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

创造潜力（CP）是指导致创造力的潜在特质，能力和经验（Feist，2018; Zhang，2012）;认知，情感和个性因素的混合构成了CP的一般因素，具有不同的特定领域CP因素概况（这是我的哲学硕士的重点）。虽然许多研究集中在艺术中的CP，但这与STEM中的CP不同，特别是数学（卡森，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和Schoevers 2017; Lubinski等人，（2014年）;这项研究的重点是创造力作为天赋的一个要素，尽管最近的共识认为CP是一种日常结构，而不仅仅限于那些高能力的人。因此，通过考虑一系列的能力，（例如，数学天才、典型的数学学习者和数学困难者）和态度（包括乐趣、自我效能和数学焦虑），不仅可以更全面地了解个体在数学方面的差异，而且可以确定我们开始如何迎合数学学习中的这些差异;创造力在解决这一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往往（a）只承认创造力是一种产品，而不是受环境因素影响的认知的复杂方面（例如社会经济地位），（B）只关注一组个人（c）只专注于能力或态度，而忽略两者之间的相互影响。本研究旨在解决这一问题，考虑一个复杂的数学认知模型，包括CP，数学创造力，能力和态度。然而，由于创造力，高成就和具有发散思维模式之间的原始关联（Feist，2008），假设这项研究可能对理解天才数学最有益。由于参与者数量有限，这是认知心理学和神经科学研究中研究非常不足的领域（Myers等人，（2017年）;方法和样本：目的是考虑主要使用心理测量和认知能力测试的数学教育的不同阶段的个人;最初的想法可能会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包括来自以下各组的100人：必修数学学生（GCSE），那些已经开始专业化（A-level）和那些更高级的数学（不同级别的大学和学术界）。除了使用一般的CP测试，最初的重点将是概念化，选择或开发一个基于任务/问题的数学创造力的措施。这可以与包括数学能力-学业成绩、数学教育水平、数学特定认知能力的问卷相结合（例如奇偶判断、符号大小比较以及数字和空间推理测试成绩）-以及数学态度（数学焦虑，享受和自我效能），同时考虑社会人口因素因此，本研究利用多变量分析，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、情感和特质预测因子是什么？这在那些有数学焦虑的人、典型的数学学习者和有天赋的数学学习者之间有什么不同吗？2.一般领域合作原则和特定领域合作原则与数学能力、数学态度之间的关系如何？3.教育和社会人口因素（如性别，社会经济地位，教育水平，学科研究）在这种关系中发挥什么作用，特别是对弱势群体或

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