The foundations of understanding fractions and decimal numbers

理解分数和小数的基础

• 批准号: ES/W005654/1
• 负责人: Silke Goebel
• 金额: $ 58.83万
• 依托单位: University of York
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=ES%2FW005654%2F1
• 关键词: foundations; understanding; fractions; decimal; numbers

Many children and adults struggle with fractions (e.g., 1/3) and decimal numbers (e.g., 2.1) in daily life. However, fractions and decimal numbers are common in the workplace and proficiency with those numbers is important for health-related and financial decisions. Furthermore, a solid understanding of fractions and decimal numbers is necessary for mathematics and other STEM-subjects. This research project will establish how to overcome the difficulties many children and adults encounter when dealing with fractions and decimal numbers. Fractions are often introduced into the curriculum before decimal numbers, nevertheless performance is worse with fractions. Previous research has mainly focused on fractions and highlighted several areas of difficulties. The magnitude of a fraction is less accessible, because it is not defined by the values of the component numbers, but instead by the relationship between two numbers. Children and adults are often biased by the magnitudes of the component numbers, for example judging 3/9 to be larger than 1/3. Fraction arithmetic procedures also remain difficult for many, because not all principles that are true for whole numbers apply to fractions (e.g., multiplying by a fraction does not necessary lead to a larger number). Furthermore, when fractions and decimal numbers are introduced, children have to learn new number forms and new notations.Which skills help children to successfully overcome those hurdles? When children enter primary school they need to shift from using mainly spoken numbers words (e.g., 'twenty-three') to being able to write down the correct multi-digit Arabic strings (e.g., '23') upon hearing spoken number words. This is called number transcoding and fundamental for mathematical development. In a previous research project we found that children's ability in number transcoding predicted their early fraction understanding two years later. Better number transcoding ability might be beneficial when learning new notations for fractions and decimal numbers. In this research project we will assess whether transcoding skills are foundational for a solid understanding of fractions and decimal numbers. We will do this in the context of measuring other numerical skills that have been suggested to support the development of fraction learning such as proportional reasoning and children's knowledge about the magnitude of whole numbers.First, we will continue an ongoing longitudinal study, following children's mathematical development from Year 6 to 8, with a focus on their learning of fractions. This study will enable us to discover which skills in early mathematical development predict better later understanding of fractions. Identifying predictors, however, is only the first step. To make further theoretical and practical contributions it is essential to identify the mechanisms by which those skills support the learning of fractions. We will establish which of these skills are causal mechanisms in two further series of studies. We will use laboratory-based studies to investigate the processing of fractions in-depth, comparing groups of children and adults with different levels of expertise in fractions. In these studies we will measure individual differences in the proposed predictor skills and link those to task performance and strategy use. To measure strategy use we will use both explicit measures (self-report) and implicit measures (eye-movements). Finally, in training studies with both children and adults we will identify whether training those predictor skills leads to improvement in proficiency with fractions and, if so, how best to train those skills. In addition to increasing our knowledge about the learning of fractions and decimal numbers, this research project will in the long run help children and adults who struggle with fractions and decimal numbers.

许多儿童和成人都在与分数作斗争（例如，1/3）和十进制数（例如，2.1)在日常生活中然而，分数和小数在工作场所很常见，熟练掌握这些数字对于健康和财务决策很重要。此外，对于数学和其他STEM科目来说，对分数和小数的扎实理解是必要的。这个研究项目将建立如何克服许多儿童和成人在处理分数和十进制数时遇到的困难。分数通常在小数之前引入课程，然而分数的表现更差。以前的研究主要集中在分数和突出的几个领域的困难。分数的大小不太容易获得，因为它不是由分量数的值定义的，而是由两个数之间的关系定义的。儿童和成年人经常被分量数的大小所偏见，例如判断3/9大于1/3。分数算术程序对许多人来说也仍然很困难，因为并非所有对整数适用的原则都适用于分数（例如，乘以分数不一定导致更大的数）。此外，当分数和十进制数被引入时，孩子们必须学习新的数字形式和新的符号。哪些技能可以帮助孩子成功克服这些障碍？当孩子们进入小学时，他们需要从使用主要是口语的数字词（例如，'二十三'）到能够写下正确的多位阿拉伯字符串（例如，”（23）“听”字。这被称为数字转码，是数学发展的基础。在以前的研究项目中，我们发现儿童的数字转码能力预测了他们两年后的早期分数理解。更好的数字转码能力可能是有益的，当学习新的分数和十进制数的符号。在这个研究项目中，我们将评估转码技能是否是扎实理解分数和十进制数的基础。我们将在测量其他被建议用于支持分数学习发展的数字技能（如比例推理和儿童对整数的大小的知识）的背景下进行这项研究。首先，我们将继续进行一项持续的纵向研究，跟踪6至8年级儿童的数学发展，重点关注他们的分数学习。这项研究将使我们能够发现早期数学发展中的哪些技能可以更好地预测以后对分数的理解。然而，确定预测因素只是第一步。为了做出进一步的理论和实践贡献，有必要确定这些技能支持分数学习的机制。我们将在两个进一步的系列研究中确定哪些技能是因果机制。我们将使用基于实验室的研究来深入调查分数的处理，比较具有不同分数专业知识水平的儿童和成人组。在这些研究中，我们将测量所提出的预测技能的个体差异，并将其与任务绩效和策略使用联系起来。为了测量策略的使用，我们将使用外显测量（自我报告）和内隐测量（眼球运动）。最后，在对儿童和成人的训练研究中，我们将确定训练这些预测技能是否会导致分数熟练度的提高，如果是的话，如何最好地训练这些技能。除了增加我们对分数和十进制数学习的知识外，这个研究项目从长远来看将帮助那些与分数和十进制数斗争的儿童和成人。