The purpose of this study was to investigate university students' conceptions of the definite integral in the process of finding the volume of a solid of revolution. The participants were four students enrolled in a university calculus course in Turkey. Data were obtained by task-based interviews, in which the participants had to work on a problem…

This study used task-based interviews to examine students' reasoning about multivariable optimization problems in a volume maximization context. There are four major findings from this study. First, formulating the objective function (i.e. the function whose maximum or minimum value(s) is to be found) in each task came easily for 15 students who…

Background and Context: Block-based programming is a popular approach to teaching introductory programming. Block-based programming often works in the context of microworlds, where students solve specific puzzles. It is used, for example, within the Hour of Code event, which targets millions of students. Objective: To identify design guidelines…

Background: The idea of computational thinking is underpinned by the belief that anyone can learn and use the underlying concepts of computer science to solve everyday problems. However, most studies on the topic have investigated the development of computational thinking through programming activities, which are cognitively demanding. There is a…

Teachers and caregivers use children's books (i.e., trade books) to support mathematics learning in school and home settings; shared book reading offers a unique opportunity to support students' understanding of operations and schema development. No prior studies have examined the representations of addition, subtraction, multiplication, and…

The paper offers three examples of passionate immersion with strange objects and working with peculiar multispecies assemblages, such as the assemblage of a dove called Romeo and the technology to humidify a greenhouse called 'Princess', or the experiment of orienteering in forests for years, accounting for slips, scratches and tumbles as being…

Complex problem solving (CPS) is considered to be one of the most important skills for successful learning. In an effort to explore the nature of CPS, this study aims to investigate the role of inductive reasoning (IR) and combinatorial reasoning (CR) in the problem-solving process of students using statistically distinguishable exploration…

We are all fascinated by loops and their formation in space. When a line cuts itself, it forms an intersection point and creates a space. This is an experimental study done by analyzing several loops, forming a concrete formulation by visualizing the patterns observed, and then proving the formulations proposed using the known standard…

This study aims to explore the influences of the CS-unplugged activities in developing problem solving skills of preschool children. The participants were 11 children (4-5 aged) enrolled in a public preschool and Code.org activities were used as an instructional package. Activity evaluation form and interviews were used to understand children's…

Problems involving the composition of mixtures are common in chemical practice and are thus part of introductory Chemistry courses at the early undergraduate level. However, they are often perceived by students as a rather obscure matter, which may be due to poor familiarity with algebraic manipulations. Furthermore, to increase the distaste of…

Expertise is featured by continued high performance in a particular domain. Expertise research has primarily focused on absolute expertise in structured domains such as chess and emphasized the significance of deliberate practice for expertise development. We investigated the development of relative expertise in commercial domains as part of…

Effective learning is viewed as an evolutionary process, and as such, it involves an expanded version of the Crenshaw-Collins view of "intersectionality." It demands an in-depth view of the complex socio-cultural-ethnic milieu in which students are embedded. Even more, effective learning requires effectance problem-solving, investigation…

A new approach, termed the "scale factor method," is presented for solving a variety of stoichiometry problems. Students taught to solve mass-mass stoichiometry problems using this method found it more intuitive and had a higher rate of success than students using the traditional dimension analysis approach. The scale factor approach…

The purpose of this study was to determine effects of implementing metacognitive practices on the engagement of students in secondary mathematics courses. The study was guided by two primary inquiry questions that focused on the current implementation of metacognitive practices in the mathematics courses as well as the perceived change in student…

Competency in skills associated with collaborative problem solving (CPS) is critical for many contexts, including school, the workplace, and the military. Innovative approaches for assessing individuals' CPS competency are necessary, as traditional assessment types such as multiple-choice items are not well suited for such a process-oriented…