Students' Mathematization Process of the Concept of Slope within the Realistic Mathematics Education

Abstract

ABSTRACT:The aim of this study is to analyze eight grade students' mathematizing processes of the concept of slope in light of the teaching process designed based on Realistic Mathematics Education. Participants of this design based research study were chosen via purposeful sampling in accordance with results of an open-ended test intended for prerequisite information before design teaching-learning environment. Survey data was acquired from open-ended test, researcher log, individual and group study papers and clinical interviews. Contexts, which provide opportunities to reflect preliminary conceptions of slope to teaching process are revealed. Conceptualization process of slope as ratio started with the need to be base of informal linear constant. Then it develops with the need of measurement of slope. Students reinvent that the slope is also an algebraic ratio by reflecting geometric ratio representation to coordinate plane. Designed teaching in this study was revealed that mathematization is important in transition among representations. Development of right triangle model occurred in three phases: (i) a context-dependent interpretive tool, (ii) a physical tool used to calculate the slope, (iii) a cognitive tool that that is no longer needed to be represented physically. Keywords: Slope, Mathematization, Realistic Mathematics Education ÖZ: Bu çalışmada Gerçekçi Matematik Eğitimine dayalı olarak desenlenen öğretim sürecinde sekizinci sınıf öğrencilerinin eğim kavramını matematikleştirme süreçlerinin incelenmesi amaçlanmıştır. Desen tabanlı bu araştırmanın katılımcıları, ön koşul bilgilere yönelik olarak hazırlanan açık uçlu testin sonuçlarına göre amaçlı örneklem yolu ile seçilmiştir. Araştırmanın verileri, açık uçlu test, araştırmacı günlüğü, bireysel ve grup çalışma kâğıtları ile katılımcılarla öğretim boyunca birebir gerçekleştirilen üçer klinik görüşmeden elde edilmiştir. Eğimin başlangıç kavramsallaştırmalarının öğretim sürecine yansıtılmasına fırsat veren bağlamlar ortaya konmuştur. Eğimin bir oran olarak kavramsallaştırılması süreci informal olarak edinilen doğrusal sabitlik kavramsallaştırmasına dayanak yaratma gereksinimi ile başlamıştır. Ardından eğimi ölçme gereksinimi ile gelişim göstermiştir. Eğimin geometrik oran temsilinin koordinat düzleminde yansıtılması yoluyla aynı zamanda cebirsel bir oran oluşunun öğrenciler tarafından keşfedilmesi sağlanmıştır. Ortaya konan öğretim temsiller arası anlamlı geçişlerde matematikleştirmenin önemini ortaya koymuştur. Ayrıca öğrenciler tarafından geliştirilen dik üçgen modelinin gelişimi üç aşamada olmuştur: (i) duruma bağlı olarak yorumlamaya yarayan bir araç, (ii) eğimin hesaplanmasında kullanılan henüz fiziksel olarak ortaya konulma gereği duyulan bir araç (iii) fiziksel olarak ortaya konulma gereği duyulmayan bilişsel bir araç.

The Effectiveness of Applying Realistic Mathematics Education Approach in Teaching Statistics in Grade 7 to Students' Mathematical Skills

“…According to Freudenthal (1973) and Gravemeijer (1997), the RME theory has three core heuristics in teaching process design: didactic phenomenon guided reconstruction and self-development model (cited from Sumirattana, Makanong, and Thipkong (2017); Deniz and Kabael (2017); Wahyudi, Joharman, and Ngatman (2017); Uzel and Uyangor (2006); Gravemeijer and Doorman (1999); Yilmaz (2020)). The didactic phenomenon forms the foundation for designing the teaching process in which students explore mathematics by expressing the relationships between a concept and concepts, methods, and other knowledge (Deniz & Kabael, 2017). The second principle -guided reconstruction -reflects the teaching process that gives students the opportunity to self-explore concepts and performs mathematically from real-world problems.…”

“…Accordingly, math history can be seen as an inspiration to enable students to experience the same process as when that mathematical concept was conceived (Gravemeijer (1997); cited from Sumirattana et al (2017)). It is important to visualize a possible teaching process so that students can reconstruct concepts (Gravemeijer and Doorman (1999); cited from Deniz and Kabael (2017)). Besides, according to Andriani and Fauzan (2019), self-developed models play a crucial role in bridging the gap and creating a relationship between common knowledge and formal knowledge.…”

“…Besides, according to Andriani and Fauzan (2019), self-developed models play a crucial role in bridging the gap and creating a relationship between common knowledge and formal knowledge. Accordingly, students need to be facilitated to develop models themselves and use them in problem-solving (cited by Deniz and Kabael (2017)). Students' initial strategy is typically determined by chance and can be any strategy they wish they have learned before.…”

Implementation of technology enhanced activities for teaching slope in daily life situations

“…Moreover, there are few empirical studies reporting teachers' ways of teaching about slope in the middle school classroom setting (Lobato et al, 2003;Smith, Seshaiyer, Peixoto, Suh, Bagshaw, & Collins, 2013). In addition to this, in Turkey, some studies focused on students' individual conceptions of slope in a teaching experiment context (Deniz & Kabael, 2017a, 2017b. Different from those, how an instructional sequence about conceptualizing the slope of an object dynamically in a computer-assisted classroom environment should be structured and how it works is an emerging issue.…”

A Study of Geometry Concept Mathematization Process on Blind Student Visual Imagery

“…The constructed knowledge is synthetic a priori whose existence depends on experience. Therefore, the process of developing concepts and problem-solving in the learning of mathematics can attribute to a phenomenon once experienced by students or informal knowledge of previous students, known as mathematization [1]. According to [2], mathematization refers to various ways of organizing activities related to mathematical characteristics: generality, certainty, exactness, and brevity.…”