mathematics

数学
  • 文章类型: Journal Article
    种族刻板印象对黑人青少年和数学学术领域很重要;然而,很少有研究研究种族刻板印象影响数学成就的社会认知机制。这项为期2年的纵向研究(N=790年级6,8和10年级的学生;一年级的50.7%的女孩和49.3%的男孩)调查了(a)对积极和消极的种族刻板印象的认可在多大程度上预测了黑人青少年的数学表现通过他们的认知参与和能力心态以及(b)性别和种族种族认同是否缓和了这些联系。结果表明,对负面偏见的刻板印象的认可与2年的认知投入减少和数学得分降低有关(p<0.05)。此外,青少年的种族认同承诺缓和了第二年刻板印象认可和数学认知参与之间的负面联系(p<0.05)。当考虑数学能力思维的中介作用时,积极和消极的种族刻板印象的认可对数学表现的影响是通过其与两年中更强的固定能力心态信念的联系(p<.05)。在第一年,性别也缓和了种族刻板印象认可对数学心态信念的影响(p<.01)。这项研究的发现推进了该领域对种族刻板印象运作的心理社会机制的理解,从而使教育工作者能够制定量身定制的做法,促进公平获得数学学习机会。
    Racial stereotypes are salient to Black adolescents and to the academic domain of mathematics; however, few studies have examined the socio-cognitive mechanisms through which racial stereotypes impact math achievement. This 2-year longitudinal study (N = 790 Grade 6, 8, and 10 students during Year 1; 50.7% girls and 49.3% boys) investigated (a) the extent to which the endorsement of positively and negatively biased racial stereotypes predicted Black adolescents\' math performance through their cognitive engagement and ability mindset and (b) whether gender and ethnic-racial identity moderated these links. Results suggested that endorsement of negatively biased stereotypes was associated with diminished cognitive engagement and lower math scores across 2 years (p < .05). Additionally, adolescents\' ethnic-racial identity commitment moderated the negative links between stereotype endorsement and math cognitive engagement in Year 2 (p < .05). When considering the mediating role of math ability mindsets, the endorsement of both positively and negatively biased racial stereotypes operated on math performance via its links to stronger fixed ability mindset beliefs in both years (p < .05). Gender also moderated the effects of racial stereotype endorsement on math mindset beliefs in Year 1 (p < .01). This study\'s findings advance the field\'s understanding of the psychosocial mechanisms through which racial stereotypes operate, thus enabling educators to develop tailored practices that facilitate equitable access to math learning opportunities.
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  • 文章类型: Journal Article
    使用以人为本的方法,我们旨在识别不同的执行功能概况,以通过潜在概况分析评估同一学校年级内个体之间的异质性。150名2年级(7-8岁)的样本,150年级6(11-12岁),并对150名10年级(15-16岁)儿童和青少年进行了11种不同的执行任务的评估,这些任务代表了三个主要的执行功能子组件(即,抑制,认知灵活性,和工作记忆),流体智能,处理速度,解决问题,阅读理解。基于抑制的不同互动模式的三种不同执行功能概况,认知灵活性,并确定了年级内和年级之间的工作记忆。此外,这些情况与阅读理解和数学成绩有不同的关系。第二,正如预期的那样,我们没有发现这些数据与社会人口统计学变量如实际年龄或性别相关.尽管如此,流体智能和处理速度与每个等级的不同曲线有不同的关系。我们还发现,执行功能概况与每种认知技能(即,流体智能和处理速度)预测阅读理解和数学成就。这些发现为制定教育预防和干预策略提供了宝贵的见解。
    Using a person-centered approach, we aimed to identify different executive functioning profiles to assess heterogeneity across individuals within the same school grade through latent profile analysis. A sample of 150 Grade 2 (7-8 years old), 150 Grade 6 (11-12 years old), and 150 Grade 10 (15-16 years old) children and adolescents were assessed on 11 different executive tasks representative of the three main executive functioning subcomponents (i.e., inhibition, cognitive flexibility, and working memory), fluid intelligence, processing speed, problem-solving, and reading comprehension. Three different executive functioning profiles of different patterns of interactions based on inhibition, cognitive flexibility, and working memory within and between grades were identified. Moreover, these profiles were differentially related to reading comprehension and mathematical achievement. Second, as expected, we did not find these profiles to be associated with sociodemographic variables such as chronological age or sex. Still, fluid intelligence and processing speed were differentially related to the different profiles at each grade. We also found that the executive functioning profiles interacted with each cognitive skill (i.e., fluid intelligence and processing speed) in predicting reading comprehension and math achievement. These findings provide valuable insights for developing preventive and intervention strategies in education.
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  • 文章类型: Journal Article
    虽然许多学生在学校经历数学焦虑,它发生的上下文还没有得到很好的理解。需要更多地了解可能引发数学焦虑的环境情况,以更好地支持学生的数学成就。使用学科内设计,我们研究了不同数学任务时间的数学焦虑和数学表现的差异(即,公开时机与隐蔽定时)和数学任务复杂性(即,简单vs.复杂问题)与113名四年级(n=38)和五年级(n=75)的学生。ANCOVA结果显示,对于简单(p=.27)和复杂问题(p=.42),在公开和隐蔽的时间条件下,参与者对数学焦虑的报告没有显着差异。然而,参与者报告说,与从事简单数学任务相比,从事复杂数学任务时的数学焦虑水平更高(p=.01).研究结果还表明,在隐蔽的时间条件下完成复杂的数学问题时,具有中等到高基线数学焦虑的参与者更有可能报告更高水平的数学焦虑,p=.02,η2=0.13。讨论了对实践和未来研究的启示。
    Although many students experience math anxiety in school, the contexts in which it occurs are not well-understood. Increased understanding of the environmental situations that might elicit math anxiety is needed to better support students\' math achievement. Using a within-subjects design, we examined differences in math anxiety and math performance across math task timing (i.e., overt timing vs. covert timing) and math task complexity (i.e., simple vs. complex problems) with 113 fourth- (n = 38) and fifth-grade (n = 75) students. ANCOVA results showed no significant differences in participant reporting of math anxiety between overt and covert timing conditions for both simple (p = .27) and complex problems (p = .42). However, participants reported higher levels of math anxiety when working on complex math tasks compared to working on simple math tasks (p = .01). Findings also showed that participants with medium to high baseline math anxiety were more likely to report higher levels of math anxiety when completing complex math problems under the covert timing condition, p = .02, η2 = 0.13. Implications for practice and future research are discussed.
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  • 文章类型: Journal Article
    早期数字技能代表了儿童认知发展的关键里程碑,并在各种情况下与数量和数字互动多年来形成。几个连接主义计算模型试图模仿如何学习某些数字概念,代表,并在大脑中处理。然而,这些模型主要使用高度简化的输入,并专注于有限的任务。我们在两个方向上扩展以前的工作:首先,我们在具有多模态视觉和语言输入的合成环境中对视频演示进行端到端的模型训练。第二,我们使用35个任务的更全面的数据集,涵盖枚举,设置比较,符号数字,和序列化。模型获取任务的顺序反映了输入长度和可变性,由此产生的轨迹大多符合教育心理学的发现。经过训练的模型还显示符号和非符号大小和距离效果。利用可解释性研究的技术,我们研究了基于注意力的模型如何集成跨模态表示并将它们绑定到特定于上下文的关联网络中以解决不同的任务。我们比较了在有和没有符号输入的情况下训练的模型,发现纯非符号模型采用了更多的处理密集型策略来确定集合大小。
    Early number skills represent critical milestones in children\'s cognitive development and are shaped over years of interacting with quantities and numerals in various contexts. Several connectionist computational models have attempted to emulate how certain number concepts may be learned, represented, and processed in the brain. However, these models mainly used highly simplified inputs and focused on limited tasks. We expand on previous work in two directions: First, we train a model end-to-end on video demonstrations in a synthetic environment with multimodal visual and language inputs. Second, we use a more holistic dataset of 35 tasks, covering enumeration, set comparisons, symbolic digits, and seriation. The order in which the model acquires tasks reflects input length and variability, and the resulting trajectories mostly fit with findings from educational psychology. The trained model also displays symbolic and non-symbolic size and distance effects. Using techniques from interpretability research, we investigate how our attention-based model integrates cross-modal representations and binds them into context-specific associative networks to solve different tasks. We compare models trained with and without symbolic inputs and find that the purely non-symbolic model employs more processing-intensive strategies to determine set size.
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  • 文章类型: Journal Article
    儿童时期接触铅对儿童健康有害。铅暴露与小学学业成绩之间的关联在地理上的差异尚不清楚。
    使用允许BLL和考试成绩之间的关联在社区之间的空间变化的模型,估计血铅水平(BLL)与北卡罗来纳州的阅读和数学中的四年级标准化考试成绩之间的关联。
    我们链接地理编码,个人层面,北卡罗莱纳州公立学校学生四年级(2013-2016年)的标准化考试成绩数据,以及从北卡罗莱纳州儿童血铅状态登记处检索的详细出生记录和血铅检测数据,样本通常在1-6岁时收集.BLL分类为:1μg/dL(参考),2μg/dL,3-4μg/dL和≥5μg/dL。然后,我们拟合包含信息共享(平滑度)的空间变化系数模型,通过高斯马尔可夫随机场跨相邻社区,以提供BLL和测试分数之间关联的全局估计,以及人口普查道特定的估计(即,空间系数)。针对母体和儿童水平的协变量调整的模型,分别适用于阅读和数学。
    分析数据集中91,706个个体的平均BLL为2.84μg/dL。个人分布在北卡罗来纳州的2,002(在2,195)个人口普查区域中。在适应儿童性别的模型中,胎龄的出生体重百分位数,和医疗补助参与以及孕产妇种族/种族,教育程度,婚姻状况,和烟草的使用,2μg/dL的BLLs,3-4μg/dL和≥5μg/dL与-0.28的总体较低阅读测试得分相关[95%置信区间(CI):-0.43,-0.12],-0.53(-0.69,-0.38),和-0.79(-0.99,-0.604),分别。对于1μg/dL的BLL,2μg/dL,3-4μg/dL和≥5μg/dL,空间系数-也就是说,阅读测试分数相对于“全局”系数的特定调整范围分别为-9.70至2.52,-3.19至3.90,-11.14至7.85和-4.73至4.33。数学的结果与阅读的结果相似。
    铅暴露与阅读和数学考试成绩之间的关联在北卡罗来纳州社区中表现出相当大的异质性。这些结果强调了对各地铅暴露的预防和缓解努力的必要性,特别注意认知影响升高的地方。https://doi.org/10.1289/EHP13898.
    UNASSIGNED: Exposure to lead during childhood is detrimental to children\'s health. The extent to which the association between lead exposure and elementary school academic outcomes varies across geography is not known.
    UNASSIGNED: Estimate associations between blood lead levels (BLLs) and fourth grade standardized test scores in reading and mathematics in North Carolina using models that allow associations between BLL and test scores to vary spatially across communities.
    UNASSIGNED: We link geocoded, individual-level, standardized test score data for North Carolina public school students in fourth grade (2013-2016) with detailed birth records and blood lead testing data retrieved from the North Carolina childhood blood lead state registry on samples typically collected at 1-6 y of age. BLLs were categorized as: 1μg/dL (reference), 2μg/dL, 3-4μg/dL and ≥5μg/dL. We then fit spatially varying coefficient models that incorporate information sharing (smoothness), across neighboring communities via a Gaussian Markov random field to provide a global estimate of the association between BLL and test scores, as well as census tract-specific estimates (i.e., spatial coefficients). Models adjusted for maternal- and child-level covariates and were fit separately for reading and math.
    UNASSIGNED: The average BLL across the 91,706 individuals in the analysis dataset was 2.84μg/dL. Individuals were distributed across 2,002 (out of 2,195) census tracts in North Carolina. In models adjusting for child sex, birth weight percentile for gestational age, and Medicaid participation as well as maternal race/ethnicity, educational attainment, marital status, and tobacco use, BLLs of 2μg/dL, 3-4μg/dL and ≥5μg/dL were associated with overall lower reading test scores of -0.28 [95% confidence interval (CI): -0.43, -0.12], -0.53 (-0.69, -0.38), and -0.79 (-0.99, -0.604), respectively. For BLLs of 1μg/dL, 2μg/dL, 3-4μg/dL and ≥5μg/dL, spatial coefficients-that is, tract-specific adjustments in reading test score relative to the \"global\" coefficient-ranged from -9.70 to 2.52, -3.19 to 3.90, -11.14 to 7.85, and -4.73 to 4.33, respectively. Results for mathematics were similar to those for reading.
    UNASSIGNED: The association between lead exposure and reading and mathematics test scores exhibits considerable heterogeneity across North Carolina communities. These results emphasize the need for prevention and mitigation efforts with respect to lead exposures everywhere, with special attention to locations where the cognitive impact is elevated. https://doi.org/10.1289/EHP13898.
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  • 文章类型: Journal Article
    背景:本研究旨在调查与算术任务中的跨文化差异相关的认知和情感因素。
    方法:从中国和意大利招募了404名三年级和四年级学生来完成精确的算术运算,算术估计和认知任务(即,短期记忆,执行功能,和流体推理)。他们的数学焦虑也被测量。
    结果:结果显示,中国儿童在算术任务和轮班任务中的表现均优于意大利儿童。意大利儿童在视觉空间更新任务中表现更好,数学焦虑水平高于中国同龄人。多组路径分析显示,认知因素之间的关系模式(即,短期记忆,抑制和移位),数学焦虑,各组的算术性能相似。唯一的例外是,视觉空间更新唯一地预测了中国人的算术估计,而不是意大利儿童的算术估计。
    结论:中国儿童在精确算术任务中的表现优于意大利同龄人,可能是由于在中国数学教育中更加强调算术流畅性,在学校和家里。在算术估计任务中,他们也比意大利同行略有优势。在中国儿童而不是意大利儿童中发现的更新和算术估计之间的独特联系表明,尽管在这两个国家的课程中都没有强调算术估计,精确算术的指导和练习可以提高中国儿童解决算术估计问题的效率。
    BACKGROUND: This study aimed to investigate the cognitive and affective factors associated with cross-cultural differences in arithmetic tasks.
    METHODS: A total of 404 third- and fourth- graders were recruited from China and Italy to complete exact arithmetic, arithmetic estimation and cognitive tasks (i.e., short-term memory, executive functions, and fluid reasoning). Their mathematical anxiety was also measured.
    RESULTS: The results showed that Chinese children performed better than Italian children in both arithmetic tasks and in shifting task. Italian children performed better in visuospatial updating task and reported higher levels of mathematical anxiety than their Chinese peers. Multi-group path analyses showed that the patterns of relations among cognitive factors (i.e., short-term memory, inhibition and shifting), mathematical anxiety, and arithmetic performance were similar across groups. The only exception was that visuospatial updating uniquely predicted arithmetic estimation for Chinese but not for Italian children.
    CONCLUSIONS: Chinese children outperformed their Italian peers in the exact arithmetic task, likely due to the greater emphasis on arithmetic fluency in Chinese mathematics education, both in schools and at home. They also had a slight advantage than Italian peers in the arithmetic estimation task. The unique link between updating and arithmetic estimation found in Chinese children but not Italian children suggests that, although arithmetic estimation is not emphasized in the curricula of either country, instruction and practice in exact arithmetic may enhance Chinese children\'s efficiency in solving arithmetic estimation problems.
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  • 文章类型: Journal Article
    借鉴自我控制的自我调节强度模型,这项研究考察了精疲力竭与STEM注意过程之间的关系(科学,技术,工程,和数学)学生。使用STEM参与者的数据,职业倦怠被发现与更高水平的非任务思维有关,也被称为走神。Further,自我控制在倦怠和思想游荡之间的关系中起着中介作用,因此,较高的倦怠水平预示着自我控制较差,从而增加了思想游荡的倾向。此外,正念缓冲了倦怠和走神之间的关系,以至于倦怠对那些正念低下的学生的注意力产生了最有害的影响。使用约翰逊-尼曼方法,结果揭示了正念调节作用的上限。在STEM背景下,为学生提供了特殊的基础,讨论了科学和实践的结果和含义。
    Drawing on self-regulatory strength models of self-control, this research examined the relationship between burnout and attentional processes for STEM (science, technology, engineering, and mathematics) students. Using data from participants in STEM, burnout was found to be associated with higher levels of off-task thinking, also known as mind-wandering. Further, self-control acted as a mediator in the relationship between burnout and mind-wandering such that higher levels of burnout predicted poor self-control that subsequently increased the mind\'s tendency to wander. Additionally, mindfulness buffered the relationship between burnout and mind-wandering such that burnout had the most detrimental impact on attention for those students who were low in mindfulness. Using the Johnson-Neyman approach, results reveal the upper limits for the moderating impact of mindfulness. Results and implications for science and practice are discussed with a special grounding for students in the STEM context.
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  • 文章类型: Journal Article
    在这种探索性混合方法分析学生对STEM专业入门STEM课程的理解中,我们要求学生对他们的班级进行评分,并提供对他们的评分的开放文本解释。分析1930年的定性响应,得出了一个包含学术的码本,身份,和非特定类别。大多数回答(>80%)引用了学术因素,例如学生与教师之间的互动或课程要素和政策。大多数学术回应与基于证据的教学实践相结合,促进包容,描述一系列的策略和政策教师可以实施,以提高学生的包容性的看法。少数学生的回答表明,他们对课程所需知识背景的看法影响了课程的包容性。在所检查的亚组之间发现频率分布的差异很少(性别,种族和民族,自我报告的包容得分,和纪律)。此外,在三门课程中追踪学生的子集(135名)发现,大多数(80%)引用了影响他们对每门课程的包容性的不同因素。这表明学生对包容性实践的看法是复杂的,大多数学生认识到影响他们融入的多种因素。总的来说,我们的研究结果表明,教师可以通过使用多种包容性教学策略和课程政策来显著影响学生对包容性的看法。
    In this exploratory mixed-methods analysis of students\' perceptions of inclusion in introductory STEM courses for STEM majors, we asked students to rate inclusion in their class and to provide an open-text explanation of their rating. Analyzing 1930 qualitative responses resulted in a codebook containing academic, identity, and nonspecific categories. The majority of responses (>80%) cited academic factors such as interactions between students and instructors or course elements and policies. Most academic responses aligned with evidence-based teaching practices fostering inclusion, describing a range of strategies and policies instructors can implement to increase students\' perceptions of inclusion. A small number of student responses indicated that their perception of the required knowledge background for the course impacted course inclusivity. Few differences in frequency distributions were found between subgroups examined (gender, race and ethnicity, self-reported inclusion score, and discipline). Additionally, tracking a subset of students (135) across three courses revealed that most (80%) cited different factors influencing their perception of inclusion in each course. This suggests students\' perceptions of inclusive practices are complex, and most students recognize multiple factors that influence their inclusion. Overall, our findings suggest instructors can significantly influence students\' perceptions of inclusion by using multiple inclusive teaching strategies and course policies.
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  • 文章类型: Journal Article
    儿童的数学发展依赖于几个潜在的认知功能,包括执行功能(EF),工作记忆(WM),和视觉运动能力,如视觉-运动整合(VMI)。了解这些认知因素如何影响儿童的数学表现对于支持数学学习和长期数学成功至关重要。当前的准实验候补名单对照研究(N=28)旨在(a)检查EF的独特贡献,WM,和VMI对5-8岁有神经发育困难的儿童的数学能力;(b)确定支持这些认知过程的数学干预(数学互动学习经验;MILE)在修改后交付给学校环境中的小组时是否有效,(C)检查是否有任何参与者的特征,比如年龄或智商,与干预后数学分数变化相关。在基线,参与者的数学分数在所有数学内容领域均显著低于标准平均值(ps<.01).EF,WM,和VMI与数学能力高度相关;然而,言语WM是回归分析中数学能力的唯一独特预测因子。与waitlist控制组相比,即时MILE干预组的儿童总体数学成绩显著提高.当所有最终完成干预的儿童一起考虑时,在超过一半的数学内容领域观察到显著改善。此外,在个人层面,85.7%的参与者在至少一个数学内容领域表现出可靠的变化。讨论了支持神经发育困难儿童数学学习的含义。
    Math development in children relies on several underlying cognitive functions, including executive functions (EF), working memory (WM), and visual-motor abilities, such as visual-motor integration (VMI). Understanding how these cognitive factors contribute to children\'s math performance is critical to supporting math learning and long-term math success. The present quasi-experimental waitlist control study (N = 28) aimed to (a) examine the unique contributions of EF, WM, and VMI to math abilities among children ages 5-8 years old with neurodevelopmental difficulties; (b) determine whether a math intervention (the Mathematics Interactive Learning Experience; MILE) that supports these cognitive processes was effective when modified to be delivered to small groups in a school setting, and (c) examine whether any participant characteristics, such as age or IQ, were correlated with post-intervention math score changes. At baseline, participants\' math scores were significantly below the normative mean in all math content areas (ps < .01). EF, WM, and VMI were highly correlated with math ability; however, verbal WM was the only unique predictor of math ability in regressions analysis. Compared to a waitlist control group, children in the immediate MILE intervention group achieved significantly greater math gains overall. When all children who ultimately completed the intervention were considered together, significant improvement was observed in more than half of math content areas. Furthermore, at the individual level, 85.7% of participants showed reliable change in at least one math content area. Implications for supporting math learning in children with neurodevelopmental difficulties are discussed.
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  • 文章类型: Journal Article
    众所周知,一般焦虑与适应性情绪调节的较低使用和适应性情绪调节的较高使用有关。然而,以前没有研究调查认知情绪调节对学业焦虑的影响。使用中学生样本(N=391),这项研究探讨了认知情绪调节对数学和科学焦虑的影响。数学焦虑与适应性情绪调节的相关性强于适应性不良,而一般焦虑与适应不良的相关性比适应性情绪调节更强。分层回归分析表明,数学焦虑与接受的高度使用有关,反省和其他指责,以及积极的重新评估和透视的低使用。然而,控制科学和普遍的焦虑,数学焦虑与大量使用反省和少量使用积极的重新评估有关。相比之下,科学焦虑与接受和其他指责的高度使用以及积极重新评估的低使用有关。重要的是,然而,控制数学和普遍焦虑,那些科学焦虑协会并没有保留。因此,这些结果可能为特异性提供重要的见解,病因学,和数学焦虑的干预。
    It is well-established that general anxiety associates with the lower use of adaptive emotion regulation and the higher use of maladaptive emotion regulation. However, no study has previously investigated the impact of cognitive emotion regulation on academic anxieties. Using a sample of secondary school students (N = 391), this study examined the impact of cognitive emotion regulation on math and science anxieties. Math anxiety showed stronger correlations with adaptive than maladaptive emotion regulation, whereas general anxiety showed stronger correlations with maladaptive than adaptive emotion regulation. Hierarchical regression analyses showed that math anxiety was associated with the high uses of acceptance, rumination and other-blame and the low uses of positive reappraisal and putting into perspective. However, with controlling science and general anxieties, math anxiety was associated with the high use of rumination and the low use of positive reappraisal. In contrast, science anxiety was associated with the high uses of acceptance and other-blame and the low use of positive reappraisal. Importantly, however, with controlling math and general anxieties, those science anxiety associations did not remain. Accordingly, these results might provide important insights for the specificity, etiology, and intervention of math anxiety.
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