Facing increased pressure to improve retention and graduation rates, engineering departments are increasingly scrutinizing whether they are getting their desired outcomes from core mathematics coursework. Since mathematics courses are a significant source of attrition and many engineering faculty are unhappy with students’ mathematical abilities, more engineering departments are increasingly looking at drastic options of taking students out of mathematics courses and teaching students mathematics themselves. To mitigate this trend, it may be valuable to better understand what engineering faculty hope students learn from their mathematics coursework. When engineering faculty explain why they require these high-failure prerequisites, many claim that “mathematical maturity”, not calculus skill, is the desired outcome of completing the core math sequence of courses. To better understand what engineering faculty mean by “mathematical maturity”, we conducted a qualitative thematic analysis of how 27 engineering faculty members define “mathematical maturity”. We found that these engineering faculty believed that the mathematically mature student would have strong mathematical modeling skills supported by the ability to extract meaning from symbols and the ability to use computational tools as needed. Faculty frequently lamented that students had underdeveloped epistemic beliefs that undermined their modeling skills, thinking that mathematics is unrelated to the real world and has little practical value. They attributed these dysfunctional epistemic beliefs to their perception that mathematics is too often taught without genuine physical context and realistic examples. We suggest potential avenues for reform that will allow mathematics departments to better serve their client departments in engineering and thus retain control of their courses.

中文翻译：

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工科学生的数学成熟度

面对提高保留率和毕业率的更大压力，工程部门越来越多地在审查他们是否从核心数学课程中获得了预期的成绩。由于数学课程是减员的重要来源，并且许多工程系教师对学生的数学能力不满意，因此越来越多的工程系正在寻求使学生脱离数学课程并自己教学生数学的激烈选择。为了缓解这种趋势，更好地了解工程学院希望学生从数学课程中学到什么可能是有价值的。当工程学院的老师解释为什么他们需要这些高失败的前提条件时，许多人声称“数学成熟度”而不是演算技能，是完成课程核心数学顺序的理想结果。为了更好地理解工程系教师的“数学成熟度”的含义，我们对27位工程系教师如何定义“数学成熟度”进行了定性的主题分析。我们发现这些工程学院的教师相信，数学上成熟的学生将具有强大的数学建模技能，这得益于从符号中提取含义的能力以及根据需要使用计算工具的能力。教师经常感叹学生对数学的认识不足，削弱了他们的建模能力，认为数学与现实世界无关，几乎没有实用价值。他们将这些功能失常的认知信念归因于他们的看法，即人们常常没有真正的物理背景和实际例子来教授数学。我们建议进行改革的潜在途径，使数学系可以更好地为客户部门提供工程服务，从而保持对课程的控制。