Related papers: Some instructive mathematical errors
In the spreadsheet error community, both academics and practitioners generally have ignored the rich findings produced by a century of human error research. These findings can suggest ways to reduce errors; we can then test these…
In this chapter, I discuss teaching mathematical tools specifically tailored for economics students. A typical one-semester course in this area seeks to blend a range of topics: from foundational elements of subjects such as linear algebra…
Grammatical error classification plays a crucial role in language learning systems, but existing classification taxonomies often lack rigorous validation, leading to inconsistencies and unreliable feedback. In this paper, we revisit…
During lab studies of text entry methods it is typical to observer very few errors in participants' typing - users tend to type very carefully in labs. This is a problem when investigating methods to support error awareness or correction as…
Most models of machine teaching and learning assume the learner makes no errors in its internal deductive inference. However, humans and large language models in few-shot learning regimes are two important examples of learners where this…
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
The book "A Course in Constructive Algebra" (1988) shows the way of understanding classical basic algebra in a constructive style similar to Bishop's Constructive Mathematics. Classical theorems are revisited, with a new flavour, and become…
The philosophy of mathematical practice (PMP) looks to evidence from working mathematics to help settle philosophical questions. One prominent program under the PMP banner is the study of explanation in mathematics, which aims to understand…
With machine learning models being increasingly used to aid decision making even in high-stakes domains, there has been a growing interest in developing interpretable models. Although many supposedly interpretable models have been proposed,…
Much research on Machine Learning testing relies on empirical studies that evaluate and show their potential. However, in this context empirical results are sensitive to a number of parameters that can adversely impact the results of the…
People use large language models (LLMs) when they should not. This is partly because they see LLMs compose poems and answer intricate questions, so they understandably, but incorrectly, assume LLMs won't stumble on basic tasks like simple…
Many undergraduate students of engineering and the exact sciences have difficulty with their mathematics courses due to insufficient proficiency in what we in this paper have termed clear thinking. We believe that this lack of proficiency…
User studies are paramount for advancing science. However, researchers face several barriers when performing them despite the existence of supporting tools. In this work, we study how existing tools and their features cope with previously…
Computer programs do not always work as expected. In fact, ominous warnings about the desperate state of the software industry continue to be released with almost ritualistic regularity. In this paper, we look at the 60 years history of…
Data errors are widespread in real-world databases and severely impact downstream applications, such as machine learning pipelines or business analytics reports. Causes of such errors are manifold and can arise during both the design phase…
Thanks to their flexibility and capability to perform different tasks and organize data in the best form and format, spreadsheets are widely used in different organizations and by different end users. Many business organizations rely on…
This chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom…
While functional programming is an efficient way to express complex software, functional programming languages have a steep learning curve. Haskell can be challenging to learn for students who were only introduced to imperative programming.…
We carry out a thorough bibliometric analysis of recent publications in mathematics based on the database Web of Science. The individual relations between various features and the citations are provided, and the importance of the features…