Gestures Enhance Executive Functions for the Understating of Mathematical Concepts

Give your ideas a hand: the role of iconic hand gestures in enhancing divergent creative thinking

Hand gestures play an integral role in multimodal language and communication. Even though the self-oriented functions of gestures, such as activating a speaker's lexicon and maintaining visuospatial imagery, have been emphasized, gestures' functions in creative thinking are not well-established. In the current study, we investigated the role of iconic gestures in verbal divergent thinking-a creative thinking process related to generating many novel ideas. Based on previous findings, we hypothesized that iconic gesture use would facilitate divergent thinking in young adults, especially those with high mental imagery skills. Participants performed Guildford's Alternative Uses Task in a gesture-spontaneous and in a gesture-encouraged condition. We measured fluency (number of ideas), originality (uniqueness of ideas), flexibility (number of idea categories), and elaboration (number of details) in divergent thinking. The results showed that producing iconic gestures in the gesture-encouraged condition positively predicted fluency, originality, and elaboration. In the gesture-spontaneous condition, producing iconic gestures also positively predicted elaboration but negatively predicted flexibility. Mental imagery skills did not interact with the effects of gestures on divergent thinking. These results suggest that iconic gestures are a promising candidate for enhancing almost all aspects of divergent thinking. Overall, the current study adds a new dimension to the self-oriented function of iconic gestures, that is, their contribution to creative thinking.

The role of Mathematical Semiotic Signs in Enhancing Working Memory and Inhibition as the Components of Executive Functions

In this paper, we draw on Charles Sanders Pierce's typology of semiotic signs and suggest that the three types of signs (icon, index, and symbol) enhance working memory and inhibition through three different mechanisms: icons support the process of embodiment; indexes strengthen focus of attention; symbols enhance the process of generalization. Mathematical icons enhance the process of embodying mathematical entities. They help the individual hold the information associated with a mathematical entity in the visual working memory and suppress information that is irrelevant to the task. Indexes strengthen focus of attention by directly referring to the place of mathematical entities and disregarding contextually-irrelevant stimuli. Symbols enhance the process of generalization by suppressing low-level information and reducing the load on working memory. Since cognitive flexibility as the third component of executive functions builds on working memory and inhibition, it can be hypothesized that mathematical signs contribute to this component as well.

Embodiment of infinity in mathematics

In this article, we discuss the embodiment of infinity as one of fundamental concepts in mathematics. In contrast to the embodiment of many other mathematical concepts, the embodiment of infinity is an endless dynamic process. In embodying +∞, an object moves rightward toward a previously-set limit and passes it. Then, a new limit is set on the right side of the moving object. The moving object continues its movement and passes it as well. The moving object can pass any limit. In other words, there is no impassable limit for it. In embodying -∞, a similar process happens but the movement is leftward. Embodiment of infinitely small quantities has a basic similarity to the embodiment of infinitely large quantities, although it is different in some respects. We call the embodiment of infinity as iterative embodiment. It is iterative because the process of setting a new limit and passing it is repeated endlessly. Finally, it is suggested that in the process of embodying infinitely large and infinitely small quantities, the visual system and the motor system play important roles, as this process involves spatial concepts and movement.

The Roles of Gestural and Symbolic Schematizations in Inhibition as a Component of Executive Functions

The role of gestural schematization in enhancing thinking processes has been the subject of a large body of works. In this process, contextually unimportant or irrelevant information related to a concept (or a system of concepts) is deleted or ignored, while relevant spatial information is maintained. This process is a special type of inhibition, which is one of the key components of executive functions. In this short paper, it is suggested that gestural schematization is a special type of symbolic schematization, a much more general process through which irrelevant information related to features of a concept (or a system of concepts) is suppressed, while relevant information (spatial and non-spatial) is maintained. Through symbolic schematization, abstract structural similarity between two concepts or between two systems of concepts can be discovered. In this way, an individual's knowledge about the first situation can be generalized to the second situation. Symbolic schematization is the basis of abstraction, knowledge generalization, and knowledge development. This is particularly the case with abstract mathematical thinking. This proposal offers a picture of cognitive mechanisms through which knowledge of abstract mathematical concepts is created and developed in the mind.

The role of perceptual and action effector strength of graphs and bases of mathematical metaphors in the metaphorical processing of mathematical concepts

Metaphors that describe an abstract concept in terms of a motion concept are widely used to enhance our understanding of abstract concepts. These metaphors are used not only in our daily language but also in learning mathematics. As an example, in the process of understanding the abstract representation of a mathematical concept, a graphical representation may play the role of a mediatory domain. This graphical representation could have a high degree of perceptual and action effector strength. This is particularly the case when a gestures (as a motion) is used to depict the graphical representation. After looking at this example, we discuss perceptual and action effector strength of the base domains of several mathematical metaphors that describe mathematical concepts in terms of spatial and motion concepts. Then, based on the data in the Lancaster Sensorimotor Norms, it is suggested that high degrees of perceptual and action effector strength of the base domains of these metaphors play an important role in the grounding of abstract mathematical concepts in the physical environment.

How can transforming representation of mathematical entities help us employ more cognitive resources?

This article discusses the cognitive process of transforming one representation of mathematical entities into another representation. This process, which has been called mathematical metaphor, allows us to understand and embody a difficult-to-understand mathematical entity in terms of an easy-to-understand entity. When one representation of a mathematical entity is transformed into another representation, more cognitive resources such as the visual and motor systems can come into play to understand the target entity. Because of their nature, some curves, which are one group of visual representations, may have a great motor strength. It is suggested that directedness, straightness, length, and thinness are some possible features that determine degree of motor strength of a curve. Another possible factor that can determine motor strength of a curve is the strength of association between shape of the curve and past experiences of the observer (and her/his prior knowledge). If an individual has had the repetitive experience of observing objects moving along a certain curve, the shape of the curve may have a great motor strength for her/him. In fact, it can be said that some kind of metonymic relationship may be formed between the shapes of some curves and movement experiences.

A Study of Using Metaphoric and Beat Gestures with Motion-Based and Non-Motion-Based Metaphors during Retelling Stories

In this paper, we classify metaphors into four categories: motion-based metaphors, static space-based metaphors, static object-based metaphors, and static event-based metaphors. Then, a study that investigated the use of gestures with these types of metaphors is reported. The aim was to examine how these types of metaphors are used with metaphoric and beat gestures during the process of re-telling stories. The participants of the study listened to three audio stories. Each story contained two motion-based metaphors, two static space-based metaphors, two static object-based metaphors, and two static event-based metaphors. After listening to each story, they had to retell the stories in front of a camera. The videos were analyzed to determine the number of metaphoric gestures and beat gestures that had been used by participants during the retelling of the stories. The results showed that the highest number of metaphoric gestures had been used with static space-based metaphors. This was followed by motion-based metaphors, static object-based metaphors, and static event-based metaphors, respectively. On the other hand, the highest number of beat gestures was used with static event-based metaphors. These findings indicate that the use of metaphoric gestures and beat gestures accompanying metaphors is highly dependent on the spatial and motoric properties of the base of the metaphors, which supports the idea of embodied metaphor comprehension.