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Curriculum learning--ordering training examples in a sequence to aid machine learning--takes inspiration from human learning, but has not gained widespread acceptance. Static strategies for scoring item difficulty rely on indirect proxy…
The school choice problem concerns the design and implementation of matching mechanisms that produce school assignments for students within a given public school district. Previously considered criteria for evaluating proposed mechanisms…
Studying Mathematics requires a synthesis of skills from a multitude of academic disciplines; logical reasoning being chief among them. This paper explores mathematical logical preparedness of students entering first year university…
The use of games within the classroom is in constant growing, however, there are still demands for better solutions to problems such as reconciling leisure with class or the lack of attention of children. This work demonstrates…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
Studies on software tutoring systems for complex learning have shown that confusion has a beneficial relationship with the learning experience and student engagement (Arguel et al., 2017). Causing confusion can prevent boredom while signs…
Investigations related to expertise in problem solving and ability to transfer learning from one context to another are important for developing strategies to help students perform more expert-like tasks. Here we analyze written responses…
A contract is an economic tool used by a principal to incentivize one or more agents to exert effort on her behalf, by defining payments based on observable performance measures. A key challenge addressed by contracts -- known in economics…
Mathematical modelling (MM) is a key competency for solving complex real-world problems, yet many students struggle with abstraction, representation, and iterative reasoning. Artificial intelligence (AI) has been proposed as a support for…
Teachers intentionally pick the most informative examples to show their students. However, if the teacher and student are neural networks, the examples that the teacher network learns to give, although effective at teaching the student, are…
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair…
Inspired by human learning, researchers have proposed ordering examples during training based on their difficulty. Both curriculum learning, exposing a network to easier examples early in training, and anti-curriculum learning, showing the…
Problem Roulette (PR), an online study service at the University of Michigan, offers points-free formative practice to students preparing for examinations in introductory STEM courses. Using four years of PR data involving millions of…
We present a formula for the norm of an elementary operator on a C*-algebra that seems to be new. The formula involves (matrix) numerical ranges and a kind of geometrical mean for positive matrices, the tracial geometric mean, which seems…
The "Mathematics in Three Acts" approach, proposed by Dan Meyer, aims to transform the teaching of mathematics through a model that encourages active student participation, fostering creativity, problem-solving, and metacognition. This…
In an era where learning is considered a problem, we decided to go for problems for the sake of learning! The purpose of this study was to throw light on the issues involved in two forms of PBL viz., Case Study Based PBL and Research Based…
It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case…
English Language Learners (ELLs) are frequently left on the periphery of classroom interactions. Due to misalignment of language skills, teachers and peers communicate with these students less often, decreasing the number of opportunities…
Recent developments in computer programming and in mathematics suggest that there is a strong case for a new way of introducing programming to enhance the learning of school mathematics. The article describes a collaboration of mathematics…
The aim of this paper is to present a didactical sequence that fosters the development of meanings related to fractions, conceived as numbers that can be placed on the number line. The sequence was carried out in various elementary school…