There are ongoing efforts to understand female adolescents' motivation in math, as part of the science, technology, engineering, and math fields. The current study aimed to examine the temporal relations among expectancies, task values (intrinsic and utility value), and perceived costs (emotional and effort cost) in math to understand the underlying motivational processes for math-related career intention and achievement among middle school girls. To this end, we collected responses from 638 Korean middle school girls three separate times within a year. The autoregressive cross-lagged results revealed that there was no reciprocal relationship between expectancies and task values, but there appeared to be unidirectional positive prediction paths from utility value to self-efficacy. Regarding the costs, there were reciprocal relations between intrinsic value and emotional cost, which negatively affected each other. Consequently, utility value indirectly enhanced girls' math achievement by fostering self-efficacy, whereas emotional cost indirectly hindered their career intentions in math by dampening their intrinsic value. These findings suggest that it is important not only to increase task values, but also to manage costs to help adolescent girls adhere to their math-related career goals.

作为科学、技术、工程和数学领域的一部分，目前正在努力了解女性青少年的数学动机。目前的研究旨在检查数学中的期望、任务价值（内在价值和效用价值）和感知成本（情感和努力成本）之间的时间关系，以了解初中女生与数学相关的职业意向和成就的潜在动机过程. 为此，我们在一年内分三次收集了 638 名韩国中学女生的回复。自回归交叉滞后结果显示，期望值和任务值之间没有相互关系，但似乎存在从效用值到自我效能的单向正向预测路径。关于费用，内在价值和情感成本之间存在相互关系，相互产生负面影响。因此，效用价值通过培养自我效能感间接提高了女孩的数学成绩，而情感成本通过抑制内在价值间接阻碍了她们的数学职业意向。这些研究结果表明，不仅要增加任务价值，而且要管理成本以帮助青春期女孩坚持与数学相关的职业目标。