While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns,…

This study analyzes the mathematical knowledge of 40 preservice Chilean Early Childhood and Primary Education teachers when designing mathematical tasks on patterns, in the context of teaching early algebra. Based on the domains of the Mathematical Knowledge for Teaching (MKT) model, we have adopted a descriptive qualitative methodological…

Hands-on cybersecurity training allows students and professionals to practice various tools and improve their technical skills. The training occurs in an interactive learning environment that enables completing sophisticated tasks in full-fledged operating systems, networks, and applications. During the training, the learning environment allows…

Knowing what kinds of patterns are easy for children to recognize early in their kindergarten year, and what kinds are difficult, can be a useful guide for patterning instruction. Hence, the ability of children to recognize complex patterns early in their kindergarten year was assessed in two experiments. One experiment showed that the children…

Transform mathematics instruction with the comprehensive mathematical competencies (CMC) framework--a research-based model that integrates seven essential competencies: conceptual and procedural integration, problem solving, logical reasoning, communication, tool use, pattern recognition, and student engagement. Through practical classroom…

Mathematical and computational thinking (CT) are closely interrelated, yet CT integration into mathematics instruction remains limited. This study aims to analyze the effectiveness of the teaching process for straight-line equations in enhancing students' CT skills and to propose improvements based on the findings. A qualitative case study…

Contract cheating is a major problem in Higher Education because it is very difficult to detect using traditional plagiarism detection tools. Digital forensics techniques are already used in law to determine ownership of documents, and also in criminal cases, where it is not uncommon to hide information and images within an ordinary looking…

Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…

MOOCs can be considered as a powerful alternative in extraordinary situations where people cannot reach formal education. In recent years, the widespread use of the internet worldwide and especially the COVID-19 has increased the need of people for MOOCs. However, in order to increase the effectiveness of MOOCs, and to provide a better learning…

Mathematically gifted students have a potential for understanding and connecting mathematics concept. Pattern generalization as a part of functional thinking becomes one of the benchmarks for gifted students in mathematics. The mathematics curriculum in Indonesia that has not accommodated the functional thinking ability of elementary school…

Everyone agrees that infants possess general mechanisms for learning about the world, but the existence and operation of more specialized mechanisms is controversial. One mechanism--rule learning--has been proposed as potentially specific to speech, based on findings that 7-month-olds can learn abstract repetition rules from spoken syllables (e.g.…

Purpose: A large body of literature showed that word reading and listening comprehension-two proximal predictors of reading comprehension according to the simple view of reading -- are related. Grounded on the direct and indirect effects model of reading, we examined the extent to which the relation is explained by domain-general cognitions or…

Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

Background: Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children's ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns. Aims: The present study aimed to explore 4- to 5-year…