Mathematical modeling is a challenging and creative process. If one considers only interim or final solutions to modeling problems or interviews modelers afterward, often only their "explicit" models are accessible -- those expressed in work products or evinced in verbal and written reflections. The inner world of tacit knowledge and its…

A detailed characteristic of teaching and learning approaches used within the new concept of Learning by Being (LBB) is given. The evolution of educational paradigms from Learning by Doing (LBD) and Learning by Understanding (LBU) toward LBB is analyzed. The basic idea of LBB is students' ownership on cognitive goals, or the assumption of learning…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

This paper reports qualitative research on constructing critical thinking scenarios in online legal English classes at a private university in Colombia. This study aimed to enhance law students' critical thinking skills development in EFL (English as a Foreign Language) classroom through virtual tools by implementing a descriptive case analysis.…

The RBC+C abstraction model is an effective model in mathematics education because it gives the opportunity to analyze research data through cognitive actions. For this reason, we aim to examine the abstraction process of the limit knowledge of two volunteer participant students using the RBC+C abstraction model. With this aim, the students'…

Geometric constructions have already been of interest to mathematicians. However, studies on geometric construction are not adequate in the relevant literature. Moreover, these studies generally focus on how secondary school gifted students solve non-routine mathematical problems. The present study aims to examine the geometric construction…

This article reports on an investigation with first year undergraduate Product Design and Management students within a School of Engineering and Applied Science. The students at the time of this investigation had studied fundamental engineering science and mathematics for one semester. The students were given an open ended, ill-formed problem…

Inquiry-based learning (IBL) is a more student-centered approach to mathematics teaching that is recommended by many policy and curriculum documents across Europe. However, it is not easy for teachers to change from a more teacher-centered way of teaching to inquiry-based teaching as this involves a change of their role in class. Professional…

In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers'…

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

This study marries collaborative problem solving and learning study in understanding the onset of a cycle of teacher professional development process within school-based professional learning communities (PLCs). It aimed to explore how a PLC carried out collaborative problem finding--a key process involved in collaborative problem solving--that…

This multiple-case study examined how advanced learners solved a complex problem, focusing on how their frequency and application of cognitive processes contributed to differences in performance outcomes, and developing a mental model of a problem. Fifteen graduate students with backgrounds related to the problem context participated in the study.…

This case study provides an explanatory account on the underachievement of three gifted students studying physics in a Taiwanese university. The students' physics underachievement was diagnosed by Sato's student-problem analysis chart. These students were invited to complete a questionnaire and a follow-up interview in order to (1) understand the…

Learning theory provides a powerful framework for analyzing instructional consultations and increasing their effectiveness. In this paper, the authors review the main tenets of learning theory, apply them to consultation scenarios, and present a complex case study to show how they can guide analysis and problem solving around challenging…

This study addresses the problem of mathematics teachers' resistance to problem-solving models that align with constructivist perspectives because they feel pressure to utilize more teaching approaches that focus on preparing students for high-stakes tests. The purpose of this qualitative study was to explain how ninth grade mathematics students…