It is contended that constructing a mathematical proof is one of the prominent learning objectives in many countries, as it is a fundamental activity and a key component in mathematics education and curriculum. Furthermore, understanding or constructing proof is an important component of mathematical competence. Thus, it is substantial for students to build their understanding of related concepts to read mathematical problems and construct a mathematical proof. In addition, it is compulsory for teachers to comprehensively understand mathematics and its flexibility in order to support students who learn meaningful mathematics. Teachers without depth understanding will face problems in teaching mathematics effectively.
However, students/prospective teachers face difficulties to understand, validate and construct a mathematical proof. Research findings show that there are several sources of the students' difficulties in doing proofs, namely (1) understanding and stating definitions, axioms, and theorems, (2) constructing and validating proofs, (3) lack of concept images (conceptual image), (4) obtaining structure of proofs, (5) understanding and using mathematical language and notation, (6)circular reasoning. In addition, mathematical proof construction has been a timeless university mathematics subject and serves as a research focus in mathematics education. A considerable amount of research on the subject has been done, not only focusing on mathematical proof construction, but also on the ability to understand validate proof. Nevertheless, there is a relatively small number of research studies on classroom-based interventions to address important issues of the teaching and learning of proof.
There are some significant findings regarding contributing factors on construction competence, especially constructing the geometric proof. Research conducted by Miyazaki et al. claims that explicit teaching of the structure of proofs enhances the quality of the teaching and learning of the proofs. Another research indicates that Flow-chart proof as scaffolding enhances student to understand the structure of the proof. Then, The use of a Digital Geometry System function as semiotic mediation to evoke and understand the geometric terms, geometric definitions, postulates, and theorems (elements of proofs).
The purpose of the present research is to contribute to an empirically grounded a local instructional theory for mathematics education, particularly mathematical proof competence. Such a model should pattern in learning as well as the means which support the understanding of geometry proof. Consequently, the development of an instruction theory incorporates the design of such instructional means and research of how these means foster students’ geometry proof understanding. We limit the topic to Euclidean geometry proof, a topic presented in the first year of university level in a State University of Malang in Indonesia to prospective mathematics teachers. The research questions which fits to the aim are:
How can prospective mathematics teacher students with little mathematical proof background develop geometry proof understanding?
How can the use of Flow-chart Proof and Digital Geometry System (DGS) scaffold students’ structural understanding of proof?
|Last modified:||24 January 2019 4.50 p.m.|