Math

数学
  • 文章类型: Journal Article
    利用高中纵向研究,美国高中生的全国代表性样本,这项研究调查了预测性别数学能力的不同信念的因素,以及学生选择进入性别隔离科学的潜在后果,技术,工程,和大学数学(STEM)专业。在其他结果中,分析表明,虽然大约25%的学生报告了传统上对男性优势的刻板印象,大约20%的人表示反对女性优势的陈规定型观念;在女学生中,这种信念在黑人学生中更为普遍。Further,模型揭示了持有反陈规定型观念与女性选择生物科学专业的可能性之间的强烈关联,女性占主导地位,与非STEM字段相比。在男性中,持有反陈规定型观念与物理科学专业的可能性较低有关,计算机科学,数学,和工程领域,男性占主导地位,与非STEM字段。讨论了STEM领域对性别不平等的影响。
    Utilizing the High School Longitudinal Study, a nationally representative sample of U.S. high school students, this study investigates the factors that predict different beliefs about gendered math ability and the potential consequences for students\' choices to enter gender-segregated science, technology, engineering, and mathematics (STEM) majors in college. Among other results, analyses reveal that while about 25 percent of students report a traditionally stereotypical belief in male superiority, about 20 percent report a counter-stereotypical belief in female superiority; among female students, such beliefs are more common among black students. Further, models reveal a robust association between holding counter-stereotypical beliefs and the likelihood that women choose biological science majors, which are female dominated, compared to non-STEM fields. Among men, holding counter-stereotypical beliefs is associated with a lower likelihood of majoring in physical science, computer science, math, and engineering fields, which are strongly male dominated, versus non-STEM fields. Implications for gender inequality in STEM fields are discussed.
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  • 文章类型: Journal Article
    众所周知,数学和阅读技能是相关的,每个预测因素都得到了很好的研究。人们不太理解的是这些预测因素在多大程度上,独特和集体,彼此重叠,对不同的学术技能有不同的重要性,并解释了数学和阅读的重叠。我们检查了来自四个领域的20个潜在预测因子(工作记忆,处理速度,注意,和语言)使用潜在变量以及定时和非定时成就技能,在一个有风险的中学生样本(N=212)中,其中一半是英语学习者。预测因子约占成就技能重叠的一半,暗示其他因素(例如,领域特定技能)也可能与重叠相关。我们还发现了一些差异预测(阅读语言,数学工作记忆)。本研究结果扩展并完善了我们对这些认知预测因子对阅读和数学的贡献的理解。
    Math and reading skills are known to be related, and predictors of each are well researched. What is less understood is the extent to which these predictors, uniquely and collectively, overlap with one another, are differentially important for different academic skills, and account for the overlap of math and reading. We examined 20 potential predictors from four domains (working memory, processing speed, attention, and language) using latent variables and both timed and untimed achievement skill, in a sample (N=212) of at-risk middle schoolers, half of whom were English learners. The predictors accounted for about half of the overlap among achievement skills, suggesting that other factors (e.g., domain specific skills) might also be relevant for the overlap. We also found some differential prediction (language for reading, working memory for math). The present results extend and refine our understanding of the contribution of these cognitive predictors for reading and math.
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  • 文章类型: Journal Article
    课程材料中男孩和女孩范例的表现如何影响学生的学习?我们测试了关于性别范例对学习的影响的两个相互竞争的假设:第一,符合社会学习理论,儿童可能表现出相同性别的偏见,因此他们更喜欢从与他们的性别(H1)相匹配的样本中学习。第二,与儿童对性别和数学的刻板印象的研究一致(例如,将男孩与数学能力相关联),孩子们可能更喜欢从符合他们关于谁擅长数学的刻板印象的榜样中学习(H2)。我们在中学的孩子身上测试了这些假设(N=166),一个刻板印象根深蒂固的发展时期,但是在数学成绩出现性别差异之前。孩子们看到了两种截然不同的数学策略,每个由男孩或女孩的例子。然后,我们检查了儿童在随后的数学测试中采用的策略,以及他们与榜样的相似性以及他们对性别数学刻板印象的认识或认可。儿童不优先从同性范例中学习。然而,与不将男孩与数学联系起来的儿童相比,具有刻板印象的儿童更有可能学习由男孩示例提出的更困难的策略。这项研究的结果为儿童的刻板印象如何影响他们的真实世界学习提供了有价值的见解。研究重点:儿童课程材料中男孩和女孩范例的表现如何影响他们的学习?过去的研究表明,儿童更喜欢从相同性别的范例中学习,但也有一种刻板印象,认为男孩更擅长数学。在目前的研究中,我们测试孩子是否优先采用男孩或女孩的数学策略。与不认可这种刻板印象的孩子相比,那些相信男孩数学更好的孩子更有可能从男孩榜样中学到困难的策略。
    How does the representation of boy and girl exemplars in curricular materials affect students\' learning? We tested two competing hypotheses about the impact of gender exemplar on learning: First, in line with Social Learning Theory, children might exhibit a same-gender bias such that they prefer to learn from exemplars that match their gender (H1). Second, consistent with research on children\'s stereotypes about gender and math (e.g., associating boys with math competence), children might prefer to learn from exemplars who match their stereotypes about who is good at math (H2). We tested these hypotheses with children in middle school (N = 166), a time of development in which stereotypes are well-engrained, but before gender differences in math achievement appear. Children viewed two distinct math strategies, each presented by a boy or girl exemplar. We then examined which strategy children employed on a subsequent math test as well as their perceived similarity to the exemplars and their awareness or endorsement of gender-math stereotypes. Children did not preferentially learn from same-gender exemplars. However, children with stereotypes associating boys with math were more likely to learn the more difficult strategy when it was presented by a boy exemplar than children who did not associate boys with math. The results of this study provide valuable insight into how children\'s stereotypes impact their real-world learning. RESEARCH HIGHLIGHTS: How does the representation of boy and girl exemplars in children\'s curricular materials affect their learning? Past research demonstrates that children prefer to learn from same-gender exemplars, but also hold a stereotype that boys are better at math. In the current study, we test whether children preferentially adopt a math strategy presented by a boy or girl exemplar. Children who held the belief that boys are better at math were more likely to learn a difficult strategy from boy exemplars than children who did not endorse this stereotype.
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  • 文章类型: Journal Article
    这项对126名青年的fMRI研究探讨了N-back任务背后的神经机制,通常用于检查对工作记忆内容的执行控制,与阅读和数学学业成绩的个体差异有关。此外,这项研究探讨了这些关系是否发生,无论在工作记忆中被操纵的刺激的性质如何(字母,数字,无意义形状),或者这些关系是否特定于成就领域和刺激类型(即,用于阅读的字母和用于数学的数字)。结果表明,无论刺激类型如何,阅读和数学方面的较高学业成绩都与N背任务中背外侧前额叶皮层的更大激活有关(即,字母和数字没有差异),这表明这些学术领域的神经机制的至少某些方面在本质上是执行的。此外,无论学术成就水平如何,前额叶区域对字母的参与程度大于数字,而不是无义形状。相比之下,无义形状比字母和数字产生更大的海马激活。讨论了这种发现模式的潜在原因。
    This fMRI study of 126 youth explored whether the neural mechanisms underlying the N-back task, commonly used to examine executive control over the contents of working memory, are associated with individual differences in academic achievement in reading and math. Moreover, the study explored whether these relationships occur regardless of the nature of the stimulus being manipulated in working memory (letters, numbers, nonsense shapes) or whether these relationships are specific to achievement domain and stimulus type (i.e., letters for reading and numbers for math). The results indicated that higher academic achievement in each of reading and math was associated with greater activation of dorsolateral prefrontal cortex in the N-back task regardless of stimulus type (i.e., did not differ for letters and numbers), suggesting that at least some aspects of the neural mechanisms underlying these academic domains are executive in nature. In addition, regardless of level of academic achievement, prefrontal regions were engaged to a greater degree for letters than numbers than nonsense shapes. In contrast, nonsense shapes yielded greater hippocampal activation than letters and numbers. Potential reasons for this pattern of findings are discussed.
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  • 文章类型: Journal Article
    数学焦虑(MA)是关于学习的学术焦虑,正在做,评估数学,通常在学校人口和成年人中学习。然而,马可能在孩子上学之前就有它的起源。例如,研究表明,与初中相比,小学中日常事件的一般焦虑(GA)与MA的分离程度较低。这表明GA可以是MA的前体。出于这个原因,在这里,我们已经检查了GA是否已经与幼儿园结束时的数学成绩相关。
    我们测试了488名5.7至6.9岁的匈牙利幼儿园儿童(55%的女孩),并分析了GA的影响,性别,和家庭SES对幼儿园儿童数学成绩的影响。
    引人注目的是,确认小学生的结果,我们发现,在该学龄前人群中,GA与数学成绩已经呈负相关。较高的GA水平对女孩数学成绩的负面影响比男孩更强。然而,幼儿园数学成绩无显著性别差异。此外,家庭社会经济地位是数学成绩的最强预测指标。
    我们推测,学龄前儿童的高GA可能是后期高MA的早期前兆。早期干预可能旨在在儿童开始正规教育之前控制GA水平。
    UNASSIGNED: Math anxiety (MA) is an academic anxiety about learning, doing, and evaluating mathematics, usually studied in school populations and adults. However, MA likely has its origins before children go to school. For example, studies have shown that general anxiety (GA) for everyday events is less separable from MA in primary than in early secondary school. This suggests that GA may be a precursor of MA. For this reason, here, we have examined whether GA is already associated with math achievement at the end of kindergarten.
    UNASSIGNED: We tested 488 Hungarian kindergarten children aged 5.7 to 6.9 years (55% girls) and analyzed the effect of GA, sex, and family SES on math achievement in kindergarten children.
    UNASSIGNED: Strikingly, confirming results from primary school children, we found that GA negatively correlated with math achievement already in this preschool population. Higher GA levels had a stronger negative effect on girls\' than boys\' math achievement. However, there were no significant sex differences in math achievement in kindergarten. Additionally, family socioeconomic status was the strongest predictor of math achievement.
    UNASSIGNED: We speculate that high GA in preschool is a plausible early precursor of later high MA. Early interventions could aim to control GA levels before children start formal schooling.
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  • 文章类型: Journal Article
    这项研究将一个交叉框架与来自2009年高中纵向研究的15,000名美国九年级学生的数据相结合,以调查青少年学习障碍状况交汇处九年级数学课程的差异,种族,和社会经济地位(SES)。描述性结果支持增加责任的观点,对于在种族和/或SES方面享有特权的青少年,学习障碍与数学课程安置之间的负相关更大。调整后的结果表明,学习障碍青年的数学课程较低的原因是由于种族和社会经济背景不同的青年过渡到高中的累积劣势,而不是与残疾相关的不平等。除了证明交叉视角的重要性之外,这项研究通过引入增加责任的新视角与广泛采用的多重边缘化视角相结合,为未来的研究提供了路线图。
    This study integrates an intersectional framework with data on 15,000 U.S. ninth graders from the High School Longitudinal Study of 2009 to investigate differences in ninth-grade math course placement at the intersection of adolescents\' learning disability status, race, and socioeconomic status (SES). Descriptive results support an increased liability perspective, with the negative relationship between a learning disability and math course placement larger for adolescents more privileged in terms of their race and/or SES. Adjusted results suggest that the lower math course placements of youth with learning disabilities are due to cumulative disadvantage rather than disability-related inequities in the transition to high school for youth of diverse racial and socioeconomic backgrounds. In addition to demonstrating the importance of intersectional perspectives, this study provides a roadmap for future studies by introducing the new perspective of increased liability to be used in conjunction with the widely employed perspective of multiple marginalization.
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  • 文章类型: Journal Article
    高等教育机构正在促进采用创新的方法和教学方法,以吸引和促进学生的个性化学习路径。基于游戏化的几种策略,人工智能,和数据挖掘被用来创建一个以学生为中心的交互式教育环境。在这种个性化的学习环境中,学生参与度显着提高,教育成果得到改善。MathE平台,2019年推出的在线教育系统是专门设计的,旨在支持学生在理解高等教育水平的数学方面遇到困难,或者支持那些渴望加深对不同数学主题理解的学生——所有这些都按照自己的节奏进行。MathE平台提供多项选择题,按主题和子主题分类,与高等教育课程的内容保持一致。世界各地的学生都可以访问,该平台使他们能够通过这些资源训练他们的数学技能。当学生登录平台的培训区时,他们选择一个主题来研究,并指定他们喜欢基本还是高级问题。然后,该平台从所选主题下的可用问题中选择一组七个多项选择题,并为学生生成一个测试。完成并提交测试后,答案被记录并存储在平台上。本文描述了存储在MathE平台中的数据,专注于833个问题的9546个答案,由来自8个国家的372名学生提供,他们使用平台上可用的问题(和其他资源)练习他们的技能。本文的信息将有助于研究主动学习工具,以支持未来教育的改进,尤其是在更高的教育水平。此外,这些数据对于理解学生的学习模式很有价值,评估平台功效,获得数学教育的全球视野,并促进高等教育主动学习工具的发展。
    Higher education institutions are promoting the adoption of innovative methodologies and instructional approaches to engage and promote personalized learning paths to their students. Several strategies based on gamification, artificial intelligence, and data mining are adopted to create an interactive educational setting centred around students. Within this personalized learning environment, there is a notable boost in student engagement and enhanced educational outcomes. The MathE platform, an online educational system introduced in 2019, is specifically crafted to support students tackling difficulties in comprehending higher-education-level mathematics or those aspiring to deepen their understanding of diverse mathematical topics - all at their own pace. The MathE platform provides multiple-choice questions, categorized under topics and subtopics, aligning with the content taught in higher education courses. Accessible to students worldwide, the platform enables them to train their mathematical skills through these resources. When the students log in to the training area of the platform, they choose a topic to study and specify whether they prefer basic or advanced questions. The platform then selects a set of seven multiple-choice questions from the available ones under the chosen topic and generates a test for the student. After completing and submitting the test, the answers are recorded and stored on the platform. This paper describes the data stored in the MathE platform, focusing on the 9546 answers to 833 questions, provided by 372 students from 8 countries who use the platform to practice their skills using the questions (and other resources) available on the platform. The information in this paper will help research about active learning tools to support the improvement of future education, especially at higher educational level. Furthermore, these data are valuable for understanding student learning patterns, assessing platform efficacy, gaining a global perspective on mathematics education, and contributing to the advancement of active learning tools for higher education.
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  • 文章类型: Journal Article
    虽然孩子们学到更多的当老师的手势,尚不清楚手势如何支持学习。这里,我们试图调查记忆过程的性质,这些记忆过程是观察到的手势对持久学习的益处的基础。我们假设带有手势的指令可能会创建特别抗干扰的内存表示。我们在对402名二年级和三年级儿童的课堂研究中调查了这种可能性。参与者使用带有或不带有手势的视频接受了数学等效性的课堂教学。指示后,孩子们解决的问题要么在视觉上与所教导的问题相似,并且与等号(干扰)的操作解释一致,或在视觉上与等效问题不同,并且没有等号(控制),以便在学习后评估手势在抵抗干扰中的作用。手势促进学习,但是手势和干扰的影响取决于所解决的问题的类型以及儿童在教学前用来解决问题的策略。一些孩子从手势中受益,而其他人没有。这些发现对于理解手势对数学学习的有益作用的潜在机制具有重要意义。揭示手势不通过一般机制,如提高注意力或参与,将适用于所有形式的先验知识的儿童。
    Although children learn more when teachers gesture, it is not clear how gesture supports learning. Here, we sought to investigate the nature of the memory processes that underlie the observed benefits of gesture on lasting learning. We hypothesized that instruction with gesture might create memory representations that are particularly resistant to interference. We investigated this possibility in a classroom study with 402 second- and third-grade children. Participants received classroom-level instruction in mathematical equivalence using videos with or without accompanying gesture. After instruction, children solved problems that were either visually similar to the problems that were taught, and consistent with an operational interpretation of the equal sign (interference), or visually distinct from equivalence problems and without an equal sign (control) in order to assess the role of gesture in resisting interference after learning. Gesture facilitated learning, but the effects of gesture and interference varied depending on type of problem being solved and the strategies that children used to solve problems prior to instruction. Some children benefitted from gesture, while others did not. These findings have implications for understanding the mechanisms underlying the beneficial effect of gesture on mathematical learning, revealing that gesture does not work via a general mechanism like enhancing attention or engagement that would apply to children with all forms of prior knowledge.
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  • 文章类型: Randomized Controlled Trial
    乐器训练与提高儿童的学术和认知能力有关,但目前尚不清楚为什么会发生这种情况。此外,获得仪器培训并不总是可行的,从而使不幸的儿童没有机会从这种培训中受益。尽管基于音乐的视频游戏可能更适合更广泛的人群,缺乏关于它们对学术和认知表现的益处的研究。为了解决这个差距,我们评估了一个定制设计的,数字节奏训练游戏作为乐器训练的代理,以评估其在数学和阅读能力方面产生收益的能力。此外,我们测试了与数学和阅读相关的核心认知功能的变化,以告知节奏训练如何促进学术能力的提高。8-9岁儿童的教室被随机分配接受6周的节奏训练(N=32)或照常接受课堂教学(对照;N=21)。与对照组相比,结果表明,节奏训练改善了阅读,但不是数学,流利。认知评估表明,节奏训练还可以改善节奏时间和基于语言的执行功能(Stroop任务),但没有持续的关注,抑制控制,或工作记忆。有趣的是,只有节奏时间的改善与阅读能力的改善相关。一起,这些结果提供了新的证据,表明数字平台可以作为乐器训练的代理,以促进儿童的阅读流利,并且这种阅读改善与增强的节奏计时能力有关,而不是与阅读表现相关的其他认知功能。研究重点:课堂上的数字节奏训练可以提高8-9岁儿童的阅读流畅性。反过来,可以促进学术技能。
    Musical instrument training has been linked to improved academic and cognitive abilities in children, but it remains unclear why this occurs. Moreover, access to instrument training is not always feasible, thereby leaving less fortunate children without opportunity to benefit from such training. Although music-based video games may be more accessible to a broader population, research is lacking regarding their benefits on academic and cognitive performance. To address this gap, we assessed a custom-designed, digital rhythm training game as a proxy for instrument training to evaluate its ability to engender benefits in math and reading abilities. Furthermore, we tested for changes in core cognitive functions related to math and reading to inform how rhythm training may facilitate improved academic abilities. Classrooms of 8-9 year old children were randomized to receive either 6 weeks of rhythm training (N = 32) or classroom instruction as usual (control; N = 21). Compared to the control group, results showed that rhythm training improved reading, but not math, fluency. Assessments of cognition showed that rhythm training also led to improved rhythmic timing and language-based executive function (Stroop task), but not sustained attention, inhibitory control, or working memory. Interestingly, only the improvements in rhythmic timing correlated with improvements in reading ability. Together, these results provide novel evidence that a digital platform may serve as a proxy for musical instrument training to facilitate reading fluency in children, and that such reading improvements are related to enhanced rhythmic timing ability and not other cognitive functions associated with reading performance. RESEARCH HIGHLIGHTS: Digital rhythm training in the classroom can improve reading fluency in 8-9 year old children Improvements in reading fluency were positively correlated with enhanced rhythmic timing ability Alterations in reading fluency were not predicted by changes in other executive functions that support reading A digital platform may be a convenient and cost-effective means to provide musical rhythm training, which in turn, can facilitate academic skills.
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  • 文章类型: Journal Article
    数学学习是通过认知之间的相互作用来解释的,情感,和社会因素。然而,研究很少调查这些因素如何相互作用来解释数学表现。本研究旨在通过使用功能磁共振成像(fMRI)来了解父母社会经济地位(SES)与儿童数学态度之间相互作用的神经认知机制,从而填补文献中的空白。为了这个目标,57个孩子解决了扫描仪内部的乘法问题。我们通过根据父母的职业创建两个小组来测量父母的SES,并使用问卷测量儿童的数学态度。我们进行了聚类回归分析,检查了这两个变量之间的相互作用,同时控制了SES的主要影响,数学态度,完整的IQ分析显示左额下回(IFG)有一个簇,这是由于来自高社会经济地位家庭的积极数学态度的儿童在解决大乘法问题时表现出更大的IFG激活,与他们的消极态度高SES同龄人相比,这表明他们表现出更多的检索工作来解决大型乘法问题。我们讨论这可能是因为他们是唯一完全参与其环境提供的数学机会的人。
    Math learning is explained by the interaction between cognitive, affective, and social factors. However, studies rarely investigate how these factors interact with one another to explain math performance. This study aims to fill this gap in the literature by using functional magnetic resonance imaging (fMRI) to understand the neurocognitive mechanisms underlying the interaction between parental socioeconomic status (SES) and children\'s math attitudes. To this aim, 57 children solved multiplication problems inside the scanner. We measured parental SES by creating two groups based on parents\' occupations and measured children\'s math attitudes using a questionnaire. We ran a cluster-wise regression analysis examining the interaction between these two variables while controlling for the main effects of SES, math attitudes, and full IQ. The analysis revealed a cluster in the left inferior frontal gyrus (IFG), which was due to children with positive math attitudes from high socio-economic status families showing greater IFG activation when solving large multiplication problems as compared to their negative attitudes high SES peers, suggesting that they exhibited more retrieval effort to solve large multiplication problems. We discuss how this may be because they were the only ones who fully engaged in math opportunities provided by their environment.
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