Abstract:

Doing mathematics has a lot to do with solving problems. Yet, for many students, mathematics is a problem! Students struggle with an array of issues related to the activity of problem solving, from understanding the problem statement, to devising a plan to solve it, to carrying out that plan, and to evaluating the adequacy of the solution found. Though solving problems is a challenging activity for students, at all grade levels, there are other challenges in students’ learning paths. One of such challenges deals with the transition from arithmetic to algebra. In particular, the learning of algebraic topics such as linear equations poses students a large number of difficulties.

Being aware of those difficulties, we decided to challenge ourselves and investigate how the use of playful elements influences the learning of linear equations at 7th grade (pupils aged 12 years-old) - exactly when these two worlds collide in a significant manner: the arithmetic world and the algebraic world. Privileging problem solving activities and using games, humor, comics, applets, and other interactive elements, we designed a teaching experiment aimed at facilitating the transition from arithmetic to algebra, supporting students’ meaningful learning of linear equations.

Several research questions guided our study:
1) how do students solve tasks of different nature in playful contexts?
2) what are students’ main difficulties when solving diversified tasks in playful contexts and how do they overcome them?
3) how do students react to tasks in playful contexts? and
4) how does students’ work in diversified tasks in playful contexts contribute to a meaningful learning of linear equations?

We followed an exploratory approach to teaching and learning to conduct the teaching experiment with two classes of 7th graders (55 pupils) in a public school in northern Portugal. Twenty Due to the pandemic context, the intervention was carried out completely at distance, involving many moments of group work and collective discussions.

Data were collected using different sources and instruments. All lessons of the teaching experiment were audio-recorded using the affordances of the Teams platform, which the school chose to support the emergency remote learning approach adopted due to the pandemic constraints. We conducted task-based interviews, and collected selected students’ written productions on various types of tasks. Preliminary data analysis suggests that the approach taken in the teaching experiment was quite motivating to students, who eagerly engaged in all task proposals. Despite the limitations imposed by distance learning, this emergency response to a nationwide lockdown ended up offering new opportunities for students’ class work, such as group work. This form of organizing students’ mathematical activity was quite important in the development of the teaching experiment. Students reacted very positively to the playful contexts of the tasks, be they games, comics or humor situations.

Keywords:

Playful contexts, linear equations, teaching experiment, algebraic understanding, distance learning.