Geometry in early years: sowing seeds for a mathematical definition of squares and rectangles

Abstract

In early years schooling it is becoming common to propose activities that involve moving along paths, or programming robots to do so. In order to promote continuity towards the introduction of geometry in primary school, we developed a long-term teaching experiment (with 15 sessions) carried out over 4 months in a first grade classroom in northern Italy. Students were asked to program a robot to move along paths, to pretend to act as robots and to represent the sequence of commands and the resulting paths. In particular, in this teaching experiment, an overarching mathematical aim was to sow the seeds for a mathematical definition of rectangles that includes squares.\ud Within the paradigm of semiotic mediation, we intended to foster the students’ transition from a dynamic perception of paths to seeing paths also as static wholes, boundaries of figures with sets of geometric characteristics. The students’ situated productions were collected and analysed together with the specific actions of the adults involved, aimed at fostering processes of semiotic mediation. In this paper we analyse the development of the situated texts produced by the students in relation to the pivot signs that were the beginnings of an inclusive definition of rectangles

Kâğit Katlamanin Semi̇yoti̇k Arabuluculuk Teori̇si̇ Açisindan İncelenmesi̇

“…Ancak gerçekleştirilen bu çalışma sonucunda, terim olarak bildikleri bu dörtgenlerin özelliklerini derinlemesine düşünebilmiş ve kâğıt katlama ile de düşüncelerinin doğruluğunu test ederek zihinlerinde yapılandırma imkânı bulmuşlardır. Şimdiye kadar gerçekleştirilen çalışmalarda, didaktik döngüye tartışma ile başlayıp etkinlikle bitirilmesine rastlanmamış ve genellikle öğrenciler tarafından öncelikle artifakta bağlı işaretler üretilmiştir (Bussi ve Baccaglini-Frank, 2015;Faggiano, Montone ve Mariotti, 2016;Faggiano, Montone ve Rossi, 2017;Maschietto, 2015;Mariotti, 2009;Montone, Faggiano ve Mariotti, 2017). Mevcut çalışmada beklenenin tersi bir durum ortaya çıkması, aslında SAT'ın sadece matematiksel kavramları oluşturma değil, bilinen kavramların özellikleri üzerine derin düşünme imkânı sunabilecek bir teori de olabileceği fikrini akla getirmektedir.…”

Recent research on geometry education: an ICME-13 survey team report

“…The simultaneous presence of the body experience, the perception of sounds and path, the production of gestures and other signs is also at the foreground of another teaching experiment on the approach to inclusive definition of squares and rectangles (Bartolini Bussi & Baccaglini-Frank 2015) by means of programming a small robot (bee-bot) (see Fig. 2a).…”

“…Specifically it is reported that Japanese learners' path might be square/ rhombus, rectangle/parallelogram and finally square/rectangle. Another different technological approach towards an inclusive definition of squares/rectangles was explored with young children by using a programmable robot with LOGO-type instructions (Bartolini Bussi & Baccaglini-Frank 2015). Gal and Lew (2008) introduced Korean ninth-grade low achievers to parallelograms via dynamic and continuous shape changes using parallelograms made of strips and hinges.…”

Geometry Education, Including the Use of New Technologies: A Survey of Recent Research

“…Theories being applied to geometry education include prototype phenomenon (Gal & Linchevski, 2010), semiotic mediation (Bartolini Bussi & Baccaglini-Frank, 2015;Bartolini Bussi & Mariotti, 2008), variation (Gu, Huang, & Marton 2004;Huang & Li, 2016), the cK¢ (conception, knowing, concept) model (Balacheff, 2013), discursive, embodied, ecocultural and material perspectives (Ng & Sinclair, 2015a, b;Owens, 2014Owens, , 2015 and instrumental genesis (evident in research on the use of digital technologies) (Hegedus & Moreno-Armella, 2010). These theoretical approaches illustrate the wide scope of geometry education research.…”

“…Bartolini Bussi & Baccaglini-Frank, 2015;Bartolini Bussi & Mariotti, 2008;Ng & Sinclair, 2015a, b). Here we consider historical-cultural perspectives that underscore the role of semiotic processes and artefacts in geometry teaching and learning.…”