Understanding individual differences in mathematics learning and cognition: The role of creative potential and mathematical creativity and giftedness

创造潜能（CP）是指导致创造力的潜在特征、能力和经验（Feist, 2018; Zhang, 2012）；认知因素、情感因素和人格因素的混合构成了CP的一般因素，具有不同领域特定的CP因素概况（这是我的哲学硕士课程的重点）。虽然许多研究都集中在艺术领域的CP，但这与STEM领域的CP不同，尤其是数学领域（Carson, 2005）。然而，在个体的一生中，创造力和数学认知之间存在着重要而复杂的关系（Kroesbergen and Schoevers 2017; Lubinski et al., 2014）；这项研究将创造力作为天赋的一个因素，尽管最近的共识表明，创造力是一种日常建构，而不仅仅局限于那些高能力的人。因此，通过考虑一系列的能力（例如，有天赋的数学，典型的数学学习者，以及那些有数学困难的人）和态度（包括享受，自我效能和数学焦虑），可以确定一个更完整的画面，不仅是个体在数学上的差异，而且我们如何开始适应这些数学学习的差异；创造力在解决这个问题方面发挥着重要作用（Howard-Jones, 2012）。然而，尽管这种关注是合理的，但数学教育心理学的研究倾向于(a)只承认创造力是一种产品，而不是受环境因素（例如SES）影响的认知的复杂方面，(b)只关注一个群体（例如那些有数学焦虑或计算障碍的人）或一个学科，(c)明显关注能力或态度，忽略了两者的相互作用。本研究旨在通过考虑一个由CP、数学创造力、能力和态度组成的复杂数学认知模型来解决这一问题。然而，由于创造力、高成就和与常规思维模式不同之间的原始联系（Feist, 2008），假设这项研究可能对理解天才数学最有帮助。由于参与者数量有限，这是认知心理学和神经科学研究中一个极度缺乏研究的领域（Myers等人，2017）；样本量小也使得很难得出明确的结论。方法和样本：目的是考虑个体在不同阶段的数学教育主要使用心理测量和认知能力测试；最初的想法可以根据获得的技能和对现有方法的审查进行调整。这个样本实际上可以由以下每组的100个人组成：必修数学学生（GCSE），那些已经开始专业（A-level）和那些更高级的数学（不同水平的大学和学术界）。除了使用一般的CP测试外，最初的重点将放在概念化、选择或开发基于任务/问题的数学创造力测量方法上。这可以与调查问卷相结合，包括数学能力——学术成绩、数学教育水平、数学特定认知能力（如平价判断、符号大小比较、数字和空间推理测试成绩）和数学态度（数学焦虑、享受和自我效能），以及考虑社会人口因素（如性别、社会经济地位、最高教育水平等）。因此，本研究通过多变量分析，可以帮助我们了解数学学习和认知的个体差异，解决：1。数学创造力的认知、情感和基于特质的预测因素是什么？这在数学焦虑症患者、典型数学学习者和天才数学学习者之间有区别吗？领域通用CP和领域特定CP、数学能力和态度之间的关系是什么？教育和社会人口因素（如性别、社会经济地位、教育水平、所研究的学科）在这种关系中起什么作用

Creative potential (CP) refers to the underlying traits, abilities and experiences that lead to creativity (Feist, 2018; Zhang, 2012); a mixture of cognitive, affective and personality factors constitute general factors of CP, with different domain-specific CP factor-profiles (this was the focus of my MPhil). Whilst much research focusses on CP in the arts, this differs from CP in STEM, particularly mathematics (Carson, 2005). However, there is an important yet complex relationship between creativity and mathematical cognition across an individual's lifetime (Kroesbergen and Schoevers 2017; Lubinski et al., 2014); this research focusses on creativity as an element of giftedness, although recent consensus suggests CP is an everyday construct, not just limited to those of high ability. Thus, by considering a spectrum of abilities (e.g. gifted maths, typical maths learners, and those with mathematical difficulties) and attitudes (including enjoyment, self-efficacy and maths anxiety), a more complete picture of not only how individuals differ in mathematics, but also how we begin to cater for these variations in mathematical learning, can be ascertained; creativity plays an important role in addressing this (Howard-Jones, 2012). However, despite this focus being justified, research in the psychology of maths education tend to either (a) only acknowledge creativity as a product rather than a complex aspect of cognition that is affected by environmental factors (e.g. SES), (b) focus only on one group of individuals (e.g. those with maths anxiety or dyscalculia) or one discipline and (c) focus distinctly on either ability or attitude, ignoring the interplay of the two. This study aims to address this by considering a complex model of mathematical cognition consisting of CP, mathematical creativity, ability and attitude. However, due to the original association between creativity, high achievement and having divergent patterns of thinking to the norm (Feist, 2008) it is hypothesised that this study may be most beneficial in understanding gifted mathematics. This is an extremely understudied area in cognitive psychology and neuroscience research due to a limited number of participants (Myers et al., 2017); small sample sizes also make definite conclusions difficult.Methods and Sample: The aim is to consider individuals at different stages of maths education predominantly using psychometric and cognitive ability tests; the initial ideas may be adapted depending on skills acquired and a review of existing methods. This sample could realistically consist of 100 individuals from each of the following groups: compulsory maths students (GCSE), those who have started specialising (A-level) and those in more advanced mathematics (different levels of university and academia). Alongside using general CP tests, the initial focus will be on conceptualising, selecting or developing a task/problem-based measure of mathematical creativity. This can be combined with questionnaires including maths ability-academic grade, level of maths education, math-specific cognitive ability (e.g. parity judgement, symbolic magnitude comparison and numerical and spatial reasoning test scores)- and mathematics attitude (maths anxiety, enjoyment and self-efficacy) alongside a consideration of sociodemographic factors (e.g. gender, SES, highest level of education etc).Thus, using multivariate analysis, this study could help us understand individual differences in mathematics learning and cognition, addressing: 1. What are the cognitive, affective and trait-based predictors of maths creativity? Does this differ between those with maths anxiety, typical and gifted maths learners?2. What is the relationship between both domain-general and domain-specific CP, maths ability and attitude?3. What roles do educational and sociodemographic factors (eg gender, SES, level of education, discipline studied) play in this relationship, especially for disadvantaged or