So we decided to call “straight line” (…): Mathematics students’ interaction and negotiation of meaning in constructing a model of elliptic geometry

Abstract

In this paper, we investigate university students' interaction in an attempt to construct a model of elliptic geometry. In order to study the several ways in which geometrical meaning is produced through context and practices, we introduce three different types of use of geometrical concepts, namely as (1) elements of representation of spatial experience, (2) objects of traditional school practice, and (3) constituents of an abstract mathematical theory. The analysis of students' dialog according to this framework reveals how students develop their ability to communicate mathematically and negotiate their meanings. Students with a different use of geometrical concepts were able to interact and understand their peers.

Gender Specific Study of Students' Spatial Inference in Solving Geometry Problem

“…What is meant by spatial reasoning is reasoning that involves objects with spatial components such as mental rotation, spatial orientation, and spatial visualization (Kaisari & Patronis, 2010;Mashami & Gunawan, 2018). Other experts state that spatial reasoning is an activity to perceive, store, create, and communicate objects in three-dimensional space to conclude from the information provided (Engle & Conant, 2002).…”

Small Groups: Student Productive Interactions in Learning Cooperative (Case Study of Mathematics Learning at Junior High School in Pakis, Malang)

“…In other words, learning must have interactions that occur in the classroom, the interaction occurs between the teacher and their students, or students with students. Research on interaction in learning has been studied by several researchers, such as Howe and Mercer (2007), who revealed that interaction with friends is helpful in stimulating learning in the classroom; and Kaisari and Patronis (2010) investigated student interactions to create elliptical geometry models based on (1) representation of experience, (2) concrete objects, and (3) mathematical geometry. Student interactions in the classroom need to be noted.…”

Εισαγωγή των μαθητών λυκείου στη δισδιάστατη γεωμετρία Minkowski μέσω διδακτικών σεναρίων και νοητικών πειραμάτων

“…(Klein 2004, p. 174, δηθή καο απφδνζε) Δθηφο απφ ηηο επηζηεκνινγηθέο δπζθνιίεο πνπ νθείινληαη ζηελ ηζηνξηθή εμέιημε ηεο Γεσκεηξίαο, 3 ε ίδηα ηεο ε δηδαζθαιία απνηξέπεη νπζηαζηηθά ηνπο καζεηέο απφ ην λα πξνβιεκαηηζηνχλ θαη λα έξζνπλ ζε γλσζηηθή ζχγθξνπζε (cognitive conflict), δεδνκέλνπ φηη θάζε άιιν παξά σο δηεξεπλεηηθφ πξφηππν (inquiry based) ιεηηνπξγεί. Δηδηθφηεξα αλαθεξφκαζηε εδψ ζηελ επηξξνή πνπ αζθεί ε ζρνιηθή Γεσκεηξία ζηε δηακφξθσζε ησλ αληηιήςεσλ ησλ καζεηψλ -θπξίσο ηνπ Λπθείνπ-γηα ηνλ ρψξν θαη ηα γεσκεηξηθά αμηψκαηα (Patronis 1994;Kaisari & Patronis 2010).…”

“…Με ηε βνήζεηα ηεο πηινηηθήο έξεπλαο ζα δηαπηζηψλακε ηνλ βαζκφ εκπινθήο, ην επίπεδν ησλ γλψζεσλ θαη ηα ελδηαθέξνληα ηνπ θάζε καζεηή, έηζη ψζηε λα κπνξέζνπκε λα δεκηνπξγήζνπκε κηα θαηά ην δπλαηφλ "αληηπξνζσπεπηηθή" νκάδα καζεηψλ, κε ελδηαθέξνλ γηα ην project, αθνχ έλαο απφ ηνπο δηδαθηηθνχο καο ζηφρνπο ήηαλ ε ζε βάζνο δηεξεχλεζε ησλ δπλαηνηήησλ ησλ καζεηψλ. Σαπηφρξνλα, βαζηζκέλνη ζηηο αληηδξάζεηο ησλ παηδηψλ, ζα είρακε ηελ επθαηξία λα ειέγμνπκε ην δηδαθηηθφ καο ζελάξην γηα ηπρφλ αζάθεηεο ή παξαιείςεηο.Ζ δηαδηθαζία ηεο πηινηηθήο έξεπλαο φζνλ αθνξά ηελ επηινγή ηεο ηειηθήο νκάδαο ησλ ζπκκεηερφλησλ ήηαλ παξφκνηα κε απηήλ ησλKaisari & Patronis (2010), ζηελ νπνία σζηφζν ε ηειηθή νκάδα επηιέρζεθε ζχκθσλα κε ηελ ηδηαίηεξε εκπινθή πνπ επέδεημε ν θάζε θνηηεηήο ζε έλα αθεγεκαηηθφ θείκελν. Γψζακε ζηνπο καζεηέο έλα θείκελν πέληε ζειίδσλ, ζπλνδεπφκελν απφ δχν πίλαθεο δεδνκέλσλ, θαη ηνπο δεηήζακε λα γξάςνπλ ζρφιηα θαη παξαηεξήζεηο επί ηνπ θεηκέλνπ απηνχ.…”