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. In the context of the training of future primary teachers and childhood educators, an activity was developed in the context of the curricular unit of mathematical recreation with 15 students. The theme of algebraic thinking assumes current relevance because according to Vale and Pimentel (2011) it has become a cross-cutting theme of the curriculum. In order to know the level of algebraic thinking, 4 tasks with repetition patterns were proposed from elements of the manipulable material: pattern blocks. 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. Repeat patterns were proposed from the simplest to the most complex (ABAB, ABBABB, ABCABC, ABCCABCC). For this proposal, we have considered Vitz and Todd (Threlfall, 1999), who present a model of repetition pattern classification. In each task we proposed 2 questions that involved near generalization (10th term and 15th term) and 2 distant generalization questions (35th 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 90 seconds. 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 71,67% (average of the questions). Regarding the near generalization, we obtained a percentage of success in the order of 70%. On the other hand, in relation to the distant generalization, we obtained a percentage of success in the order of 73,33%. We also observed that students showed greater ease in the ABBABB pattern, with a success rate of 80% and greater difficulty in ABAB with a success rate of 56.67%. Regarding the ABCABC standard, we obtained a success rate of 75% and a success rate for the ABCCABCC standard.

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] I. Vale e T. Pimentel, Padrões em Matemática: Uma proposta didática no âmbito do novo programa para o Ensino Básico, Lisboa: Texto Editores, 2011.
[3] J. Threlfall, “Repeating Patterns in the Early Primary Years,” em Pattern in the Teaching and Learning of Mathematics, A. Orton, Ed., London, Cassel, 1999, pp. 18-30.
[4] D. Guimarães, “Kahoot: quizzes, debates e sonsagens,” in Apps para dispositivos móveis: manual para professores, formadores e bibliotecários, Lisboa, ME, 2015, pp. 203-224.

Keywords:

Algebraic Thinking, Kahoot, generalization, ICT, Repeating patterns.