A Game-based Approach to Improving the Learning of Arithmetic

学习算术需要同时发展流利性和理解力[1]。然而，强调流畅性的课程可能会以牺牲其他学习活动为代价优先考虑算法练习，并且可能会很无聊，因此会让孩子们感到不快[2]。此外，如果练习没有经过精心设计，那么流利性可能会以理解为代价，导致顽固的误解[3]，以及不易转移到其他上下文的高度定位的知识[4]。许多电脑游戏旨在帮助儿童学习算术运算，但往往优先考虑通过算法练习而不是理解来提高流畅性，例如[5]。相比之下，App Stick and Split（SaS）是开创性的，因为它体现了从属关系，这是第一位主管开发的一种学习方法，利用了我们有动力完成任务时需要获得新技能的概念[6]。这种方法涉及目标学习服从于学习者容易理解的任务目标。SaS体现了从属性，因为与许多教育游戏不同，数学是主要游戏的一个侧面[5，7]，算术练习推动游戏的进步。重要的是，SaS允许学习者犯错误，并立即看到游戏进展方面的后果。因此，它可能为持续练习提供动力，从而发展流利性，并提供固有的有意义的反馈，从而发展理解。RQ 1.当孩子们与SaS互动时，算术是如何练习和学习的？RQ 2.在SaS中学习的算术如何转移到更传统的符号环境中？RQ 3.什么原则可以给予游戏，涉及从属的学习，以及如何将这些应用到新的数学领域？为了解决RQ 1，将使用两种方法。首先，孩子们将被观察到使用SaS来理解算术是如何练习的。第二，向日葵将提供数十万个互动日志，这些日志可以跟踪数千名儿童随时间的进展。交互日志的纵向分析将有助于理解游戏关卡的进展与算术学习的关系。为了解决RQ 2，将再次使用两种方法。首先，标准化的算术测试（如WIAT-II）将被用于样本的SaS用户，以确定学习转移到传统的符号环境。第二，根据这些研究结果，将对SaS进行优化，以优化学习迁移，并通过进一步的标准化测试来测试这些优化。为了解决RQ 3，将使用RQ 1和RQ 2的研究结果的一般原则。通过向日葵学习，将这些原则应用于一个新的数学领域，开发一个新的应用程序。参考文献[1] Rittle-Johnson et al.（2015）.不是单行道：数学的过程性知识和概念性知识之间的双向关系。教育心理学评论，27，587-597。[2]Foster（2018）.发展数学流利性：比较练习和丰富的任务。数学教育研究，97，121-141。[3]McNeil（2008年）。教孩子2 + 2 = 4的局限性：典型的算术问题会阻碍数学等价的学习。儿童发展，79，1524-1537。[4]Chesney & McNeil（2014）.运算思维在算术练习中的激活阻碍了学习和迁移。问题解决杂志，7，24-35。[5]Jay et al.（2019）.以游戏为基础的培训，以促进算术流畅性。《教育前沿》，4，118。[6]休伊特（1996年）。数学流利性：实践的本质和从属性的作用。对于数学的学习，16，28-35。[7]Lowrie & Jorgensen（2015）.数字游戏和学习：新的已经是旧的了？在数字游戏和数学学习（pp。第1-9段）。斯普林格

Learning arithmetic requires developing both fluency and understanding in tandem [1]. However, a curricular emphasis on fluency risks prioritising algorithmic practice at the expense of other learning activities and can be boring and therefore off-putting to children [2]. Moreover, if practice is not carefully designed then fluency can come at the cost of understanding, resulting in stubborn misconceptions [3], and highly situated knowledge that does not transfer readily to other contexts [4]. Many computer games purport to help children learn arithmetic operations, but tend to prioritise fluency through algorithmic practice over understanding, e.g. [5]. In contrast, the App Stick and Split (SaS) is ground-breaking because it embodies subordination, a learning approach developed by the first supervisor that harnesses the notion new skills are acquired when necessary for tasks that we are motivated to complete [6]. The approach involves target learning being subordinated to task goals that learners can readily understand. SaS embodies subordination because, unlike many educational games where mathematics is an aside to the main game play [5,7], arithmetic practice drives game progress. Importantly, SaS allows learners to make mistakes and immediately see the consequences in terms of game progress. As such, it potentially provides motivation for sustained practice, thereby developing fluency, with inherently meaningful feedback, thereby developing understanding. RQ1. How is arithmetic practised and learned when children interact with SaS?RQ2. How does the arithmetic learned within SaS transfer to more traditional symbolic contexts?RQ3. What principles can be given to games which involve subordination of learning and how can these be applied to new areas of mathematics?To address RQ1, two methods will be used. First, children will be observed using SaS to understand how arithmetic is practised. Second, Sunflower will provide hundreds of thousands of interaction logs that track the progress of thousands of children over time. Longitudinal analyses of interaction logs will help understand how progressing through game levels relates to arithmetic learning.To address RQ2, there will again be two methods used. First, standardised arithmetic tests (e.g. WIAT-II) will be used to samples of SaS users to identify learning transfer to traditional symbolic contexts. Second, drawing on these findings, refinements to SaS will be made to optimise learning transfer, and test these refinements through further standardised testing.To address RQ3, general principles from the findings to RQ1 and RQ2 will be used. With Sunflower Learning, application of those principles will be applied to a novel mathematical area to develop a new App. Evaluation of the new App's initial success will be made. References[1] Rittle-Johnson et al. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27, 587-597.[2] Foster (2018). Developing mathematical fluency: Comparing exercises and rich tasks. Educational Studies in Mathematics, 97, 121-141. [3] McNeil (2008). Limitations to teaching children 2 + 2 = 4: Typical arithmetic problems can hinder learning of mathematical equivalence. Child Development, 79, 1524-1537.[4] Chesney & McNeil (2014). Activation of operational thinking during arithmetic practice hinders learning and transfer. The Journal of Problem Solving, 7, 24-35. [5] Jay et al. (2019). Game-based training to promote arithmetic fluency. Frontiers in Education, 4, 118. [6] Hewitt (1996). Mathematical fluency: the nature of practice and the role of subordination. For the Learning of Mathematics, 16, 28-35.[7] Lowrie & Jorgensen (2015). Digital games and learning: what's new is already old? In Digital Games and Mathematics Learning (pp. 1-9). Springer.