Using Area Method in Secondary School Geometry

Areas are actively used in the solution of many geometrical problems. In this work,smart and laconic solutions are found for various problems by means of the area method. The well-known trigonometric addition formula is also proved. In the area method, the given formulas are divided into the parts, whose areas are then calculated using problem data.

The influence of multimodal textualization in the conversion of semiotic representations in Italian primary school geometry textbooks

Starting from the corpus of the Swiss National Science Foundation (FNS) project Italmatica. Understanding Mathematics at school, between common language and specialized language (Italmatica. Comprendere la matematica a scuola, fra lingua comune e linguaggio specialistico), an analysis of some examples taken from geometry textbooks used in the Italian primary school is presented. The analysis is based on the application of two intertwined theoretical frameworks: Duval’s semio-cognitive approach, which addresses problems related to mathematics education, and a linguistic approach to multimodal discourse analysis inspired by Bateman. The analysis shows how certain semiotic resources used as rhetorical devices for paraphrastic reformulation (restatement) can support or hinder the semiotic conversion of representations associated with two different semiotic registers (figural and natural language) in print documents with a strong multimodality component.

Subject Matter Knowledge of Geometry Needed in Tasks of Teaching: Relationship to Prior Geometry Teaching Experience

This study proposes task of teaching as an organizer of dimensionality in teachers’ subject matter knowledge for teaching (SMK) and investigates it in the context of measuring SMK for teaching high school geometry (SMK-G). We hypothesize that teachers use different SMK-G in different aspects of their teaching work and that such differences can be scaled and associated with key elements of instruction. Analyses of 602 high school teachers’ responses to two sets of items designed to measure the SMK-G used in two particular tasks of teaching—understanding students’ work (USW) and choosing givens for a problem (CGP)—suggested the two scales of SMK-G to be distinguishable and differently related to experience in teaching high school geometry.