Abstract:

Students should be provided with learning opportunities to develop their mathematical communication skills. These involve the ability to express ideas, to interpret and understand the ideas of others, and to constructively participate in discussions about mathematical ideas, processes, and procedures. In this study, we focused on the written dimension of mathematical communication.

Students also need to be given opportunities for formative assessment, which allow them to identify what they already know and understand, and realize what they do not know yet or have trouble with, so that they can improve their learning. Engaging in peer feedback allows students to regulate their own learning by commenting on each other’s work and giving suggestions for improvement. This is particularly effective when problem-solving activities are at stake. When solving problems, students have to describe their reasoning and explain their options in ways that are understandable to others, thus exercising their written mathematical communication skills. Peer assessment activities based on problem solving tasks contribute to promote such skills.

The aim of this study is to analyze the role of peer feedback in promoting the development of students' written mathematical communication skills. Three research questions guided this research:
1) what are students’ main difficulties in communicating, in written form, their reasoning while solving problems?
2) how do students engage in the process of peer assessment? and
3) how do the students’ written mathematical communication skills evolve and what is the role of peer assessment practices in that evolution?

The participants were the 23 students of a class of 11th graders (pupils aged 16 years-old), in a public school in northern Portugal. Our teaching intervention lasted for about six weeks, and involved three cycles of peer assessment activities. In each cycle, students were invited to solve a problem individually. Each written solution was then randomly exchanged among the students. Based on a set of criteria, previously explained and negotiated with the students, they commented their peers’ work in the problem at hand. Each student received feedback from one or two peers and had the opportunity to improve his solution based on those comments and suggestions. The whole intervention was carried out at distance, using Teams, due to the restrictions imposed by the pandemics.

Data include students’ first and second written productions (on each problem), the comments given to their peers, students’ answers to a short questionnaire to assess their reactions to the experience of peer feedback, and the audio-recorded semi-structured interviews with a selected number of students. Preliminary results show that students directed their comments more frequently to the request for justifications, but they also asked their peers to more clearly convey their reasoning or problem-solving strategy used. In most cases, they did not directly correct the mistakes they found in their peers’ problem solutions, but rather alerted their peers to the need of reviewing their work and identify those mistakes. The adequacy of the feedback provided was not related to the correctness or completeness of the written production. In fact, there were students whose first written productions were weak (whether in mathematical terms or concerning communication quality) and who provided very complete and appropriate feedback to their peers.

Keywords:

Peer assessment, problem solving, written mathematical communication, distance learning.