PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Root of misconceptions – the incorporation of mathematical ideas in history
Page: 620
The evolution of a mathematical concept in history has been the process of merging different ideas to form a more rich, general, and rigorous concept. Ironically, students, when learning such well-developed concepts, have similar difficulties and make the same misconceptions again and again. To illustrate, despite the well-developed and defined concept of real numbers, many students still have difficulties in comparing fractions or doing basic operations on irrational numbers. In this poster, the incorporation of different ideas to form a general and rigorous mathematical concept in history is examined. Students’ struggles and misconceptions in learning the concepts are investigated from the perspective of the incorporation process. Finally, a model for differentiating and validating the variations of a general mathematical concept is suggested for resolving learning difficulties and misconceptions.