Abstract:
In the construction of knowledge and the reconstruction of mathematical concepts, 'examples' play a fundamental role. Good instructional examples, like a clear display, are tools for establishing communication between learners, teachers, and concepts. In this research, the perception and understanding of mathematics teachers regarding examples and how they employ them in the process of teaching a mathematical concept are investigated. The research method used in this study is a qualitative survey method. The statistical population of the research includes all secondary school mathematics teachers in Markazi Province in the academic year 2010-2011. The sample size was 75 people, selected using the simple random sampling method. The results of the research showed that teachers are aware of the necessity of using examples, but they do not have sufficient knowledge of instructional examples, and their example space is not sufficiently developed. Most teachers consider an example to be a useful and necessary tool or a common and understandable language for the learner, but at the same time, they do not consider topics such as theorems and problems, definitions, and proofs and reasoning as examples. Teachers referred to characteristics such as clarity and simplicity, mathematical correctness, learner ability, and the evaluability of an example, but a significant portion of them neglected important characteristics such as generalizability, accessibility, richness, and the strength of a mathematical example. Additionally, most participating teachers in the research use examples only in some parts of the mathematics teaching process, such as conceptualization or teaching procedures.
Machine summary:
edu** Research Expert in Educational Studies, Ministry of Education *** Master's student in Mathematics Education, Shahid Rajaee Teacher Training University common language and understandable for learners, but at the same time, they do not consider topics such as propositions and problems, definitions, and proofs and reasoning as examples.
The role of examples in mathematics education Researchers (Wiener22 1991, Zaslavsky 1995, Watson and Mason 2005, Zodick and Zaslavsky 2008) claim that in the process of concept formation, intuitive understanding often develops first, and then the learner moves toward structural understanding.
From the perspective of Goldenberg and Mason (2008), well-structured examples are those that satisfy the constraints and conditions of the concept and possess beauty and nuances, ease of understanding and expression, applicability in various contexts, continuity of reinforcement, appropriate and rich use of mathematical knowledge, issues, and techniques, represent the compositional structures of the example space, and have diverse representations (previously algebraic, geometric, and analogical) and similar characteristics.
Teachers and educators use examples to achieve understanding in concept construction or teaching procedures, based on subject matter and lesson objectives; however, the method of selecting and using examples as a specific teaching skill requires specialized mathematical knowledge.
An important point that can be derived from the data in Table 5 is that a small number of teachers have referred to the use of examples in evaluation, creativity, establishing connections, definition, research fields, and understanding mathematical structures.
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