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。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，这可能会很无聊，因此会让孩子们感到不快。此外，如果练习不是精心设计的，那么流利就会以理解为代价，导致顽固的误解，以及高度定位的知识不容易转移到其他环境中。许多电脑游戏声称是为了帮助孩子们学习算术运算，但往往优先考虑通过算法练习的流畅性，而不是理解，例如b[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，这是一种由第一位主管开发的学习方法，它利用了新技能在必要时获得的概念，我们被激励去完成任务。这种方法将目标学习从属于学习者容易理解的任务目标。sa体现了从属关系，因为与许多将数学作为主要游戏玩法的次要内容的教育游戏不同[5,7]，算术练习推动着游戏进程。重要的是，sa允许学习者犯错误并立即看到游戏进程的后果。因此，它潜在地提供了持续练习的动力，从而发展流利，具有内在的有意义的反馈，从而发展理解。RQ1。当儿童与sa互动时，他们是如何练习和学习算术的？在sa中学习的算术如何转移到更传统的符号环境中？什么原则可以赋予涉及学习从属性的游戏？这些原则如何应用于新的数学领域？要处理RQ1，将使用两种方法。首先，孩子们将使用情景模拟来了解如何练习算术。其次，葵花将提供数十万个互动日志，跟踪数千名儿童的进展情况。对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之间的关系。要处理RQ2，将再次使用两种方法。首先，标准化算术测试（例如WIAT-II）将用于sa用户样本，以确定向传统符号上下文的学习迁移。其次，根据这些发现，将对情景情景进行改进，以优化学习迁移，并通过进一步的标准化测试来测试这些改进。为了解决RQ3，将使用从研究结果到RQ1和RQ2的一般原则。通过葵花学习，将这些原理应用于一个新的数学领域，开发一个新的应用程序。将对新应用程序的初步成功进行评估。参考文献[1]little - johnson et al.（2015）。不是单行道：数学的程序性知识和概念性知识之间的双向关系。教育心理，27,587-597.[j]福斯特(2018)。发展数学流畅性：比较练习和丰富的任务。数学教育研究，1997,121-141。[3]麦克尼尔（2008）。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.[j]Chesney & McNeil（2014）。运算思维在算术练习中的激活会阻碍学习和迁移。问题解决学报，7,24-35。[5] Jay et al.（2019）。以游戏为基础的训练，促进算术流畅性。教育前沿，4,118。[6]休伊特（1996）。数学流畅性：练习的性质和从属的作用。数学之学，16,28-35.[j]Lowrie & Jorgensen（2015）。数字游戏和学习：什么是新东西已经过时了？《数字游戏与数学学习》（第1-9页）。施普林格。

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.