Mathematical ideas are developed and spread during argumentative whole class discussions between a teacher and her students. The goal of the current study is to characterize how ideas about quadratic functions emerge and are spread during a whole-class discussion among ninth graders. To this end, we recorded both discussions between pairs of…

In their recent article on teachers' proportional reasoning, Copur-Gencturk et al. (2022) draw attention to a type of strategy that they call "relative", lodged right between additive and multiplicative thinking. This strategy raised interest in our research team, as it aligned well and helped give stronger meaning to some strategies…

Research has identified some sources of student difficulty in understanding the horizontal translation of a function. The present study presents and focuses on another source for the difficulties: student conceptions of symbols involved in the horizontal translation of the graph of a function. We explored which student conceptions of the symbols…

Many science students struggle with using scientific language and making sense of scientific phenomena. Thus, there is an increased interest in science education research and public policy with regard to understanding and promoting scientific language use and sensemaking in science classrooms. However, there is a lack of comparative studies on how…

The most famous equation in physics, E = mc[superscript 2], is rarely introduced in middle school physics curricula. Recent research has shown that teaching Einsteinian concepts at the middle school level is feasible and beneficial. This paper analyses an Einsteinian energy teaching module for Year 8 students (13-14 years old), which encompasses…

It is important for students to develop a relational understanding of the equal sign, but students often have simultaneous operational and relational conceptions (i.e., SOR conceptions). This case study carefully explored how a student's conception of the equal sign changed during a classroom teaching experiment and analyzed the possibilities and…

This study contributes to the understanding of the relationship between emotions and development of scientific understanding by examining (1) how students perform in scientific sensemaking in the context of a three-cycle predict-observe-explain (POE) activity, (2) what kind of trajectories of situational epistemic emotions students show when…

In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students' concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition--concept image as reported by Tall and Vinner ("Educational Studies in Mathematics" 12:151-169, 1981), a…

This study used fraction number line estimation tasks to evaluate students' developmental patterns, and the relationship of such tasks with whole number bias was explored. In total, 189 fourth-grade students in a northern Taiwan elementary school were followed over 2 years. The results demonstrated that the students' fraction learning development…

An ability to engage in system thinking is necessary to understand complex problems. While many pre-college students use system modeling tools, there is limited evidence of student reasoning about causal relationships that interact in diverging and converging chains, and how these affect system behavior. A chemistry unit on gas phenomena was…

Cosmology concepts encompass complex spatial and temporal relations that are counterintuitive. Cosmology findings, because of their intrinsic interest, are often reported in the public domain with enthusiasm, and students come to cosmology with a range of conceptions some aligned and some at variance with the current science. This makes cosmology…

This qualitative case study investigated how computational models can help students engage in scientific practice and influence their emotional, epistemic, and conceptual aspects. Twenty-four sixth-graders were guided to conduct scientific practices as they predicted and modified the computational models on food web using StarLogo Nova. Three…

Previous research has shown that students form fragmented understandings about variability even after instruction and that these primitive notions function as obstacles to a robust understanding of variability. To investigate the effect of disruptions to students' primitive notions of variability, we examined undergraduate students' reasoning…

This study aimed to determine the effect of the model-based science writing heuristic (M-SWH) approach on students' conceptual understanding and construction of model-based argumentations in elementary school science. Participants (N = 107) were students enrolled in 4 fourth-grade classes of a public elementary school. Two classes were assigned as…

External representations such as diagrams often appear in teachers' repertoire of pedagogical tools to support students' conceptual learning and problem-solving activities. The study of diagrams and diagrammatic representations has received growing interest from diverse disciplines. Diagrams remain a central feature of science, technology,…