Analogical reasoning has played an important role in the development of modern mathematics. However, there has been critique of analogies for the purpose of learning new mathematics. In this article, I counter that students can productively reason by analogy to learn new mathematics and even develop new mathematics themselves. I display examples…

Learning endocrine physiology can be challenging. Some physiological concepts are abstract, making the process of learning more difficult for students. The comprehension of basic concepts, such as chemical hormone classification, is essential to understand the differences in synthesis, secretion, transport, and mechanism of action of hormones. To…

Teachers need ways to efficiently assess students' cognitive understanding. One promising approach involves easily adapted and administered item types that yield quantitative scores that can be interpreted in terms of whether or not students likely possess key understandings. This study illustrates an approach to analyzing response process…

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…

Starting with the hypothesis that analogical reasoning consists of a search of semantic space, we used eye-tracking to study the time course of information integration in adults in various formats of analogies. The two main questions we asked were whether adults would follow the same search strategies for different types of analogical problems and…

Background: Eye movement modelling examples (EMME) are demonstrations in which learners' not only see a model's (e.g., a teacher's) task performance on a computer screen (as in regular video examples) but also the model's eye movements (represented as moving coloured dots overlaid on the screen). Thereby EMME help guide learners' attention towards…

Lockwood has argued that taking a set-oriented perspective is critical for successful combinatorial enumeration. To date, however, the research literature has not yet captured the cognitive processes involved in taking such a perspective. In this theoretical paper, we elaborate the constructs of spatial structuring and spatial-numerical linked…

The study of dialectical logic has a history of nearly one hundred years in China. It is significant for understanding both the growth of Chinese logic and the Sinicization of Marxism to review dialectical logic in the context of introducing the study of Marxism in China. Debates about dialectical logic in Chinese academic circles involve not only…

Background: There is a growing evidence base for the importance of spatial reasoning for the development of mathematics. However, the extent to which this translates into practice is unknown. Aims: We aimed to understand practitioners' perspectives on their understanding of spatial reasoning, the extent to which they recognize and implement…

An ongoing debate in the literature on human reasoning concerns whether or not the logical status (valid vs. invalid) of an argument can be intuitively detected. The finding that conclusions of logically valid inferences are liked more compared to conclusions of logically invalid ones--called the logic-liking effect--is one of the most prominent…

Measurement uncertainty is a key topic in the university physics laboratory curriculum. In this study, we investigate students' ability to draw conclusions from measurement data and reasoning about measurement uncertainty in inquiry labs. This investigation centres around a task where students conclude whether measurements from two experiments…

The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…

Mark Creager noticed that how we teach students to reason mathematically may be counter-productive to our teaching goals. Sometimes a linear approach, focusing on sub-processes leading to a proof works well. But not always. Students should be made aware that reasoning is not always a straight forward process, but one filled with false starts and…

Young children often struggle to answer the question "what would have happened?" particularly in cases where the adult-like "correct" answer has the same outcome as the event that actually occurred. Previous work has assumed that children fail because they cannot engage in accurate counterfactual simulations. Children have…

Assessing digital scholarship services offered either through academic libraries or elsewhere on campuses is important for both program development and service refinement. Digital scholarship support is influenced by fluid campus priorities and limited resources, including staffing, service models, infrastructure, and partnership opportunities…