Från de komplexa talens rötter till klassrummet

Abstract

This research overview examines what research says about upper secondary school students' difficulties with complex numbers. The three main areas covered are general difficulties with complex numbers, how to teach the subject, and whether the history of complex numbers can be beneficial in this teaching. A historical deep dive into the history of complex numbers is also included to further investigate this idea. The results show that upper secondary school students struggle with complex numbers in various ways. The name of the subject creates a negative connotation, as it is initially perceived by students as fictional and complicated. Furthermore, a consequence of the inherently abstract nature of complex numbers is that gaining a comprehensive understanding of them is challenging. Students have difficulty switching between different representations of complex numbers and visualizing them. Students also struggle to understand that complex numbers are an extension of real numbers. Also, the results highlight several approaches to working with complex numbers to address these difficulties. Introducing complex numbers through problem-solving, for instance, to demonstrate their usefulness, is an alternative to the more traditional approach that often leads to misconceptions about complex numbers. Furthermore, practicing transitioning between different representations proved to be important. Similarly, the visualization of complex numbers using dynamic digital tools like GeoGebra was also emphasized. Potential benefits of integrating the history of mathematics into teaching were explored, with the argument that historical contexts can provide students with a more comprehensive understanding of complex numbers and their relevance. The results indicated that there are various ways to incorporate the history of mathematics in teaching, and there are potential benefits to doing so, but further research is needed.