Researchers have identified many ways that students think about rectangular area. However, research about students' understanding of triangle area is relatively scarce. Although it may seem simple to apply the triangle area formula, there is more to students' understanding of triangle area. In this dissertation, I obtained data to help answer the…

[This paper is part of the Focused Collection on Qualitative Methods in PER: A Critical Examination.] Identifying student ideas about particular physics topics is one of the earliest and longest-standing foci of physics education research. This paper presents a method for identifying common conceptual resources for understanding physics, using…

Problem-based STEM education can be defined as the solving of real-life problems by using science, technology, engineering, and mathematics disciplines. This study aims to determine the effect of problem-based STEM practices on pre-service teachers' conceptual understanding. The pre-service science teachers participated in 12 weeks of STEM…

The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

Videos are an increasingly popular medium for supporting learning in various educational settings. Nowadays, newly designed video-based environments contain enhanced tools that allow for specific interactions with video materials (such as adding annotations and hyperlinks) which may well support generative learning and conceptual understanding.…

Explaining is a vital spontaneous process for human beings, as through explanations we make sense of the surrounding phenomena. While the role and structure of explanations have been explored in each science, technology, engineering and mathematics (STEM) area, little is still known regarding what counts as a good explanation for a STEM problem.…

Making sense of algebraic expressions in context is multifaceted and extends beyond representing real-world situations using algebra. As part of Project MathTalk, the authors created videos that feature a pair of Grade 9 algebra 1 students coming to understand algebraic expressions in context. The students found three aspects of making sense of…

This qualitative research study explored levels of social presence in Second Life (virtual world) associated with phases of knowledge construction. The study explored images and data collected from users at two discussion-based activities. The findings revealed the three levels of social presence, according to the Interactional Process Model of…

The article describes a study carried out on pupils aged 12-13 with no prior programming experience. The study examined how they learn to use loops with a fixed number of repetitions. Pupils were given a set of programming tasks to solve, without any preparatory or accompanying instruction or explanation, in a block-based visual programming…

Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…

The development of the mathematical concept of the infinite, through the reflections that arise from personal notions and perceptions and the analysis of some ideas of Galileo and Cantor, invites us to investigate the relationship between intuition and formalization for the understanding of the said concept. This paper aims to observe and describe…

Numerous activities and measures can be observed in the context of digitization. However, these are often not interrelated or sufficiently anchored institutionally and structurally with regard to overarching goals. The aim of this study is therefore to carry out a theory-based clustering of connotations with the concept of digit(al)ization in…

Magnetic molecular models help students explore molecular structures and interactions. In this study, we investigated how pairs of students used magnetic models to explore hydrogen bonding and the 6-fold symmetry of snowflakes. Fourteen first-year students enrolled in a chemistry unit participated in pairs. Students' interactions with the magnetic…

The rapid growth of personal electronics has promoted a surge of e-waste worldwide. Among the e-waste stream, waste printed circuit boards (WPCBs) contain a lot of recyclable valuable metals that can incentivize the recycling operation when recovered. This pedagogical exercise demonstrates a simple electrocatalytic metal recovery strategy that…

Preservice teachers (PSTs) are expected to possess a relational understanding (i.e., knowing how to do and why) of mathematics for ambitious instruction. This study aimed to shed some light on the possibilities of supporting PSTs' development of relational understanding of fractions through engaging them in writing collective argumentation.…