Learning from and Adapting the Theory of Realistic Mathematics education

Abstract

This article focuses on the critical role of design theory in our work as mathematics educators. We give particular attention to a specific design theory, Realistic Mathematics Education (RME). We first clarify the enduring contributions of RME to design in mathematics education and then discuss three adaptations that we made to RME theory while conducting a series of classroom design experiments. The first of these adaptations involves taking a broader perspective on the means of supporting students' mathematical learning to include both the organization of classroom activities and the nature of classroom discourse. The second adaptation involves a change in orientation that acknowledges the mediating role of the teacher. The goal of instructional design then becomes to develop resources that teachers can use to achieve their instructional agendas rather than to support students' learning directly. The third adaptation again centers on the teacher and concerns the potential contribution of designed instructional resources as a means of supporting teachers' as well as students' learning.

8th Grade Student’s Skill of Connecting Mathematics to Real Life

“…The materials that the students will mathematise must be real for them (Cobb, Zhao, & Visnovska, 2008). These real situations may be contextual problems or authentic contexts (Barnes, 2004).…”

Exploring Realistic Mathematics Education in a Flipped Classroom Context at the Tertiary Level

“…RME is particularly associated with instructional design, in which the mathematical tasks students engage with should guide learners from informal to formal mathematical knowledge. Cobb, Zhao, and Visnovska (2008) mention three central tenets of the design theory in RME. The first tenet is that an instructional sequence or a task design should be experimentally real for the students, so that they can engage immediately in personally meaningful mathematical activity.…”

The embodiment of cases as alternative perspective in a mathematics hypermedia learning environment

“…The National Council of Teachers of Mathematics (NCTM 2014) and Common Core State Standards for Mathematics (National Governors Association Center 2010) advocate for more complexivist approaches to mathematics education. Cobb et al (2008) and others (Figueiredo et al 2009;Gravemeijer and Cobb 2006) continue to advocate for teaching practices that encourage students to mathematize-that is, to take their informal understandings of math and make them more formal. Rather than facts, procedures, and concepts comprising the learning environment as the normative routine, math educators stress the developing of a ''mathematical point of view'' through activities such as investigating patterns and relationships, finding and solving problems, reasoning flexibly (articulated as ''conjecturing, generalizing, justifying, and communicating one's mathematical ideas'') (Henningsen and Stein 1997, p. 525; see also Schoenfeld 1992Schoenfeld , 1994.…”