Using a mixed methods approach, we explore a relationship between students' graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers,…

The importance of introducing students to mechanistic reasoning (MR) early in their schooling is emphasised in research. The goal of this case study was to contribute with knowledge on how early primary students' (9-10 year-olds) MR in chemistry is expressed and developed in a classroom practice framed by model-based inquiry. The study focuses on…

Introduction: Psycholinguistics presents a challenge to teaching and learning because of the many abstract models in the field. Language-related games provide a vehicle for students to ground and demonstrate their understanding of these models. Statement of the problem: Models in psycholinguistics are challenging to teach and learn because they…

Human decision-making is underpinned by distinct systems that differ in flexibility and associated cognitive cost. A widely accepted dichotomy distinguishes between a cheap but rigid model-free system and a flexible but costly model-based system. Typically, humans use a hybrid of both types of decision-making depending on environmental demands.…

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…

The starting reasoning and promoting switch from intuitive system 1 to deliberate system 2 for provoking creative thinking is lacking feasible model, especially during the global pandemic. We established a visible, trainable and learnable (VTL) model with digital technique to promote this dual switch for creative thinking. This study was…

In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…

Mental model (Johnson-Laird, 2001) and probabilistic theories (Oaksford & Chater, 2009) claim to provide distinct explanations of human reasoning. However, the dual strategy model of reasoning suggests that this distinction corresponds to different reasoning strategies, termed "counterexample" and "statistical,"…

The literature on scientific modelling practices in science education has provided a fruitful discussion on how learners tend to view models vs. how and what they should think about them. One approach is to teach students that models are abstractions so that they do not view them as a copy of phenomena they represent. Although teaching students…

In this paper, I propose a new construct named "analytic equation sense" to conceptually model a desired way of reasoning that involves students' algebraic manipulations and use of equivalent expressions. Building from the analysis of two existing models in the field, I argue for the need for a new model and use empirical evidence to…

In this commentary, I discuss why, despite the existence of gradience in phonetics and phonology, there is still a need for abstract representations. Most proponents of exemplar models assume multiple levels of abstraction, allowing for an integration of the gradient and the categorical. Ben Ambridge's dismissal of generative models such as…

During language acquisition children generalise at multiple layers of granularity. Ambridge argues that abstraction-based accounts suffer from lumping (over-general abstractions) or splitting (over-precise abstractions). Ambridge argues that the only way to overcome this conundrum is in a purely exemplar/analogy-based system in which…

There is strong evidence from research conducted in the United States that fraction magnitude understanding supports mathematics achievement. Unfortunately, there has been little research that examines if this relation is present across educational contexts with different approaches to teaching fractions. The current study compared fourth and…

One of the aspects of programming that novices often struggle with is the understanding of abstract concepts, such as variables, loops, expressions, and especially Boolean operations. This paper aims to explore the effects of programming tools with different degrees of embodiment on learning Boolean operations in elementary school. To this end, 67…

Individuals draw conclusions about possibilities from assertions that make no explicit reference to them. The model theory postulates that assertions such as disjunctions refer to possibilities. Hence, a disjunction of the sort, "A or B or both," where "A" and "B" are sensible clauses, yields mental models of an…