Reciprocal teaching and peer discussion in mathematics: a proposal for lower secondary education

To address the challenge of teaching mathematics in lower secondary school, we decided to develop a teaching proposal inspired by the BEST (Best Evidence Science Teaching) project, created by the University of York for science education. The BEST project is a collection of resources designed to help teachers test and reinforce students' understanding of key scientific concepts. Each resource is designed to promote dialogic teaching and reciprocal learning, following recommendations from educational research. To begin, we focused on a single topic—areas and perimeters of polygons—identifying three key aspects: height, polygon area, and variations in areas and perimeters. For each aspect, we developed a roadmap highlighting the learning objective and the necessary steps for students' conceptual progression. Each step is structured through one or more worksheets, which include a section for students and one for teachers. The student worksheets serve as prompts for reflection: they generally contain short, targeted questions focused on a single idea and are quick to complete. They can be used individually with pen and paper, in small groups, or projected to the entire class on an interactive whiteboard (IWB), with responses shared through hand-raising or a voting system. What matters most is the sharing of results, and the attention teachers give to students’ answers and reasoning, encouraging discussion and metacognition. The teacher notes provide guidance on how to conduct the lesson and interpret students' responses, as well as references to educational research on the key concept being addressed. A trial of these worksheets was conducted in five classes at the IC “F.lli Trillini” in Osimo (AN), and the results were generally encouraging.