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本研究以幼兒階段數感與基本算術能力的發展為目標，設計以心理數線為理論背景的數位數線遊戲，探究心理數線遊戲對幼兒數感與基本算術能力的學習成效，並進行心理數線遊戲及非心理數線遊戲的成效差異比較。本研究採前、後測實驗研究設計，實際研究參與對象為臺灣東部地區的幼兒共105位，將研究對象分為三組（心理數線遊戲組、非心理數線遊戲組與控制組）。結果顯示，以心理數線概念所建構的數位數線遊戲，在數感能力的提升上確實能獲得顯著的學習成效，且傳統的非心理數線概念所設計的數字概念學習遊戲亦同樣能提升幼兒的數感能力。然而，在基本算術能力（加減法）的學習成效上，心理數線遊戲的學習成果明顯比非數線遊戲來得好。研究結果建議，幼教相關教學人員在建構幼兒的數感能力與基礎算術能力時，使用心理數線遊戲是一個很好的教學工具選項。 Background and Purpose The main purpose of teaching number sense to young children is to establish a core knowledge framework for number concepts, thereby enabling young children to understand a wide range of number problems and providing a basis for children to learn more complex number concepts in the future. Number sense is also fundamental for learning formal mathematics later in life. Studies have associated a lack of number sense in early childhood with a subsequent decline and difficulty in mathematical learning. Therefore, cultivating number sense in early childhood is essential for future mathematics achievement. The development of young children’s numerical cognition and mathematical skills is closely linked to the establishment of a mental number line. Additionally, studies have discovered a strong correlation between an individual’s innate perception of the mental number line and their proficiency in a range of mathematical abilities, including understanding number concepts, estimating quantities, and performing arithmetic. With the goal of developing young children’s number sense and basic arithmetic skills, this study designed a set of targeted intervention tools in the form of digital number line games. These tools were designed to help young children develop an understanding of mental number lines, thereby improving their number sense and basic arithmetic skills. This study also compared the improvement effects of the number line game and a non-number line game on the aforementioned learning objectives to determine which game was more effective at improving the relevant learning outcomes. Literature Review The meaning of number sense Number sense can be described as an individual’s ability to understand, relate, and connect numbers. Children with number sense can understand the relevant concepts and principles of numbers. Number sense includes several mathematical aspects, such as the ability for estimating small quantities, counting and cardinality, comparing numbers, recognizing number patterns, and transforming numbers. The concept of number sense in early childhood refers not to a single mathematical ability but rather encompasses a set of essential cognitive components that aid in comprehending numbers and abstract numerical symbols. These components include a conceptual understanding and the ability to perform practical numerical operations. Development of a mental number line and the relationship between a mental number line and number sense in children The ability to place numbers on a mental number line is associated with the development of number sense, which is the ability to understand, relate, and connect numbers. Relevant studies have suggested that an individual’s perception of the mental number line influences their development of several number sense components (e.g., estimating, counting, and transforming numbers). Therefore, as soon as young children are capable of counting, connecting, and estimating the size of numbers and have learnt the numeral system and the spatial arrangement of numbers, they may acquire the ability to perceive a mental number line. Through educational activities, children can learn how to spatially arrange numbers (i.e., visualize a mental number line) and effectively develop a complete understanding of advance number concepts, including number transformation. Relationship between the construction of a mental number line and basic arithmetic The construction of a mental number line involves spatially arranging numbers by size in the mind. Numbers are arranged in a continuous, quantity-based analogical format in ascending order (from left to right). When constructing a mental number line, basic arithmetic is performed. For example, the number after 6 is 7. To arrive at 7, addition arithmetic (6 + 1) must be performed. Therefore, the construction of a mental number line plays an important role in the development of basic arithmetic skills. Methods This study employed an experimental research design. A total of 105 preschool children from rural areas in eastern Taiwan were enrolled into this study. Participants were randomly divided into three groups: two experimental groups and a control group. A pretest-posttest analysis was performed to explore the influence of number line games on number sense and basic arithmetic skills. One-way analysis of covariance was performed to determine whether significant differences were present between the pretest and posttest results and between the three groups to eliminate the influence of confounding variables. Results Results for the number sense Covariate analysis revealed significant differences in posttest scores between the three groups (F(2,101) = 64.47, p < .05, eta squared η 2 = .56). Furthermore, the improvement in number sense in the two experimental groups was significant. Both interventions (a number line game and a non-number line game) significantly improved the number sense to a similar extent. Results for basic arithmetic skills Significant differences were observed in the improvement of addition and subtraction skills between the two experimental groups and the control group. Basic arithmetic skills were better in the two experimental groups than in the control group. Additionally, the group that played the number line game performed significantly better than the group that played the non-number line game. Conclusion This research is one of the few studies that has explored the development of number sense among young children by using a number line game. The findings indicate that the number line game, which was designed in accordance with the mental number line concept, can effectively enhance number sense among young children. However, in terms of improving number sense, similar learning outcomes can also be achieved by using non-number line games. In terms of improving basic arithmetic skills (addition and subtraction), the number line game was more effective than the non-number line game (traditional number decomposition and synthesis game). Furthermore, the non-number line game was more effective than the intervention in the control group. Overall, the digital game intervention aimed at improving mathematical learning among young children (whether it involves a number line game or a traditional non-number line game) had a positive effect on improving numerical ability, including number sense and basic arithmetic. The number line game was more effective than the non-number line game and the intervention in the control group. These findings are expected to advance the theoretical literature of mathematics education in early childhood and the teaching practices of mathematics for young children.

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