The History of Mathematics: From Ancient Times to Modern Era
In a conventional classroom Introduction into a mathematical concept begins with reflection of prior knowledge of the concept. In this history of mathematics essay I will be examining the development of math. Origins and roots pertaining to a concept can rarely be found in a lesson development. Introducing the factors or circumstance as to why a theorem was created will contribute to the cognitive assimilation of the concept being taught. In this essay I will unpack the effects of adding the history of mathematics into mathematical teaching and learning and investigate its impacts on learners ability to develop an understanding to mathematical concepts.
According to Youchu understanding the history of mathematics is beneficial to not only learners but to educators as well, it is explained that once and educator understands the history of math he or she may be able to appreciate the creativity behind mathematics and not just its product. This then serves as a tool to understand the curriculum better and thereafter adjust his or her teaching approch. In a study done Youchu it was observed that once pre-service teachers completed a course on the history of mathematics they began to incorporate their new experiences into their teaching program. An example of this adjustment is When educators were proving the irrationality of √2, prior to the completion of the course, teachers would use a calculator to show that √(2 ) is neither a terminating or recurring decimal and give notes and thereafter examples to supplement their lesson, however they began to modify their methods of teaching, post teaching course, by increasing their explanation and development time and decreasing their exercise time, proof by contradiction as well as storytelling was also integrated into their lessons. This then inspired creativity amongst learners and teachers.
Oral story telling is an ancient practice that was used by society to pass on their culture from one generation to another. Storytelling as a teaching technique can be used to introduce the history of mathematics according to Lemonidis and Kaiafa storytelling is beneficial to learners because it keeps learners engaged, motivated, provides an alternate context to understand mathematics as well as promotes a problem-solving atmosphere in a mathematical atmosphere.
In an investigation done by Xenofontos and Papadopoulos which critiqued textbooks which included the history of mathematics in Greece and Cyprous, used a picture of an Egyptians which had inscribing of hieroglyphics, were presented to learners, two questions were posed to grade 7 learners, write down the number he has inscribed and write your date of birth using hieroglyphic symbols. This activity is one of the many approach’s educators can use to incorporate the history of mathematics in a classroom, this activity was used as foundation exercise to develop the number system concept. These activities will allow learners to develop mathematics in relation to the world and see it used in real life context rather than mathematics being developed in isolation. Another example used in the study is the story of Achilles and the Tortoise. This exercise used story telling to teach learners the concept of ratio, considering that the tortoise could never catch up to Achilles because for every two steps the tortoise took Achilles took seven. Another example refers to an ancient Greek mathematician Diophantus which uses a picture of his tomb which encourages learners to calculate the age of death thus integrating equations into the history of math.
The nature of mathematics stem from the work of Plato and Aristotle. These two views of mathematics stand at two opposite poles in a spectrum when it comes to mathematics and its relation to the world. Schoenfeld says that the belief of mathematics teacher is a determining factor of the nature of the learning environment created in the classroom, this then in turn is a factor that influence the student’s beliefs of the nature of mathematics. This means the way in which a teacher views the nature of mathematics will ultimately determine from which stand point they will deliver mathematical knowledge to their learners. In this essay I will critically evaluate the link between a teacher’s beliefs about mathematics and the way in which they approach teaching and learning.
In conclusion, the nature of mathematics can be seen as stemming from the work of Plato and his Student Aristotle. A Platonian view sees the existence of mathematics in a dimension of its own, beyond the mind in an external world. This means that mathematics is seen as set of unrelated axioms and formula waiting to be discovered by mathematicians. In contrast to the platonic view is the Aristotelian view of mathematics were by mathematics is as a result of accumulated experiences, experimentation and observation of objects in relation to each other. These two contrasting views have over the years manifested itself to many other mathematical views of mathematics such as formalism originating from the beliefs of Plato and constructivism which takes into consideration the findings of Aristotle.
