smart pens” to combine verbal and written communication. In the first step of the analysis, the mathematical discourse was studied regarding differences in the content of the participants’ utterances. The second step of analysis focused on the interaction flow of the group to understand more of the differences in each student’s participation and contribution to the communication.
The results point to big differences regarding participation and content in student communication, both at group level and individual level. The development of students’ mathematical discourse benefits from the use of multiple mediators to represent the mathematical objects. When connections to a previously acquired discourse are offered, this leads to discursive advancements. Students were observed to have difficulties to interpret and use the formal mathematical symbolic language that would support their mathematizing. Students’ interpretation of the equality sign, the sign for inequality, and the symbol f´(x) on a process level, create obstacles to developing the mathematical discourse in the desired direction. The discourse about the participants and their own traits (identification) constitutes about 10% of all utterances and are almost all negative reviews, frequently used in order to exclude or incorporate themselves or others from participating in the mathematizing activity.
This research study points to a need for more knowledge about how mathematics teachers can best organize work in small groups to increase student engagement and the quality of their mathematizing. The study also indicates the importance of mathematics teachers highlighting and varying the use of different mediators to represent the mathematical objects to learn. The case study also highlights the importance of building up a permissive environment in which students do not evaluate themselves and others, but instead dare to ask questions that will make them increasingly involved in the mathematical discourse. A need emerges for further research not only on the assessment between teacher and student, but also on the assessment that goes on in the classroom between the students, which can affect what roles they take or are assigned to in the classroom. This can be assumed to be of great importance to the way students communicate about mathematics with other students in the classroom, which is also likely to influence learning.