Challenges and Pedagogical Approaches in Teaching Negative Numbers: A Study with Mathematics Graduates at UFRRJ
Negative Numbers. Undergraduate Mathematics. Number Line. Operations with Negative Numbers.
This dissertation aims to engage with mathematics undergraduates about the aspects and difficulties students face in understanding relative numbers. The research maps studies on the use of games and materials on the topic and is supported by research that discusses epistemological and historical aspects of the development of this class of numbers. It also designs and implements a group discussion environment in a Mathematics undergraduate course at the Federal Rural University of Rio de Janeiro. A questionnaire was administered to collect data, and after analyzing how students learned these numbers and what strategies they intend to use for teaching them, tasks on operations with whole numbers were developed and administered using the number line. Data collection will be conducted through field journals, written responses to activities, and audio recordings during sessions. In the task where they were asked to solve operations using a number line as a support, the undergraduate students demonstrated insecurity and resorted to the memorized rule, indicating the answer on the line, without being able to formulate a coherent or visual explanation. Although there was an attempt to use the line as a support, a deeper understanding of the underlying geometric or arithmetic model was still lacking, indicating the need for greater educational investment in the relationship between representation and concept. Analysis of the responses allowed us to identify the difficulties and strategies developed by the undergraduate students and to develop an educational product consisting of a task plan based on the activities.