Reversibility thinking carried out mentally in mathematical operations has an important role in the process of understanding concepts as it involves developing a thinking process from beginning to end and from end to beginning. This qualitative research aims to describe students' reversible thinking processes in solving algebra problems,…

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking…

Productive struggle (PS) has emerged as a critical construct in mathematics education, emphasizing the importance of persistence, cognitive engagement, and conceptual understanding in problem-solving. However, inconsistencies in its conceptual and operational definitions have hindered its effective implementation and assessment. This study…

In mathematics education, representations are used in place of mathematical structures, ideas, or relationships to concretize, transform, and represent them. When students interact with these representations, they engage in various cognitive activities such as thinking, reasoning, understanding, remembering, problem-solving, attention, and…

How can we prepare students for a world where data-driven decision-making shapes nearly every aspect of life? "Data Minds: How Today's Teachers Can Prepare Students for Tomorrow's World" helps K-8 educators infuse data literacy into everyday lessons across disciplines, without overwhelming existing curricula. Data literacy is an ability…

This study sought to understand how students activate number sense in determining the position of fractions on a number line and identify how the natural number bias and number sense influences students' thinking processes. The study utilized the Cognitive Task Analysis (CTA), involving four fifth-grade elementary students as the research…

Background/purpose: This study investigates the effectiveness of Problem-Based Learning (PBL) integrated with scaffolding in enhancing problem-solving skills among students with varying levels of prior knowledge. The main objective is to determine how scaffolding, when combined with PBL, can support students in developing stronger problem-solving…

The ability of solving problems collaboratively has been increasingly significant. This research takes mathematics open-ended problems as the tasks and carries out collaborative problem solving with multi-machine video recording in the classroom environment aimed at 112 student pairs and 56 four-person student groups stemming from 224 students in…

Studies have demonstrated that task-evoked pupillary responses (TEPRs) can be adopted to measure the examinee's cognitive load. This study compared three approaches for the measurement of TEPRs, mean pupil diameter, mean pupil dilation, and mean percentage of pupil dilation, to determine the best-fit measuring method. The valid participants of…

Digital game-based learning (DGBL) has emerged as an effective strategy to enhance students' learning effectiveness. Concept mapping, recognized as a valuable tool for knowledge construction, has been widely implemented in educational settings. However, research indicates challenges when integrating concept maps into games, particularly when the…

Even after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the…

Most research has focused solely on understanding high school or college students' mathematical creative thinking abilities while understanding younger students' creative thinking in mathematics was ignored. These studies of older students have focused mainly on students' creative products rather than creative processes. The authors of the present…

Many students persistently misinterpret histograms. This calls for closer inspection of students' strategies when interpreting histograms and case-value plots (which look similar but are different). Using students' gaze data, we ask: "How and how well do upper secondary pre-university school students estimate and compare arithmetic means of…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

Prior work has established that cognitive and perceptual processes influence students' attention to notational structures in mathematical expressions, which in turn affects their problem-solving approaches and performance. Advances in educational technology provide opportunities to further investigate these processes, improve student learning, and…