Numerous curricula aim to develop students’ mathematical reasoning, which is an essential aspect of their education. Students can develop reasoning skills through various tasks that go beyond the formal curriculum (McFeetors & Palfy, 2018). However, appropriate tasks are essential to support students’ mathematical reasoning in the classroom (Brodie, 2010; Jeannotte & Kieran, 2017). Mathematical reasoning can be developed and elicited through meaningful and challenging learning experiences (Stein et al., 1996). Moreover, it has been suggested that tasks should encourage students to make conjectures and generalisations, search for similarities and differences between objects, and use their prior knowledge and other generalisations with which they are already familiar (Jeannotte & Kieran, 2017). Games play an essential role in these educational tasks because they provide students with an appropriate environment for presenting and defending their arguments (Mousoulides & Sriraman, 2014). Furthermore, strategic games have a large number of potential strategies that include a number of different components. Therefore, while playing these games, students use various reasoning skills without realising it (McFeetors & Palfy, 2018).

The role of mathematical games in the teaching and learning of mathematics has been recognised for decades (Dienes, 1963; Brousseau & Gibel, 2005). According to Ernest (1986), games have the potential to positively influence the development of students’ conceptual reasoning, higher-order thinking, and motivation to learn mathematics. Moreover, carefully designed mathematical games can help students develop problem-solving skills (Pintér, 2010) and effectively apply the critical actions of mathematical reasoning (McFeetors & Palfy, 2018). Although reasoning is a significant component of student achievement in mathematics, few studies have reported how students demonstrate reasoning skills while playing games. Our research aims to examine the reasoning process of fifth-grade students while they play a strategy game.

The ability to reason is essential to understanding mathematics (The Programme for International Student Assessment [PISA], 2022). Lithner (2000, p. 166) defines reasoning as a way of thinking that is adopted to make claims and reach conclusions. It is critical for educators to develop students' reasoning skills to prepare them for more advanced learning (Vale et al., 2017). Many elements of reasoning are closely related to elementary school mathematics, such as forming hypotheses, sampling, comparing, recognising patterns, justifying, and generalising (Lampert, 2001). According to reSolve: Assessing Mathematical Reasoning (Australian Academy of Science [AAS] and Australian Association of Mathematics Teachers [AAMT], 2017) these actions of reasoning can be classified into three main categories: analysing, verifying, and generalising.

This paper focuses on the actions students display during the process of analysis, including the first steps of mathematical reasoning. We expect this study to provide new insights into the different types of reasoning students use when playing strategic games and the function of these games in early grades.

This research was designed to investigate mathematical reasoning as a process that can emerge from playing appropriate games rather than as a directly taught skill (Jeannotte & Kieran, 2017). We conducted the study with 5th graders (ages 10–11) and evaluated student responses based on analysing which is highlighted in the literature relating to mathematical reasoning as a first process. Mathematical reasoning framework developed by reSolve: assessing reasoning (AAS & AAMT, 2017) was utilized in this study. This framework was utilized because it provides insight into different types of reasoning processes and is a comprehensive guide to their function in early years classrooms. Mathematical games without a chance factor allow students to develop strategies and thus can be an effective tool for the reasoning process. The Chomp game is a type of nim game, and it was chosen to provide students with an opportunity to use reasoning skills. During the game, two players take turns removing different rectangular areas from a particular rectangular area (e.g. 3x3, 4x5), and the person who gets the last piece loses. Nim games require only a limited background in mathematics, so they can be practised by individuals of all ages. They pose a series of problems that allow the students to demonstrate their reasoning abilities. Furthermore, winning depends on the development of strategies because there are no chance factors in these games. The students were asked questions about their strategies during the game, and their reasoning skills were assessed based on their answers. Both written and verbal data were collected while playing the games in pairs. Data analysis was conducted by using a coding tool based on reSolve: assessing reasoning (AAS & AAMT, 2017) reasoning framework. In this study, only the act of analysing was addressed, and this process was evaluated within the scope of three basic understandings: 1) Exploring the problem and connecting it with known facts and properties, 2) Comparing and contrasting cases, and 3) Sorting and categorizing cases (AAS & AAMT, 2017). Based on these understandings, indicators and examples were created, and student actions were analysed with the coding tool.

As a result of the research, it was observed that students initially made random movements while becoming familiar with the game. With time, students began to observe their own movements and those of their opponents in order to make more informed decisions. Throughout the game, students had to use a variety of reasoning processes since there was no chance factor involved. It is common for these activities to begin with the discovery of patterns and the prediction of future events, which involve the analysis process. The findings indicate that students performed different types of analysis while playing games. The following quotes from students’ arguments exemplify the analysing process of reasoning: S1 – 'The most difficult of the three games was 4x5. 3x3 and 4x4 were similar. One was different because they were both squares. The other was different because it was not a square’. (Distinguishing/comparing similarities and differences) S2 – ‘If I begin the game first and consistently get two squares, I will win 95% of the games’. (Create claims from data/experiences) On the other hand, it was observed that as they played the game, they were able to present deeper mathematical arguments and support them systematically. Additionally, researchers encouraged students by asking prompt questions that acted as catalysts for them to articulate their reasoning in this process. The preliminary findings indicate that mathematical games presented in a supportive environment allow students to experience a variety of reasoning processes, including analysis. Moreover, our findings support the idea that all students can provide informal justifications and that strategically designed games assist pupils’ progress in reasoning (McFeetors & Palfy, 2018).

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