Abstract:

The aim of the study was to know the level of development of algebraic thinking in Higher Education students. During the investigation, we wanted to measure the success rate in the size of the next generalization and the dimension of distant generalization and measure the degree of difficulty in the various proposed patterns. We developed this research with 15 students from a teacher training course. In the pedagogical context of the formation of future primary teachers and childhood educators, an activity was promoted in the context of mathematical recreation. In order to know the level of students' algebraic thinking, 4 tasks with pictorial growth patterns were proposed. Vale and Pimentel (2011) consider the tasks presented in figurative contexts are a good starting point for algebraic thinking based on the generalization of patterns and allow the construction of various mathematical knowledge such as mental calculation, operations properties and relations, counting, writing of numerical expressions and equivalence of various expressions The tasks were presented through kahoot, an applet that allows, according to Wang (2015) and Guimarães (2015), to increase motivation, to improve concentration, to promote reasoning, to allow collaborative work, to reverse roles between student and teacher, use ICT in the classroom and evaluate in real time. In each task we proposed 2 questions that involved near generalization (5th term and 15th term) and 2 distant generalization questions (50th term and 100th term). In methodological terms the teacher projected each pattern and its questions on the projection screen so that all students could visualize and each student responded individually using their mobile phone, tablet, or laptop computer. For each question, the students had a resolution time of 2 minutes. In none of the questions the student's resolutions have been exhausted. The results allowed to verify that of the 16 questions proposed, there was a percentage of correctness in the 71,62% (average of the questions). Regarding the near generalization, we obtained a percentage of success in the order of 78,23%. On the other hand, in relation to the distant generalization, we obtained a percentage of success in the order of 69.35%. We also verified that the students obtained greater ease in the growth sequence, whose general term is defined by 2n with a success rate of 94.45%. Regarding the sequence defined by the general term 4n + 1, we obtained a success rate of 78.57%. The results also allowed us to verify that the sequence, whose general term is defined by an = n^2, was that the students had more difficulties, with a success rate of 61.52%. Finally, the results of the last proposed sequence defined by n^2 + 1, showed a success rate of 80.36%.

References:
[1] A. Wang, “The wear out effect of a game-based student response system,” Computers in Education, nº 82, pp. 217-227, 2015.
[2] D. Guimarães, “Kahoot: quizzes, debates e sondagens,” em Apps para dispositivos móveis: manual para professores, formadores e bibliotecários, Lisboa, ME, 2015, pp. 203-224.
[3] I. Vale e T. Pimentel, Padrões em Matemática: Uma proposta didática no âmbito do novo programa para o Ensino Básico, Lisboa: Texto Editores, 2011.

Keywords:

Algebraic Thinking, Applet, generalization, ICT, Growth Patterns.