The author presents a child-centered approach to teaching, developed through longtime connections with colleagues, which concentrates on the children and provides them time to make their own connections, to learn, to think, and to develop at their own pace with the support of their classmates. Two examples of how mathematics interlaced into…

Self-directed learning is a critical competence for living and working in our increasingly complex and unpredictable world. The concept of self-directed learning grew out of the adult learning field and scholars highlight the need to examine how self-directed learning competence can be fostered during childhood. However, there are very few…

We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise…

To ensure the learning of mathematics, teachers must be able to analyse their students' mathematical practices when solving tasks, interpret the difficulties that students encounter, and decide how to manage students' difficulties. This competence in didactic analysis and intervention allows teachers to adapt their teaching to meet individual…

This study explores the effectiveness of chatbots empowered by generative artificial intelligence (GAI) in assisting university students' creative problem-solving (CPS). We used quasi-experiments to compare the performance of dialogue dynamics, learner perceptions, and practical competencies in CPS during students' interactions with: (1) a GAI…

Purpose: To determine the factors influencing the perception of undergraduate students toward research--teaching nexus and also to examine its impact on the attitude of the students. Design/methodology/approach: The study used a quantitative design to examine the perceptions of students in higher education institutions in India. Descriptive and…

In designing an intelligent tutoring system, a core area of the application of AI in education, tips from the system or virtual tutors are crucial in helping students solve difficult questions in disciplines like mathematics. Traditionally, the manual design of general tips by teachers is time-consuming and error-prone. Generative AI, like…

The need for data-driven decision-making primarily motivates interest in analysing Big Data in higher education. Although there has been considerable research on the value of Big Data in higher education, its application to address critical issues within the sector is still limited. This systematic review, conducted in December 2021 and…

The current paper overviews a nine-month PhD study that investigated the impact of learning mathematics through sequences of challenging tasks on the mathematical competence and attitudes of Year 2 students (n = 59). Adopting a Self-Determination Theory lens, a pragmatist paradigm and a mixed-method design, the study found that at all levels of…

We investigated whether continuously alternating between topics during practice, or interleaved practice, improves memory and the ability to solve problems in undergraduate physics. Over 8 weeks, students in two lecture sections of a university-level introductory physics course completed thrice-weekly homework assignments, each containing problems…

A worked-out or an open inventing problem with contrasting cases can prepare learners for learning from subsequent instruction differently regarding motivation and cognition. In addition, such activities potentially initiate different learning processes during the subsequent ("future") learning phase. In this experiment (N = 45…

Nowadays, students often practice problem-solving skills in online learning environments with the help of examples and problems. This requires them to self-regulate their learning. It is questionable how novices self-regulate their learning from examples and problems and whether they need support. The present study investigated the open questions:…

Empirical evidence demonstrates the effect of productive failure (Kapur, 2008) on disciplinary knowledge. However, there is no clear theoretical explanation for why this is the case. Empirical evidence on argumentation and education shows the impact of curricular embedded deliberative argumentation on learning. However, these two trends of…

Government guidelines are demanding greater educational outcomes and intentional teaching in Australian preschools. The purpose of this paper is to present the results of a study of how children incorporate concepts into child-initiated play. A cohort of 18 children (aged 3.0-5.8, mean age of 4.8) were digitally observed over seven weeks…

Knowledge tracing (KT) is a method to evaluate a student's knowledge state (KS) based on their historical problem-solving records by predicting the next answer's binary correctness. Although widely applied to closed-ended questions, it lacks a detailed option tracing (OT) method for assessing multiple-choice questions (MCQs). This paper introduces…