In this article we address the historical and epistemological study of infinity as a mathematical concept, focusing on identifying difficulties, counter-intuitive ideas and paradoxes that constituted implicit, unconscious models faced by mathematicians at different times in history, representing obstacles in the rigorous formalization process of…

The present work refers to a study of 10-12-year-old students' ideas on the self- or hetero-luminosity of the Moon. To check the validity of students' reasoning on this question, we also examined their ideas on the lunar phases and how we see hetero-luminous objects. Students supported their ideas on the self- or hetero-luminosity of the Moon by…

Much recent research and theorizing in the field of reasoning has been concerned with intuitive sensitivity to logical validity, such as the logic-brightness effect, in which logically valid arguments are judged to have a "brighter" typeface than invalid arguments. We propose and test a novel signal competition account of this…

Game-based learning has gained significant attention from educational researchers because of its ability to create an engaging and enjoyable learning environment for students. However, there was a research gap regarding the design of game mechanics that specifically helped students understand abstract scientific concepts. Also, the impact of…

We investigate how students make sense of irrational exponents. The data comprise 32 interviews with university students, which revolved around a task designed to examine students' sensemaking processes involved in predicting and subsequently interpreting the shape of the graph of f(x)=x[superscript square root of 2]. The task design and data…

A key component of student mathematics achievement relates to the cognitive domains. This paper examines student mathematics achievement in three cognitive domains (knowledge, comprehension, reasoning) as per different achievement grades, across four years (2015, 2016, 2018, 2019), and by gender. This study used the Caribbean Secondary Education…

Mathematical problems can be divided into two types, namely, process-open and process-constrained problems. Solving these two types of problems may require different cognitive mechanisms. However, there has been only one study that investigated the differences of the cognitive abilities in process-open and process-constrained problem solving, and…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N=435) used a 3-step latent class analysis to examine reasoning about magnitudes on a…

We investigated second and third graders' capacity to understand microevolution, given a learning progression leveraging intuitions to build more adequate explanations, problematizing core ideas within scientific practices, and in-depth study of a single domain (botany or animal behavior). The intervention was implemented in both researcher-taught…

Researchers studying parent-child reminiscing in the preschool years have often focused on parents' and children's elaborative talk (i.e., provision of unique details). The current study proposes a novel conceptualization of parent-child reminiscing narratives by examining 4 levels of abstraction (i.e., a continuum of literal to inferential…

According to one view of linguistic information (Karttunen, 1974; Stalnaker, 1974), a speaker can convey contextually new information in one of two ways: (a) by "asserting" the content as new information; or (b) by "presupposing" the content as given information which would then have to be "accommodated." This…

Using an ethnographic approach, the aim of this study was to explore how social workers learn and make sense of experiences in their daily practices. Five events that took place during an ordinary day of child investigation work are described and serve as the basis for the analysis. The findings imply that investigation work is largely a social…

This mixed-methods study analyzed adolescents' evaluation of the trustworthiness of different kinds of evidence and their reasons for why they trusted (or did not trust) them. Specifically, we analyzed adolescents' rankings of seven kinds of evidence in the abstract and in the context of a settled historical event (school desegregation) and…

Background: Research has identified the core skills that predict success during primary school in reading and arithmetic, and this knowledge increasingly informs teaching. However, there has been no comparable work that pinpoints the core skills that underlie success in science. Aims and method: The present paper attempts to redress this by…