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…

Purpose: This paper aims to compare two types of prompts, encouraging participants to think about real-world examples or engineering principles to show how these two approaches can result in vastly different design practices. Design/methodology/approach: Two studies (N = 20, N = 40) examine the impact of two different prompts. Non-expert students,…

A critical component of scientific reasoning is the consideration of alternative explanations. Recognizing that decades of cognitive psychology research have demonstrated that relative cognitive accessibility, or "what comes to mind," strongly affects how people reason in a given context, we articulate a simple "cognitive…

If students really understand the systems they study, they would be able to tell how changes in the system would affect a result. This demands that the students understand the mechanisms that drive its behaviour. The study investigates potential merits of learning how to explicitly model the causal structure of systems. The approach and…

Post-problem reflective tutorial dialogues between human tutors and students are examined to predict when the tutor changed the level of abstraction from the student's preceding turn (i.e., used more general terms or more specific terms); such changes correlate with learning. Prior work examined lexical changes in abstraction. In this work, we…

Metacognitive knowledge of the dual-processing basis of judgment is critical to resolving conflict between analytic and experiential processing responses [Klaczynski, P. A. (2004). A dual-process model of adolescent development: Implications for decision making, reasoning, and identity. In R. V. Kail (Ed.), "Advances in child development and…

Five Inhelder-Piaget formal operations tasks were analyzed to determine the extent that the formal operational skills they assess were ordered into a stable hierarchy generalizable across samples of subjects. Subjects were 34 collegiate gymnasts (19 males, 15 females), and 22 students (1 male, 21 females) from a university nursing program.…