Strukturer och värderingar av bevis

Abstract

The main purpose of this study was to investigate the structure of Swedish students’ mathematical argumentation and what values teacher show when ranking student solutions. This qualitative study used a clinical, task-based interview (N = 4). With the aid of Toulmin’s model the study observed that students verbal and written argumentative structure can differ on one major point: students can consistently omit written motivations that lack an effective symbolic language. In other words, students verbal argumentation may contain a motivation for every single step while the written variant exclude a specific type of warrant. Furthermore, the study also determines what type of warrants find convincing. Other parts of Toulmins model are discussed as well. A second part of the study gathered data from teachers (N=48) using a questionnaire to capture if teachers omit similar reasonings from their own solutions when they present solutions to the classroom. Student solutions from the first phase was presented to the teachers who then ranked them and reflected on their evaluation. A hypothetical model was created from the data do describe how the values of a teacher can alter their rankings of a student solution. The significance of the study is primarily as a generative study, creating testable hypotheses, models, and statements. Further inquiry is required in determining the portion of students who perform better verbally, as well as if the classroom environment can be modified to alter students’ presentations. Mainly, would a strict protocol of always including warrants in teachers’ written presentations affect the students’ written solutions? Furthermore, additional research would be needed in determining what kind of argumentation is deemed acceptable in the Swedish Upper Secondary School.