Use of Mathematical Problems Rooted in Primary Historical Sources to Reveal Preservice Teachers’ Mathematical Content Knowladge

 

"Use of mathematical problems rooted in primary historical sources to reveal preservice teachers’ mathematical content knowledge", specifically in evaluating their understanding of fundamental concepts such as area and volume. The study was conducted at Aristotle University of Thessaloniki, Greece, where the history of mathematics has been integrated into the curriculum for prospective teachers as a diagnostic tool to understand and correct potential conceptual errors among students.

The research focuses on two main tasks assigned to students, which are derived from historical sources of mathematics. The first task involves calculating the area of a quadrilateral engraved on the wall of the Temple of Horus in Edfu, Egypt. This problem was designed to explore students' understanding of the concept of area, particularly how they apply basic formulas to calculate area in unusual situations. The second task relates to the Delian problem, a well-known problem in the history of ancient mathematics. This problem asks students to double the volume of a cube, requiring a deep understanding of the concept of volume and the relationship between geometric dimensions.

The results of this study show that using mathematical problems from history can reveal various levels of understanding among prospective teachers. Most students were able to correctly identify and apply formulas in standard situations, but when faced with more complex or unusual contexts, some students demonstrated incomplete or incorrect understanding. For example, in the first task, some students used the length-times-width formula without considering the actual geometric shape, indicating a tendency to overgeneralize. In the second task, some students confused the concept of volume with surface area, showing that they had not fully grasped these concepts deeply.

This study highlights the importance of the history of mathematics in education, not only as a motivational and cognitive tool but also as an effective diagnostic tool. Through the history of mathematics, educators can identify misconceptions or errors that might not be apparent in traditional teaching. Therefore, the history of mathematics can help educators design more appropriate interventions to improve students' understanding.

Additionally, the article discusses three main categories of using the history of mathematics in education: (1) as a motivational tool to make learning more engaging and relevant, (2) as a cognitive tool to help students understand complex mathematical concepts, and (3) as an evolutionary tool to help students understand how mathematical concepts have developed over time. In this context, the article emphasizes the importance of using history as a diagnostic tool that allows educators to identify conceptual errors and misconceptions in students.

Furthermore, the article refers to previous research by Jankvist and Kjeldsen (2011), which discusses how the history of mathematics can be used to support the learning process by helping students overcome epistemological obstacles. This study expands on that concept by showing how the history of mathematics can be used to evaluate students' understanding and provide more specific and beneficial feedback.

As part of this study, the authors also examine the impact of using the history of mathematics on the pedagogical beliefs of prospective teachers. The findings indicate that when prospective teachers engage with mathematical problems derived from history, they tend to develop a more critical understanding of the concepts they teach. This helps them become more reflective and aware of the importance of teaching these concepts deeply and not merely relying on mechanical procedures.

The study concludes with a discussion on the implications of these findings for teacher education and the mathematics curriculum. The article suggests that teacher education should integrate more history of mathematics into the curriculum to help prospective teachers develop a better understanding of mathematics and how to teach it. It also recommends that the history of mathematics be used as a broader diagnostic tool to assess students' understanding at all educational levels.

Overall, this article provides deep insights into the role of the history of mathematics in education, particularly in the context of teaching prospective teachers. It demonstrates that the history of mathematics can be a very useful tool not only for teaching difficult mathematical concepts but also for assessing and improving students' understanding more effectively. Thus, this article offers an important contribution to the literature on mathematics education and provides practical guidance for educators seeking to enhance their teaching quality through the integration of the history of mathematics.

(Oleh: Aulia Nurul Farikha)