This paper explores the influence of Italian high school students'
proficiency in mathematics and the Italian language on their university
enrolment choices, specifically focusing on STEM (Science, Technology,
Engineering, and Mathematics) courses. We distinguish between students from
scientific and humanistic backgrounds in high school, providing valuable
insights into their enrolment preferences. Furthermore, we investigate
potential gender differences in response to similar previous educational
choices and achievements. The study employs gradient boosting methodology,
known for its high predicting performance and ability to capture non-linear
relationships within data, and adjusts for variables related to the
socio-demographic characteristics of the students and their previous
educational achievements. Our analysis reveals significant differences in the
enrolment choices based on previous high school achievements. The findings shed
light on the complex interplay of academic proficiency, gender, and high school
background in shaping students' choices regarding university education, with
implications for educational policy and future research endeavours.

该研究探讨了意大利高中学生在数学和意大利语方面的能力对其大学入学选择的影响，特别关注科学、技术、工程和数学（STEM）课程。研究区分了高中科学和人文背景的学生，提供了对他们的入学偏好有价值的见解。此外，我们还调查了相似的以前教育选择和成就对不同性别学生的影响。研究采用梯度提升方法，该方法在预测性能和捕捉数据中的非线性关系方面表现出色，并且校正了与学生的社会人口特征和先前教育成就相关的变量。我们的分析揭示了根据高中以前的成就而存在的入学选择方面的显著差异。这些发现揭示了学术能力、性别和高中背景在塑造学生有关大学教育选择的复杂交互中的作用，对教育政策和未来研究有重要意义。

通过学生在意大利的高中背景，用机器学习方法预测大学招生选择

A machine learning approach to predict university enrolment choices  through students' high school background in Italy

While computer and communication technologies have provided effective means
to scale up many aspects of education, the submission and grading of
assessments such as homework assignments and tests remains a weak link. In this
paper, we study the problem of automatically grading the kinds of open response
mathematical questions that figure prominently in STEM (science, technology,
engineering, and mathematics) courses. Our data-driven framework for
mathematical language processing (MLP) leverages solution data from a large
number of learners to evaluate the correctness of their solutions, assign
partial-credit scores, and provide feedback to each learner on the likely
locations of any errors. MLP takes inspiration from the success of natural
language processing for text data and comprises three main steps. First, we
convert each solution to an open response mathematical question into a series
of numerical features. Second, we cluster the features from several solutions
to uncover the structures of correct, partially correct, and incorrect
solutions. We develop two different clustering approaches, one that leverages
generic clustering algorithms and one based on Bayesian nonparametrics. Third,
we automatically grade the remaining (potentially large number of) solutions
based on their assigned cluster and one instructor-provided grade per cluster.
As a bonus, we can track the cluster assignment of each step of a multistep
solution and determine when it departs from a cluster of correct solutions,
which enables us to indicate the likely locations of errors to learners. We
test and validate MLP on real-world MOOC data to demonstrate how it can
substantially reduce the human effort required in large-scale educational
platforms.

本文提出了一种基于 “数理语言处理” 的数据驱动框架来自动评分开放性数学问题实现的方案，采用不同聚类方法组成的三层模型对多步解决方案进行追踪和错误定位，并在真实的慕课数据上进行了测试和验证，说明它可以极大地减少大规模教育平台上所需的人力投入。