Abstract
Early algebra proposes to incorporate algebra in primary school from the first years of schooling. The success of this incorporation depends, to a large extent, on the training of teachers, so the objective of this article is to study whether the degree of algebraic knowledge of student teachers at the beginning of their training. To conduct this, 106 preservice teachers were given a questionnaire. This survey is based on two daily life situations. They had to propose tasks to develop algebraic reasoning in primary school students. Most of the participants designed tasks in which they assigned specific values to the indeterminate ones and solved them arithmetically. In this way, they transformed open situations and numerous opportunities to promote algebraic thinking in students through the generalization and representation of relationships and functions into closed single-solution problems that do not promote algebraic thinking. We can see from the results that the participants’ algebraic knowledge is insufficient. Therefore, it is necessary to include in their training process the programs and experiences that will allow them to design tasks in order to detect and promote algebraic thinking in their future students. Sequences of tasks are presented to develop both situations by generalizing and representing relationships and functions, which can serve as a starting point for future training programs and experiences.
Highlights
The learning of algebra causes in many students, especially in Secondary Education, difficulties that frequently provoke a rejection towards the totality of mathematics [1,2]
In recent decades, researchers in mathematics didactics were against this assessment; for example, Socas [6] considers algebraic thinking to be implicit in Primary school students, and Mason [7] considers that students come to the educational system with natural generalization abilities that allow them to develop algebraic thinking
As a starting point to begin training programs and experiences that promote the ability to find opportunities that highlight the algebraic nature of mathematics, in this paper, we study the algebraic knowledge of student teachers who have not yet started their algebraic training
Summary
The learning of algebra causes in many students, especially in Secondary Education, difficulties that frequently provoke a rejection towards the totality of mathematics [1,2] In this line, decades ago, Kieran [3] already warned that “algebraic thinking is an area very much needed in mathematical research” For Piaget [5], the students’ cognitive development occurs in stages, and the stage of development for formal or abstract thinking begins around the age of 11 and is consolidated around the age of 15 In this way, it was considered that Primary school students were not yet ready to move from concrete operational thinking to formal or abstract thinking; for this reason, traditionally, the curricula explicitly postponed the study of algebra until the first years of Secondary Education. Other researchers believe that primary school students are able to consider arithmetic operations as functions [8], algebraically symbolize arithmetic relationships [9], work with functional relationships [10] or solve problems using graphs and tables [11]
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