ChatGPT and Bard, two chatbots powered by Large Language Models (LLMs), are propelling the educational sector towards a new era of instructional innovation. Within this educational paradigm, the present investigation conducts a comparative analysis of these groundbreaking chatbots, scrutinizing their distinct operational characteristics and…

In this paper, we investigate how a research mathematician conjectures and proves when conducting her research. To be precise, the aim of this study is to achieve a comprehensive understanding of the way this research mathematician develops these mathematical practices and thus gain insight to improve the teaching and learning of these two…

We present two types of validity evidence to support inferences and decisions about use of easyCBMs in relation to state testing programs. The first type involves the use of Benchmarks in reading to use in making predictions of performance on the Smarter Balanced (SB) test. These predictions can be made both well in advance (several months) or…

Managing crowded classes in terms of classroom assessment is a difficult task due to the amount of time which needs to be devoted to providing feedback to student products. In this respect, the present study aimed to develop an automated essay scoring environment as a potential means to overcome this problem. Secondarily, the study aimed to test…

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…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

It is widely recognized that mathematical typesetting is more difficult than typesetting in most other disciplines due to the need for specialized mathematical notation and symbols. While most mathematicians type mathematical documents using LaTeX, with varying levels of proficiency, students often use other options or handwrite mathematics. Here,…

Since MOOC is suffering high dropout rate, researchers try to explore the reasons and mitigate it. Focusing on this task, we employ a composite model to infer behaviors of learners in the coming weeks based on his/her history log of learning activities, including interaction with video lectures, participation in discussion forum, and performance…

Stepwise program refinement techniques can be used to simplify program verification. Programs are better understood since their main properties are clearly stated, and verification of rather complex algorithms is reduced to proving simple statements connecting successive program specifications. Additionally, it is easy to analyse similar…

In this paper we present a novel, data-driven algorithm for generating feedback for students on open-ended programming problems. The feedback goes beyond next-step hints, annotating a student's whole program with suggested edits, including code that should be moved or reordered. We also build on existing work to design a methodology for evaluating…

The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…

This study aimed to compare 5th graders' scores obtained from Scratch projects developed in the framework of Information Technologies and Software classes via Dr Scratch web tool with the scores obtained from Computational Thinking Levels Scale and to examine this comparison in terms of different variables. Correlational research model was…

This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

The objective of this work is to examine the efficacy of natural language processing (NLP) in summarizing bibliographic text for multiple purposes. Researchers have noted the accelerating growth of bibliographic databases. Information seekers using traditional information retrieval techniques when searching large bibliographic databases are often…

The objective of this research is to validate the algorithm of learning effort which is an indicator of a new real-time and non-interfering based diagnostic technique. IC3 Mentor, the adaptive e-learning platform fulfilling the requirements of intelligent tutor system, was applied to 165 university students. The learning records of the subjects…