Finger-Counting and Numerical Structure

Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, a matter of whether devices are used in counting, which ones are used, and how they are used.

Nodes Afford Connection: A Pilot Study Examining the Design and Use of a Graphical Modeling Language

External representations such as diagrams facilitate reasoning. Many diagramming systems and notations are amenable to manipulation by actual or imagined intervention (e.g., transposing terms in an equation). Such manipulation is constrained by user-enforced constraints, including rules of syntax and semantics which help preserve the representation’s validity. We argue that the concepts of affordances and signifiers can be applied to understand such representations, and we suggest the term graphical affordance to refer to rule-constrained syntactic manipulation of an external representation. Following this argument, we examine a graphical modeling language in terms of these graphical affordances, and we present a pilot study examining how participants interact with the modeling language. Preliminary results suggest that using the modeling language, as opposed to prose representation, influences user behavior in a manner aligned with the graphical affordances and signifiers of the modeling language.

Mono- and Multi-Representational Learning of the Covariational Aspect of Functional Thinking

Using multiple external representations is advocated for learning in STEM education. This learning approach assumes that multiple external representations promote richer mental representations and a deeper understanding of the concept. In mathematics, the concept of function is a prototypical content area in which multiple representations are used. However, there are hardly any experimental studies investigating the effect of learning functional thinking with multiple representations compared to learning with only one form of representation. Therefore, this article reports on a quasi-experimental intervention study with students from Grade 7, using three measurement time points. The study compared the multi-representational learning of functional thinking with both tables and graphs with mono-representational learning with either tables or graphs. The results show that multi-representational learning led to advantages in learning qualitative functional thinking. However, in quantitative functional thinking, learning with both graphs and tables did not result in higher learning gains than learning exclusively with graphs. Furthermore, students were better able to transfer their knowledge from graphs to tables than vice versa. The results also indicate that multi-representational learning requires more time than mono-representational learning but can lead to higher learning gains. In sum, the results show that the effect of learning with representations is a complex interaction process between learning content and the forms of representation.

For 19-Month-Olds, What Happens On-Screen Stays On-Screen

Humans rely extensively on external representations such as drawings, maps, and animations. While animations are widely used in infancy research, little is known about how infants interpret them. In this study, we asked whether 19-month-olds take what they see on a screen to be happening here and now, or whether they think that on-screen events are decoupled from the immediate environment. In Experiments 1–3, we found that infants did not expect a falling animated ball to end up in boxes below the screen, even though they could track the ball (i) when the ball was real or (ii) when the boxes were also part of the animation. In Experiment 4, we tested whether infants think of screens as spatially bounded physical containers that do not allow objects to pass through. When two location cues were pitted against each other, infants individuated the protagonist of an animation by its virtual location (the animation to which it belonged), not by its physical location (the screen on which the animation was presented). Thus, 19-month-olds reject animation-reality crossovers but accept the depiction of the same animated environment on multiple screens. These results are consistent with the possibility that 19-month-olds interpret animations as external representations.

Parallel developmental changes in children's drawing and recognition of visual concepts

To what extent do visual concepts of dogs, cars, and clocks change across childhood? We hypothesized that as children progressively learn which features best distinguish visual concepts from one another, they also improve their ability to connect this knowledge with external representations. To examine this possibility, we investigated developmental changes in children's ability to produce and recognize drawings of common object categories. First, we recruited children aged 2-10 years to produce drawings of 48 categories via a free-standing kiosk in a children's museum, and we measured how recognizable these >37K drawings were using a deep convolutional neural network model of object recognition. Second, we recruited other children across the same age range to identify the drawn category in a subset of these drawings via "guessing games" at the same kiosk.We found consistent developmental gains in both children's ability to include diagnostic visual features in their drawings and in children's ability to use these features when recognizing other children's drawings. Our results suggest that children's ability to connect internal and external representations of visual concepts improves gradually across childhood and imply that developmental trajectories of visual concept learning may be more protracted than previously thought.

Cognitive Load Implications for Augmented Reality Supported Chemistry Learning

This paper presents a study about augmented-reality-based chemistry learning in a university lecture. Organic chemistry is often perceived as particularly difficult by students because spatial information must be processed in order to understand subject specific concepts and key ideas. To understand typical chemistry-related representations in books or literature, sophisticated mental rotation- and other spatial abilities are needed. Providing an augmented reality (AR) based learning support in the learning setting together with text and pictures is consistent with the idea of multiple external representations and the cognitive theory of multimedia learning. Using multiple external representations has proven to be beneficial for learning success, because different types of representations are processed separately in working memory. Nevertheless, the integration of a new learning medium involves the risk to hinder learning, in case of being not suitable for the learning topic or learning purpose. Therefore, this study investigates how the AR-use affects students’ cognitive load during learning in three different topics of organic chemistry. For this purpose also the usability of AR learning support is considered and the possible reduction of the influence of the mental rotation on learning success will be investigated.

For 19-month-olds, what happens on-screen stays on-screen

Humans rely extensively on external representations such as drawings, maps, and animations. While animations are widely used in infancy research, little is known about how infants interpret them. In this study, we asked whether 19-month-olds take what they see on a screen to be happening here and now, or whether they think that on-screen events are decoupled from the immediate environment. In Experiments 1-3, we found that infants did not expect a falling animated ball to end up in boxes below the screen, even though they could track the ball (i) when the ball was real or (ii) when the boxes were also part of the animation. In Experiment 4, we tested whether infants think of screens as spatially bounded physical containers that do not allow objects to pass through. When two location cues were pitted against each other, infants individuated the protagonist of an animation by its virtual location (the animation to which it belonged), not by its physical location (the screen on which the animation was presented). Thus, 19-month-olds reject animation-reality crossovers but accept the depiction of the same animated environment on multiple screens. These results are consistent with the possibility that 19-month-olds interpret animations as external representations.

The cyborg body: Potentials and limits of a body with prosthetic limbs

Living with an artificial limb is a reality for millions of people around the world, and it is not without its challenges. The body of the prosthesis user must adapt to the presence of an external aid and the user must learn how to act in the world by means of it. We analyze such a “cyborg body” with the help of a cognitive semiotic framework, benefiting from pheno-methodological triangulation, and the conceptual-empirical loop. Further, adopting a broad notion of phenomenological embodiment, with focus on both lived experience and external representations, we show that claims that “the cyborg” is the very nature of humanity are mistaken as they misrepresent the experiences of people with prosthetic limbs. Finally, we apply the Semiotic Hierarchy model to the levels of selfhood that need to be reconstructed when incorporating a prosthetic limb, distinguishing between subjective, intersubjective, and signitive levels. We conclude that the “lowest” level concerning the body schema, agency and ownership is hardest to reconstruct, supporting arguments for the centrality of proprioception for a sense of agency and ownership.