With the influence of the concept images shaped by prototypical and intuitive examples and linguistic factors, some students either focused on non-critical attributes of the concepts as the critical ones or omitted critical attributes of the concepts. The results indicated that middle school students identify parallel/perpendicular line segments by using three types of reasoning: visual reasoning, attribute reasoning, and language-based reasoning. One-to-one interviews were also conducted with fifteen students to support students’ written reasons. Data were collected from 83 middle school students through an identification task consisting of various examples and non-examples of the parallelism and perpendicularity of two line segments. This study investigates middle school students’ reasoning about parallelism and perpendicularity of two line segments. The MDWI approach eliminated the misconceptions in generalization, errors in concept images, and incompetence in linking geometry features. Misconceptions are one of the biggest obstacles in learning mathematics. After the exposure to the articles, the teachers exhibited a greater focus on the specific difficulties inherent in the specific task at hand and their subsequent interpretations of those difficulties and responses to those difficulties were also more specific than they had been before the intervention. Our work with an open-ended questionnaire and mixed-methods analysis revealed that exposing in-service teachers to theoretical and empirical articles may affect the three components of their professional noticing performance: attending, interpreting, and responding. The research tools used in the study included a lesson taken from the VIDEO-LM project and articles that were all presented to the teachers. Forty-one in-service Mathematics teachers participated in this study.
The aim of the current study was to investigate whether exposing teachers to theoretical and empirical background information regarding pedagogical aspects of geometrical thinking would affect their noticing abilities. Infine, si discuteranno le implicazioni teoriche e didattiche dello studio. L’analisi del discorso, accompagnata dalla costruzione e confronto tra l’albero di realizzazione atteso e l’albero della classe, consentiranno di mettere in luce sia la ricchezza del discorso di classe sia le interazioni tra realizzazioni diverse. Obiettivo principale di questo studio è documentare quali tra queste realizzazioni del significante altezza compaiono nel discorso di classe, descriverne le caratteristiche e osservare quali continuità o discontinuità presentano rispetto alle realizzazioni più comuni descritte dalla letteratura in didattica della matematica. La lezione si è svolta dopo un percorso didattico durante il quale il discorso sull’oggetto matematico altezza si è costruito a partire da diverse realizzazioni possibili. L’articolo presenta l’analisi del discorso matematico degli studenti di una classe II di scuola secondaria di primo grado, intrapreso durante una lezione sul riconoscimento di altezze di un triangolo.
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