Humanities & Social Sciences Reviews
eISSN: 2395-6518, Vol 7, No 3, 2019, pp 432-437
https://doi.org/10.18510/hssr.2019.7363
432 |www.hssr.in © Hidayatullah
COMPARISON OF PROCESSES CONSTRUCT CONCEPT OF SOLO
THEORY AND APOS THEORY IN MATHEMATICS LEARNING
Achmad Hidayatullah
Faculty of Teacher Training and Education, Universitas Muhammadiyah Surabaya, Indonesia
achmadhidayatullah08@gmail.com
Article History: Received on 20
th
February 2019, Revised on 24
th
April 2019, Published on 15
th
May 2019
Abstract
Purpose of Study: To provide a deep understanding of learning of mathematics, it is necessary to make efforts to realize
the conditions of students doing the construction of their understanding. There are many theories that describe thinking in
constructing concepts in mathematics. By constructing their understanding, the students can be called doing meaningful
learning as mentioned by Ausubel.
Methodology: This research used the comparative process of construct understanding of mathematics with SOLO and
APOS theory. SOLO theory (Structure of the Observed Learning Outcome) has five parts namely pre-structural, uni-
structural, multi-structural, relational, and extended abstract. While the theory of APOS (Action, Process, object, and
Schema). The method used in this research is the study literature from various sources.
Results: This research found the differences construct of the concept in mathematics by using both theories.
Implications/Applications: The SOLO Taxonomic Theory and APOS Theory about its use in constructing
mathematical concepts. This means to achieve an individual process needs to do the action repeatedly.
Keywords: Mathematics Construction Concept, SOLO Theory, APOS Theory
INTRODUCTION
The mathematics lesson is very complex because of the various branches such as Logic, Arithmetic, Algebra, Geometry,
Analysis, Numbers, Statistics, Opportunities, etc. When learning Logic, Geometry, and Algebra, students should
understand and master them more easily than to study other branches of mathematics because they have been known and
used in everyday life. However, the students’ practices in those fields still show that the students have difficulty in
understanding. It has become common knowledge that mathematics is regarded as a difficult, uninteresting and
frightening lesson.
So far there are two theories that are often used in learning. Both are behaviorism theories and constructivism, which are
the two poles crossing. Behaviorism provides an understanding that students need external responses to build their
knowledge, behaviorism that change due to stimulus and response relationships, they have no inherent ardor.While
constructivism spirit builds awareness and construction knowledge from within oneself. Because during this time the
spirit of building students' mathematical knowledge is more developed using behaviorism approach, they must be forced
to learn, and more difficult to understand the concept of mathematics. Although the theory of constructivism has long
been present, its application in mathematics is still taboo used.
Tall develops the theory of mathematical thinking to be grouped into three, namely (a) a world of being that begins with
interaction with real-world objects and develops based on sensual experiences through verbal descriptions and
definitions; (b) the symbolic world that evolves from action (such as counting) to symbolic calculations and
manipulations that function in dual terms as processes and concepts (prosep), and (c) the formal world based on the
axioms to build systems, based on the definitions to create new concepts, and based on formal evidence to construct
coherent theory.
According to Meyer (2005) , thinking includes three main components: (1) thinking is a cognitive activity, (2) thinking is
a process involving some knowledge manipulation in the cognitive system, and (3) thinking directed to produce problem-
solving action. Meanwhile, according to Sukowiyono(2013) said that in the process of thinking people arrange the
relationship between the knowledge that has been recorded then it is considered as the meaning used to solve the
problems faced.
The students will experience meaningful learning if they construct their own knowledge. Its opinion comes from
constructivism theory initiated by Vygotsky. The constructivism theory provides the view that the students are able to
build their own concept and understanding. "( Septiati, 2012) Through this approach, the students become more active,