The role of scientific reasoning in promoting scientific literacy during the early years of schooling is well acknowledged. Using the analytical framework for scientific reasoning skills by A. Opitz et al. (2017, "Educational Research and Evaluation," 23(3-4), 78-101), this multi-age observational study investigated the extent of…

The problem solving performed by students in solving mathematical literacy problems shows that at the developmental stage of proportional reasoning students have different strategies, especially at the developmental stage of functional and scalar relationships. The purpose of this study is to identify and explore the developmental stages of…

Background/purpose: This research aims to classify and show the characteristics of the types of abstract thinking students use when solving mathematical problems. Materials/methods: This descriptive qualitative research was conducted in a structured manner on students of the University of Muhammadiyah Surakarta, Faculty of Teacher Training and…

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…

Future students are confronted with a complex world that demands the ability to solve problems in unstructured, undefined, and unfamiliar situations. The aim of the present study was to investigate the development of problem-solving skills through the implementation of Problem-Based Learning (PBL). While previous research has primarily focused on…

This qualitative case study, grounded within the interpretive paradigm, analyzed the errors and misconceptions made by 11th-grade learners when tackling the tangent-chord theorem task in Euclidean geometry. Studying Euclidean geometry helps learners develop critical thinking skills, such as constructing arguments and applying logical reasoning.…

It is widely agreed that knowing how prospective teachers develop analogical reasoning in solving problems is essential. Problem solving is specific domain that requires particular ways of analogical reasoning skill. The purposes of this study was to reveal the development of analogical reasoning and strategies used by a prospective teacher. The…

Computational Thinking (CT) is a vital skill for digital citizens in the twenty-first Century. Investigating CT skills and their relationships with demographic and educational factors serve as the basis of CT skills cultivation. However, there is limited research focusing on high school students and inconsistent results regarding the relationship…

To reach rational conclusions, we often draw inferences about the evidence that supports one solution over another. This evidence can be "direct" and indicate why one option is correct, or "indirect" and indicate why the alternative option is incorrect. Understanding how young children interpret and use different types of…

Think-aloud protocols are a standard method to study self-regulated learning (SRL) during learning by problem-solving. Advances in automated transcription and large language models (LLMs) have automated the transcription and labeling of SRL in these protocols, reducing manual effort. However, while effective in many emerging applications, previous…

Proportional reasoning has been greatly influencing the development of students' mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students' proportional reasoning in solving the conservation…

Central to conceptual understanding of STEM disciplines is visuospatial processing. Despite its acknowledged role in assuring learners' success, less is known about the underlying reasoning students must employ when solving 3-D problems and the ways in which gaining an understanding of this can inform formative assessment and learning in STEM…

The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…

Teachers have difficulty integrating proof in their mathematics instruction due to both narrow beliefs about proofs and limited understanding of proofs. Indirect proofs seem to be a particular cause for concern. In this exploratory study, we contribute to the research area by reporting on an empirical study of Norwegian pre-service teachers'…

One way to reduce the cognitive load students feel during instruction is to change the way content is delivered. This can be achieved by optimising the instructional sequence and providing sufficient instructional support during problem-solving. However, the literature is unclear regarding whether an inductive or a deductive instructional sequence…