Capacities for abstract thinking and problem-solving are central to human cognition. Processes of abstraction allow the transfer of experiences and knowledge between contexts helping us make informed decisions in new or changing contexts. While we are often inclined to relate such reasoning capacities to individual minds and brains, they may in…

This paper reports the statistical and probabilistic reasoning of young children in terms of randomness, variability, and data representations in the context of informal inferential reasoning (IIR). Using the IIR approach, a task was designed and conducted one-on-one with 28 children aged 5 to 6 years old, in a case study setting. The researcher…

The construct of static and emergent shape thinking (Moore & Thompson, 2015) characterizes differences in students' reasoning about graphs. In our previous work with middle school students, we found that this construct may also be useful in characterizing students' reasoning about other representations such as simulations and tables. In this…

There is growing interest in the construct of "transduction", first introduced by (Kress, Cope and Kalantzis (eds), Multiliteracies: Literacy learning and the design of social futures pp.153-161, Routledge, 2000), p. 159) to name how meanings in one mode are remade in another. Science educators now broadly agree that students need to…

Moral decisions often involve dilemmas: cases of conflict between competing obligations. In two studies (N = 204), we ask whether children appreciate that reasoning through dilemmas involves acknowledging that there is no single, simple solution. In Study 1, 5- to 8-year-old US children were randomly assigned to a Moral Dilemma condition, in which…

Siegel claimed that teachers are obliged to provide grounds whenever demanded, as a result of which they must be able to subject to scrutiny whatever they teach. In this paper, however, and taking as a reference Wittgenstein's "On Certainty," it is shown that such a demand cannot work for second language teachers because their main task…

Education researchers are deeply interested in understanding the way students organize their knowledge. Card sort tasks, which require students to group concepts, are one mechanism to infer a student's organizational strategy. However, the limited resolution of card sort tasks means they necessarily miss some of the nuance in a student's strategy.…

While research on the opportunity to learn about mathematics concepts provided by textbooks at the secondary level is well documented, there is still a paucity of similar research at the undergraduate level. Contributing towards addressing this knowledge gap, the present study examined opportunities to engage in quantitative and covariational…

Mechanical reasoning is crucial for many engineering fields, yet undergraduate engineering students struggle to understand discipline-specific formalisms from their courses that model mechanical concepts. The current investigation observed undergraduate engineering students' speech during mechanical reasoning and the benefits of attending to…

A common feature of many assessment plans is the use of multiple-choice questions. Although there are criticisms of multiple-choice questions, this assessment format is here to stay--multiple-choice questions are effective means of evaluation in large classes, central to many licensing and entry exams, used in most adaptive learning platforms, and…

Mechanistic reasoning about an artifact or system involves thinking about its underlying entities and the properties, activities, and cause-effect relationships of those entities. Previous studies of children's mechanistic reasoning about engineering solutions have mostly focused on specific mechanical systems such as gear trains. Yet there is…

This article reviews the embodied theoretical basis for the meaningful learning of abstract vocabulary and reviews selected educational programs that are theoretically based and have both success and promise for abstract vocabulary development. Abstract vocabulary is a mainstay of academic vocabulary, but its nature and educational development are…

In recent years, big data has become ubiquitous in our day-to-day lives. Therefore, it is imperative for educators to integrate nontraditional (big) data into statistics education to ensure that students are prepared for a big data reality. This study examined graduate students' expressions of uncertainty while engaging with traditional and…

We explore how the concept of abstraction, which is central to mathematical activity, can lead to detachment or attachment to land, nature, culture, language, and heritage in Indigenous contexts. We wonder if students detach themselves from mathematics because they feel mathematics asking them to detach themselves from people and places to whom…

Angularity is a persistent quantity throughout K-12+ school mathematics, and many studies have shown that individuals often conflate angularity with linear attributes (e.g., the length of an angle model's sides). However, few studies have examined the productive ways in which students might reason about angularity while attending to linear…