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.…

Vertical integration and more generally, corporate-level strategy, are rather difficult for students to grasp, being such abstract concepts. This exercise provides a way for participants to experience issues leading to market failure (and vertical integration) by engaging them as buyers and sellers of a component for very unique car--a limousine…

We evaluated an individually focused version of the CLEAR IDEAS framework for innovation training. One hundred fifty online participants were randomly assigned to either an idea generation training (IDEAS), idea generation plus idea implementation training (CLEAR IDEAS), or a control group. Post-test ratings of the quality of ideas produced and…

We investigated a very long chain falling from the pile on the edge of a table to the floor both experimentally and theoretically. In this very simple and novel configuration we showed that the velocity of the chain quickly converges to its asymptotic value, and that the steady-state velocity is proportional to the square root of the height of the…

Design spaces can be read in two complementary structural and compositional dimensions: the implicit dimension, and the formal dimension. This study aimed to answer the following questions: What are the phases of the original idea transformation in the design process? Does taking advantage of the implicit dimension of others' interior spaces count…

Categorization researchers have long debated the possibility of multiple category-learning systems. The need persists for paradigms that dissociate explicit-declarative category-learning processes (featuring verbalizable category rules) from implicit-procedural processes (featuring stimulus-response associations lying beneath declarative…