Abstract |
This literature review entitled "The impact of Realistic Mathematics Education (RME) in
mathematics teaching. A critical approach." answers the following research questions: 1) What are
the key points of RME theory for mathematics teaching and curriculum? and 2) What does RME
offer to mathematics teaching and student learning? Regarding the first research question, RME
theory is defined by Freudenthal's ideas that mathematics teaching is based on context problems
that relate to students' reality and require mathematization when solving them. Mathematization
argues that mathematics education should have as its starting point mathematics as an activity,
rather than mathematics as a ready-made system (Freudenthal, 1971, 1973b, 1991).
Mathematization is divided into horizontal and vertical, according to Treffers (1987), where
horizontal involves the transformation of a realistic problem into a mathematical one through
symbolism, while vertical involves the extension of the individual's mathematical situation
(Freudenthal, 1991). Once the process of mathematization has taken place, a key process of RME is
the guided reinvention by the students themselves, which means instead of being recipients of
ready-made mathematics, students should actively participate in the educational process by
developing mathematical tools and knowledge on their own (Van den Heuvel-Panhuizen &
Drijvers, 2020). Furthermore, RME emphasizes the idea of "mathematics for all", whereby the
mathematics used by the majority of students will be for solving problems in everyday situation,
since not everyone is intended to become a mathematician (Gravemeijer & Terwel, 2000).
Regarding theory in curriculum, according to Freudenthal, it is not a predetermined set of theories,
objectives, means, contents and methods and its development requires the cooperation of students
and teachers in a school environment (Freudenthal, 1973a). According to Treffers (1993, p. 103) "in
the late 1980s the development of textbooks, assessments and curriculum is well adapted to the
national final standards and the (informal) national curriculum (De Jong, 1986) in the Netherlands.
In many other countries (Ernest, 1991) any such coordination is lacking and as a result textbooks,
national curriculum and assessments explicitly lack the views of progressive teachers." Regarding
the second research question, it seems that teaching mathematics through RME has many benefits
in terms of students' understanding. Student activities in RME are mostly interactive and designed
to cultivate students' interest in studying mathematics (Fauzan, Slettenhaar & Plomp, 2002). In
addition, RME can increase students' logical, critical and creative thinking (Ruseffendi, 1990;
Saefudin, 2012; Sembiring, Hadi, & Dolk, 2008; Usdiyana, Purniati, Yulianti, & Harningsih, 2013).
It helps to construct students' knowledge at each stage of creative thinking. Based on the literature,
the creative thinking process is actually more oriented and focused on individuals' cognitive and intellectual functions, particularly creative problem solving (Almeida, Prieto, Ferrando, Oliveira, &
Ferrandiz, 2008; Isaksen & Treffinger, 2004). Finally, hypothetical learning trajectories are believed
to be a unique and essential contribution to the field as they involve simultaneous consideration of
mathematical goals, children's thinking patterns, teachers' and researchers' thinking patterns,
sequences of instructional activities, and the interaction of these at a detailed level (Clements &
Sarama, 2004).
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