Abstract
The present document is composed of two distinct parts. The first part consists of the report carried out in the context of supervised pedagogical practice of a 11th year mathematics class. This report includes the characterization of the school environment where the traineeship took place, the description of the activities that the teacher trainee has developed or participated throughout the year, followed by a critical reflection on the pedagogical practices experienced.
The second part presents the research work carried out with a 11th year mathematics class, aiming to understand how students perceive the concept of sequence convergence. This study was guided by the following questions:
• What kind of image concepts the students build from the theoretical sequence concept and convergent sequence concept?
• What is the contribution of the distinct representations for the understanding of sequence limit concept?
• What is the relation students can establish between the formal concept definition of sequence convergence and a more intuitive approach of the same concept?
• What are the difficulties showed by the students concerning the understanding of sequence convergence concept?
To perform the study a qualitative methodology was chosen, using the case study approach. For the data collection, the adopted methodology was semistructured interviews, document analysis and observation. A literature review allowed to establish, based on cognitive theories, a categorization system for the levels of understanding found in students.
From the collected data analysis, it was verified that the students distribute by 3 categories, assigned based on the concept image levels found: incipient concept image, instrumental concept image and relational concept image. In the first case the students, have a very rudimentary understanding of the concept, based more on definitions memorization of and process mechanization. In the second category students dominate the concept from an operational point of view but fail to establish the relationships between the various elements that make up concept or to switch between different representations. Finally, we have students showing reification of the concept, presenting a perfect understanding of the concept from distinct approaches and representations.
Concerning the representation conversion and the understanding of sequence convergence concept evidenced by the students, it was concluded that 2 of 6 participants in the study were completely at ease with the conversion of representations and showed a great understanding of the concept; one student also showed great understanding but did not have the capacity to communicate it; another student was unable to alternate between representations, showing the fragility of her understanding; the remaining two students showed a very poor understanding of the concept and an inability to alternate between representations.
Concerning the difficulties evidenced by students related to the understanding of sequence convergence concept, in first place is that they cannot convert the formal definition symbolic language to another representation more familiar to them, and not being able to cope with converging sequences are not monotonous in the strict sense.
The second part presents the research work carried out with a 11th year mathematics class, aiming to understand how students perceive the concept of sequence convergence. This study was guided by the following questions:
• What kind of image concepts the students build from the theoretical sequence concept and convergent sequence concept?
• What is the contribution of the distinct representations for the understanding of sequence limit concept?
• What is the relation students can establish between the formal concept definition of sequence convergence and a more intuitive approach of the same concept?
• What are the difficulties showed by the students concerning the understanding of sequence convergence concept?
To perform the study a qualitative methodology was chosen, using the case study approach. For the data collection, the adopted methodology was semistructured interviews, document analysis and observation. A literature review allowed to establish, based on cognitive theories, a categorization system for the levels of understanding found in students.
From the collected data analysis, it was verified that the students distribute by 3 categories, assigned based on the concept image levels found: incipient concept image, instrumental concept image and relational concept image. In the first case the students, have a very rudimentary understanding of the concept, based more on definitions memorization of and process mechanization. In the second category students dominate the concept from an operational point of view but fail to establish the relationships between the various elements that make up concept or to switch between different representations. Finally, we have students showing reification of the concept, presenting a perfect understanding of the concept from distinct approaches and representations.
Concerning the representation conversion and the understanding of sequence convergence concept evidenced by the students, it was concluded that 2 of 6 participants in the study were completely at ease with the conversion of representations and showed a great understanding of the concept; one student also showed great understanding but did not have the capacity to communicate it; another student was unable to alternate between representations, showing the fragility of her understanding; the remaining two students showed a very poor understanding of the concept and an inability to alternate between representations.
Concerning the difficulties evidenced by students related to the understanding of sequence convergence concept, in first place is that they cannot convert the formal definition symbolic language to another representation more familiar to them, and not being able to cope with converging sequences are not monotonous in the strict sense.
Original language  Portuguese 

Awarding Institution 

Place of Publication  Caparica 
Publisher  
Publication status  Published  2018 