An underexplored aspect of the relationship between analogical reasoning and creativity is its phenomenology; in particular, the notion that analogical reasoning is related to insight and its associated "aha!" experience. However, the relationship between these phenomena has never been directly investigated. We adapted a set of verbal…

The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that…

The use of visual metaphors has received growing attention in recent years, but their widespread use is not without certain challenges. The most common critique of visual metaphors in teaching indicates that they can be misleading as the meaning attributed by the recipient can be far apart from the intended one. This can make learning less…

Many geoscience phenomena cannot be perceived at human temporal or spatial scales. As a consequence, we can only understand many processes that drive geological phenomena through analogical reasoning. Building deep conceptual understanding requires instruction that activates the appropriate source analogs and allows students to build useful…

This paper reports on the metaphors that 36 third-year university mathematics education students have about mathematics. These metaphors were investigated through a questionnaire with five open-ended items. An inductive analysis of the students' metaphors for mathematics indicated that students had well developed and complex metaphors about…

The instructional metaphor is an important bridge to understanding, particularly when students are undertaking tasks that are conceptually difficult and outside their previous experience. It is suggested that the limitations of the implicit metaphor of the procedural control languages are the main cause of the problems experienced with delivering…

This paper proposes a methodology to calculate both the difficulty of the basic problems and the difficulty of solving a problem. The method to calculate the difficulty of problem is according to the process of constructing a problem, including Concept Selection, Unknown Designation, and Proposition Construction. Some necessary measures observed…