In the article, we prove 18 inequalities involving inradius, a length of one side and one additional element of a given triangle. 14 of these inequalities are the necessary and sufficient conditions for the existence and uniqueness of such a triangle. All proofs are based on standard methods of calculus and can serve as a good demonstration of the…

Eye-tracking (ET) method provides a promising channel for educational researchers to connect learning outcomes to cognitive processes. The main principle of ET is that our gaze and our focus of attention are connected. Due to the advent of digital technologies, eye tracking studies are increasingly growing in different fields and in mathematics…

As artificial intelligence (AI) expands its scope of applications across society, understanding its impact becomes increasingly critical. The OECD's AI and the Future of Skills (AIFS) project is developing a comprehensive framework for regularly measuring AI capabilities and comparing them to human skills. The resulting AI indicators should help…

Large language models (LLMs), such as Codex, hold great promise in enhancing programming education by automatically generating feedback for students. We investigate using LLMs to generate feedback for fixing syntax errors in Python programs, a key scenario in introductory programming. More concretely, given a student's buggy program, our goal is…

Frequent language exposure and use are among the most important conditions for successful language learning, whether in classrooms, during study abroad, or in other informal contexts. Research probing exposure and usage often relies on one-off self-report questionnaires in which participants estimate their typical level of language exposure over…

Our article aims to show how illuminating mathematical work as a concept from didactics of mathematics is useful in understanding issues relating to proving and learning of proof, with or without technology. After posing our hypotheses on the relationship of proof with mathematical work, the pedagogical intent of historical elements of geometry…

The literature provides multiple measures of diversity along a single demographic dimension, but when it comes to studying the interaction of multiple diversity types (e.g. age, gender, and race), the field of useable measures diminishes. We present the use of decision trees as a machine learning technique to automatically identify the…

The archive is a cultural institution that creates a framework for the social and collective memory and as such is one of the collection of knowledge institutions that not only preserves and classifies "texts" but uses them to re-create collective memory and sometimes to invent cultural histories. Like all knowledge institutions, the…

This paper argues that key findings from computer-assisted language learning (CALL) research need to be replicated to permit the construction of a valid and reliable evidence-base which can inform the design of future CALL software and activities, together with language teachers' decisions about their adoption. Through the critical examination of…

Calls for replication studies are becoming more frequent, and Computer Assisted Language Learning (CALL) has now reached sufficient maturity to offer numerous studies that lend themselves to replication. Realistic and successful replications rely on transparency in terms of data, results, and methodology. Two published studies in the area of…

Factor analysis has been frequently exploited in applied research to provide evidence about the underlying factors in various measurement instruments. A close inspection of a large number of studies published in leading applied linguistic journals shows that there is a misconception among applied linguists as to the relative merits of exploratory…

Houston's experience with the Educational Value-Added Assessment System (R) (EVAAS) raises questions that other districts should consider before buying the software and using it for high-stakes decisions. Researchers found that teachers in Houston, all of whom were under the EVAAS gun, but who taught relatively more racial minority students,…

The focus of assessment in statistics has gradually shifted from traditional assessment towards alternative assessment where more attention has been paid to the core statistical concepts such as center, variability, and distribution. In spite of this, there are comparatively few assessments that combine the significant three types of statistical…

This paper argues that pedagogic efficacy of multimedia packages (interactive multimedia presentations) cannot be achieved by experimental research in the absence of a detailed pedagogical screenwriting framework. Following a summary of relevant literature, such a framework is offered, consisting of micro-level design guidelines. The guidelines…

The objective of this article is to illustrate that text mining and qualitative research are epistemologically compatible. First, like many qualitative research approaches, such as grounded theory, text mining encourages open-mindedness and discourages preconceptions. Contrary to the popular belief that text mining is a linear and fully automated…