Cover, copy, and compare (CCC) is a study strategy in which students cover their notes, attempt to copy them, and then compare for accuracy. We evaluated whether CCC could be used to establish equivalence classes with undergraduate students. A video training package and experimenter feedback were used to teach participants to engage in CCC with…

Critical thinking is a key transversal competency of the 21st century, but some students have difficulty, especially during the transition to online learning due to the COVID-19 pandemic. This study aims to identify epistemological obstacles in critical thinking related to proof, generalization, alternative answers, and problem-solving. This…

Identifying mathematically gifted students is an important objective in mathematics education. To describe skills typical of these students, researchers pose problems in several mathematical domains whose solutions require using different mathematical capacities, such as visualization, generalization, proof, creativity, etc. This paper presents an…

Algebraic thinking is the ability to generalize about numbers and calculations, find concepts from patterns and functions and form ideas using symbols. It is important to know the student's algebraic thinking process, by knowing the student's thinking process one can find out the location of student difficulties and the causes of these…

This study aimed to investigate prospective middle school mathematics teachers' noticing of students' algebraic thinking based on students' correct and incorrect solutions within the context of pattern generalization. Designed as a qualitative case study, three noticing prompts were asked of thirty-two prospective middle school mathematics…

Capacities for abstract thinking and problem-solving are central to human cognition. Processes of abstraction allow the transfer of experiences and knowledge between contexts helping us make informed decisions in new or changing contexts. While we are often inclined to relate such reasoning capacities to individual minds and brains, they may in…

The aim of this study was to examine how pre-service teachers performed in tasks related to three specific aspects of curricular noticing. The participants completed a two-part written task in which they solved three pattern generalization problems and sequenced them for teaching purposes. Inductive content analysis was used to analyze the…

Infants start to use a spoon for self-feeding at the end of the first year of life, but usually do not use unfamiliar tools to solve problems before the age of 2 years. We investigated to what extent 18-month-old infants who are familiar with using a spoon for self-feeding are able to generalize this tool-use ability to retrieve a distant object.…

Technology offers exciting possibilities for instruction with learners with autism spectrum disorder (ASD), but limited research has evaluated the use of web-based applications (apps) as learning tools for this population. We wondered if using apps would function as a precurrent response to solve problems in the form of questions on a worksheet.…

Gestures--hand movements that accompany speech and express ideas--can help children learn how to solve problems, flexibly generalize learning to novel problem-solving contexts, and retain what they have learned. But does it matter who is doing the gesturing? We know that producing gesture leads to better comprehension of a message than watching…

Given the relevance of graphs of functions, we consider their inclusion in primary education from the functional approach to early algebra. The purpose of this article is to shed some light on the students' production and reading of graphs when they solved generalization problems from a functional thinking approach. We aim to explore how 3rd and…

The study aims to define the processes of pre-service mathematics teachers in reaching spatial visualisation generalisations within the context of drawing surface nets of solids. Two theories, Polya's problem-solving steps and novice-to-expert problem-solving schemas, were used as reference frameworks to describe the participants' spatial…

In order to teach Computational Thinking (CT) skills to young students, Block-Based Programming Environments (BBPEs) are integrated into secondary school computer science (CS) education curricula. As a CT skill, abstraction is one of the prominent skills, which is difficult to enhance and measure. Researchers developed some scales for measuring…

This study aims to analyze the reliability generalization of the computational thinking scale. There are five dimensions of computational thinking: creativity, algorithmic thinking, cooperativity, critical thinking, and problem-solving. A Bonett transformation was used to standardize the reliability coefficient of Cronbach's alpha. A…

Mathematics textbooks sometimes present worked examples as being generated by particular fictitious students (i.e., "person-presentation"). However, there are indicators that person-presentation of worked examples may harm generalization of the presented strategies to new problems. In the context of comparing and discussing worked…