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.

许多儿童和成人在日常生活中与分数（例如1/3）和十进制数字（例如2.1）挣扎。但是，分数和十进制数字在工作场所很常见，而这些数字的熟练程度对于与健康相关和财务决策很重要。此外，对于数学和其他主题，对分数和十进制数字的扎实理解是必要的。该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字时遇到的困难。分数通常在小数数字之前引入课程中，但是，分数的性能差。先前的研究主要集中在分数上，并强调了一些困难领域。分数的幅度较少访问，因为它不是由组件号的值定义的，而是由两个数字之间的关系定义。儿童和成人通常会受到组件数字的幅度的偏见，例如，判断3/9大于1/3。对于许多人来说，分数算术程序也仍然很困难，因为并非所有适用于整数的原则都适用于分数（例如，乘以分数并不需要导致更大的数字）。此外，当引入分数和十进制数字时，孩子们必须学习新的数字表格和新的符号。哪种技能可以帮助孩子成功克服这些障碍？当孩子进入小学时，他们需要从主要使用口头数字单词（例如'二十三个'）转变为能够在听到口头数字时写下正确的多位数阿拉伯字符串（例如'23'）。这称为数字开发的编码和基础。在先前的研究项目中，我们发现儿童的数量转换能力预测了两年后的早期理解。在学习分数和十进制数字的新符号时，更好的数字转码能力可能是有益的。在该研究项目中，我们将评估转码技巧是否是对分数和十进制数字的扎实理解的基础。我们将在衡量其他建议的数值技能的背景下来支持分数学习的发展，例如比例推理和孩子对整数幅度的知识。首先，我们将继续进行持续的纵向研究，从6至8年级的儿童进行数学发展，重点关注分数的学习。这项研究将使我们能够发现早期数学发展的哪些技能可以预测以后对分数的更好理解。但是，识别预测因子只是第一步。为了进一步的理论和实践贡献，必须确定这些技能支持分数学习的机制。我们将在另外两项研究中确定这些技能中的哪些是因果机制。我们将使用基于实验室的研究来研究深入的分数处理，以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，我们将衡量所提出的预测能力技能的个体差异，并将其与任务绩效和策略使用联系起来。为了衡量策略使用，我们将同时使用明确的措施（自我报告）和隐式措施（眼动）。最后，在与儿童和成人的培训研究中，我们将确定培训这些预测能力的技能是否会提高分数的熟练程度，如果是这样，则如何最好地培训这些技能。除了增加我们对分数和十进制数字学习的知识外，该研究项目从长远来看还会帮助分数和小数数字​​的儿童和成年人。