Abstract:

With the idea of the embodiment of mind, the cognitive unconscious and the metaphorical thought, it can be concluded that „human beings conceptualize abstract concepts in concrete terms, using ideas and modes of reasoning grounded in the sensory-motor system. The mechanism by which the abstract is comprehended in terms of the concrete is called conceptual metaphor. Mathematical thought also makes use of conceptual metaphor, as when we conceptualize numbers as points on a line.“ (Lakoff & Nunez, 2000, p. 5).

From this embodied perspective, gestures, i.e. „hand movements that co-occur with speech“ (Goldin-Meadow, 2005, p. 4), play an important role in the learning and teaching of mathematics concepts. „Children can express thoughts in gesture that they don’t even know they have. And those thoughts tend to be on the cutting edge of their knowledge“ (Goldin-Meadow, 2005, p. 116). Gestures seem to play a crucial role when language is limited, for example in reasoning or when describing from memory.

Also when it comes to the translation of mathematics into the real world and vice versa, i.e. in a modelling cycle (Blum & Leiss, 2005), „gesturing may make it easier to link a speaker’s words to the world. […] linking words and phrases to real-world objects, is required for comprehension. Once a word is indexed to an object, the listener’s knowledge of that particular object can guide his or her interpretation of the language“ (Goldin-Meadow, 2005, p. 163).

Hypothetically, the interface of learning mathematics and real world exyperiences forces and supports the use of gestures. One possiblity to lead students into this interface is the idea of outdoor mathematics by means of the system MathCityMap. Its basic idea is a mathematical walk in the environment by which real problems are discovered and solved mathematically. This walk is supported by a smartphone app (Ludwig & Jablonski, 2020). The role of gestures in the setting of MathCityMap is the scope of the pilot study presented in this paper.

The scope is investigated in an explorative approach. Two students solving seven MathCityMap outdoor mathematics tasks are accompted with their solving processes being recorded. Their gesture while communicating about the task is analyzed in two ways. Firstly, it is examined in how far the use of mathematics at real world object leads to different types of gestures. According to McNeill (1992), iconic, metaphorical, deictic and beat gestures can be distinguished, whereby it is assumed that especially iconic gestures, i.e. representing „body movements, movements of objects or people in space, and shapes of objects or people“ (Goldin-Meadow, 2005, p. 7), and deictic gestures, i.e. „gestures used to indicate objects, people, and locations in the real world“, will be observed in the outdoor context. Secondly, the different cognitive functions of gestures (Kira, Alibali & Chu, 2017; Salle & Krause, 2021) are taken into consideration in this outdoor mathematics setting:
- Activating Spatial Information, i.e. focus on different/new information
- Manipulating Spatial Information, i.e. rearrange, translate, rotate, invert
- Structuring Spatial Information, i.e. organize information for the act of speaking
- Exploring Spatial Information, i.e. explore more complex situations and distinguish relevant and non-relevant information.

Both, types and functions of the gestures in the outdoor setting will be analyzed and presented in the paper.

Keywords:

Embodiment, Gestures, Outdoor, MathCityMap, Modelling.