(1798) DEVELOPMENT OF ALGEBRAIC THINKING WITH MATH MAGIC PROBLEMS

摘要

In this day and age, it is widely believed that mathematics is undoubtedly a challenging and uninteresting subject for a large number of pupils, which interferes with their school performance, affecting their ability to solve problems. With riddles, puzzles and mathematical curiosities, the teacher establishes a new methodology for teaching mathematics, which could be included in the math magic topic. Math magic is a playful resource that stimulates the students' motivation by developing their algebraic thinking. Due to the fact that algebra is the mathematics field that studies quantity as a general concept, using it to represent symbols, letters, or expressions, one of its main goals is the development of algebraic thinking which includes the ability to manipulate symbols, to understand patterns and to represent and understand quantitative relationships. It goes without saying that having good didactic resources is not enough to obtain positive results, it is useful to know how to use them in a classroom to explore mathematical contents and to frame them in a sequence of previously planned tasks, allowing exploration, experimentation, manipulation and the development of observation. However, to implement these tasks in the classroom, it is important that teachers have well-developed algebraic knowledge. In this sense, a study was carried out with 52 pre-service teachers, in order to answer the following research question: "Do pre-service teachers have well-defined algebraic knowledge to solve tasks related to math magic in classroom?" This study aimed to identify if the preservice teachers can use algebraic concepts in an activity in order to solve it correctly. A quantitative methodology was used to study the participants’ answers to two math magic tasks: (a) Think of a number and (b) Symbolic Challenge. Those answers were subjected to content analysis and data processing with IBM-SPSS software. We conclude that these pre-service teachers have shown reduced knowledge regarding essential algebraic concepts for the teaching of mathematics in the first years. Moreover, they present some difficulties in justifying the procedures that they used to solve the proposed tasks. In light of the above it is urgent to introduce more algebraic content in initial teacher training courses, since it will be more difficult to develop algebraic thinking in students if future teachers, faced with a task, cannot think algebraically. What is intended is not to teach in primary school pure algebra, but rather that future teachers could solve a task using algebraic concepts to more easily explain it to their pupils, tackling the difficulties of their students to learn mathematics in the first years.