This paper aims to shed light on an overlooked but essential aspect of informal reasoning and its radical implication to mathematics education research: Decentralising mathematics. We start to problematise that previous studies on informal reasoning implicitly overfocus on what students infer. Based on Walton's distinction between reasoning and…

Since statistical inference is a probabilistic generalization about a population analyzed on the basis of a sample, inferential reasoning demands producing reasons ("statistical" and "contextual") to substantiate and validate generalizations. To convey an understanding of students' inferential reasoning, we present a…

How do children learn about the structure of the social world? We tested whether children would extract patterns from an agent's social choices to make inferences about multiple groups' relative social standing. In Experiment 1, 4- to 6-year-old children (N = 36; tested in Central New York) saw an agent and three groups ("Group-A,"…

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…

In this article, examples are shown to demonstrate how open-ended mathematical activities can be used in the classroom. Open-ended activities give students opportunities to apply their understanding in unfamiliar contexts without the pressure of finding one perfect solution.

Causal reasoning is a fundamental cognitive ability that enables individuals to learn about the complex interactions in the world around them. However, the mechanisms that underpin causal reasoning are not well understood. For example, it remains unresolved whether children's causal inferences are best explained by Bayesian inference or…

The ability to consider multiple possibilities forms the basis for a wide variety of human-unique cognitive capacities. When does this skill develop? Previous studies have narrowly focused on children's ability to prepare for incompatible future outcomes. Here, we investigate this capacity in a causal learning context. Adults (N = 109) and 18- to…

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,"…

Listening to music activates representations of movement and social agents. Why? We test whether causal reasoning plays a role, and find that from childhood, people can intuitively reason about how musical sounds were generated, inferring the events and agents that caused the sounds. In Experiment 1 (N = 120, pre-registered), 6-year-old children…

This Family and Practitioner Brief discusses how deaf children who have not had access to a complete language from birth often encounter unique challenges in developing academic language skills, particularly in the realm of inference-making.

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…

Human thought can be characterised as being situated in the 'space of reasons'. That is to say that human thought is guided by the norms of theoretical and practical rationality which, in turn, enable autonomous thinking. But how do children learn to navigate the space of reasons? Building on the work of Tugendhat and Bakhurst, among others, we…

The role of statistics is wide and crucial in daily life, making statistics important. Many students have difficulty understanding statistics. This study aims to determine students' statistical reasoning about inference statistics, which is limited to the subject matter of the testing hypotheses about two-sample hypotheses testing. This study used…

Analogical reasoning is a core facet of higher cognition in humans. Creating analogies as we navigate the environment helps us learn. Analogies involve reframing novel encounters using knowledge of familiar, relationally similar contexts stored in memory. When an analogy links a novel encounter with a familiar context, it can aid in problem…

Background: Research on causal reasoning often uses group-level data analyses that downplay individual differences and simple reasoning problems that are unrepresentative of everyday reasoning. In three empirical studies, we used an individual differences approach to investigate the cognitive processes people used in fault diagnosis, which is a…