Abstract
This chapter presents a game-based learning didactic proposal to promote the development of students' mathematical processes of reasoning, problem solving, and communication in their first years at high school. The sessions combine individual free competition and collaborative work through a series of activities based on the use of six logic and visual reasoning games (Rummikub, Mastermind, Swish, Pentomino, Quadrillion, and Cortex). Learning outcomes are assessed by means of a model that incorporates gamification elements. A critical analysis of a first implementation of the didactic proposal with 135 students of Grades 7 and 8 (12-14 years old) is provided. The relevance and usefulness of the didactic material designed as well as the successful impact of the implementation of the didactic proposal on the development of students' mathematical processes are also discussed.
TopIntroduction And Theoretical Framework
During the last decades, most of the educational policies at European and international level have been oriented towards models based on the development of competencies. This approach, which seeks to “transfer, articulate and combine learning about on knowledge, know-how and know-how to be in order to solve complex functional situations” (Álvarez et al., 2008, p. 20) has led in the Spanish context to a series of curricular regulations. However, the lack of continuity of such regulations, together with the results obtained in different comparative diagnostic tests of mathematical competence, indicate that the design and implementation of competence-based teaching practices is still a challenge for Spanish mathematics teaching at all educational levels (some recent examples of such results can be found in Organisation for Economic Co-operation and Development, 2021 and International Association for the Evaluation of Educational Achievement, 2021). The case of the high school is especially significant, since the curricular contents of this educational level have traditionally been oriented to very academic mathematics, focused on procedures very close to the contents, which are rarely applied to non-mathematical contexts and leave aside competence aspects such as reasoning or problem solving. In this regard, the effort made by the most recent curricula to include a content unit on “mathematical processes, methods and attitudes” (e. g. Ministry of Education, Culture and Sports of Spain, 2015) has not materialised in consolidated effective teaching practices. This may be related to the acquired inertia of focusing learning on content commented above, or to the insufficient training received by teachers on competence-based mathematics education (López et al., 2020).
Key Terms in this Chapter
Game-Based Learning: Teaching strategy based on posing a suitable set of challenges to foster students' engagement in solving them according to certain rules, with the aim of promoting their learning. The design of such challenges appropriately balances the acquisition of learning outcomes and the motivation of students to play while finding a solution.
SWOT Analysis: Analysis strategy to evaluate the effectiveness of initiatives (business, projects, teaching proposals) in relation to the context where they are implemented. It is based on the identification of Strengths and Weaknesses, which are specific to the initiative, and Opportunities and Threats, which are specific to the context.
Problem Solving: Mathematical skill that enable students to address non-straightforward questions. Under the NCTM (2000) approach, this implies applying and adapting a variety of appropriate strategies to answer such questions, constructing new mathematical knowledge through these answers, and monitoring and reflecting on the processes developed.
Communication: Mathematical skill that enable students to express their mathematical thinking. Under the NCTM (2000) approach, this implies organising and consolidating such mathematical thinking and analysing and assessing the mathematical thinking and strategies of others.
Mathematical Competence: Set of skills that enable citizens to effectively apply useful mathematics in a variety of contexts.
Reasoning: Mathematical skill that enable students to use mathematics to draw logical conclusions from certain information. Under the NCTM (2000) approach, this implies make and investigate mathematical conjectures, develop and evaluate mathematical arguments and proofs, select and use various types of reasoning and methods of proof and recognise reasoning and proof as fundamental aspects of mathematics.
Gamification: Teaching strategy based on introducing well-defined rules and competition to motivate students to engage in tasks they otherwise would not address. This does not imply that such tasks are games in themselves.