Posts in Category: paper
paper := journal article or paper in peer-reviewed conference proceedings
Paper: Decade effects in mental addition
| The most important part of the Analytical Engine was undoubtedly the mechanical method of carrying the tens. (…) The difficulty did not consist so much in the more or less complexity of the contrivance as in the reduction of the time required to effect the carriage. (…) nothing but teaching the Engine to foresee and then to act upon that foresight could ever lead me to the object I desired… |
| Charles S. Babbage (1864), Passages from the Life of a Philosopher, p. 114 |
Classification of addition types for adding a single-digit addend a (with a∈{1…9}) to an augend Au (u denoting the augend’s unit). (See Table 1 for details.)
Hansjörg Neth, Stephen J. Payne
Decade effects in mental addition
We examine representational effects of Western numerals on mental arithmetic. An analysis of mental addition tasks using a base-10 place-value notation yields a taxonomy of addition types that is anchored in the notion of complements (i.e. additions with round sums). Two experimental studies use a paradigm of serial addition that presents lists of numbers to adult participants, who mentally represent all intermediate steps. In study 1, participants add sequences of single-digit addends in a self-paced fashion. Study 2 extends this paradigm by simultaneously presenting two addends, thus allowing for a modicum of strategic choice. Both studies vary the number of complements within the lists and measure addition accuracy and latency. Beyond decade and carry effects, our results show that lists containing or enabling complements are easier to add. Addition latencies jointly depend on addition type and problem size. When adders have some discretion about the order of choosing addends, they adaptively exploit the difficulty of addition types by tailoring their sequences to decade boundaries. One motivation for seeking complements lies in enabling subsequent post-complements. Reflecting on the dynamic interplay between numeric representations, strategic choices and cognitive adaptations, we discuss implications for psychological explanations, technology and design.
Four different addition types (A) and their hypothetical frequency (B, assuming uniform distribution of addends 1–9 and full decomposition of super-complements). (See Figure 4 in Appendix A1 for details.)
This article is part of the theme issue A solid base for scaling up: the structure of numeration systems.
Keywords: mental arithmetic, addition strategies, base notation, representational effects.
Reference: Neth, H., & Payne, S. J. (2025). Decade effects in mental addition. Philosophical Transactions of the Royal Society B, 380, 20240220. https://doi.org/10.1098/rstb.2024.0220
Related: Addition as interactive problem solving | Thinking by doing? | Immediate interactive behavior (IIB) | Arabic vs. Roman arithmetic | Taxonomy of actions | The cognitive basis of arithmetic | Interactive coin addition | The functional task environment
Resources: open access article | PDF download | Google Scholar
Paper: Perspectives on the 2×2 Matrix
Hansjörg Neth, Nico Gradwohl, Dirk Streeb, Daniel A. Keim, Wolfgang Gaissmaier
Perspectives on the 2×2 matrix: Solving semantically distinct problems based on a shared structure of binary contingencies
Abstract
Cognition is both empowered and limited by representations. The matrix lens model explicates tasks that are based on frequency counts, conditional probabilities, and binary contingencies in a general fashion. Based on a structural analysis of such perspective on representational accounts of cognition that recognizes representational isomorphs as opportunities, rather than as problems.
The shared structural construct of a 2×2 matrix supports a set of generic tasks and semantic mappings that provide a tasks, the model links several problems and semantic domains and provides a new unifying framework for understanding problems and defining scientific measures. Our model’s key explanatory mechanism is the adoption of particular perspectives on a 2×2 matrix that categorizes the frequency counts of cases by some condition, treatment, risk, or outcome factor. By the selective steps of filtering, framing, and focusing on specific aspects, the measures used in various semantic domains negotiate distinct trade-offs between abstraction and specialization. As a consequence, the transparent communication of such measures must explicate the perspectives encapsulated in their derivation.
To demonstrate the explanatory scope of our model, we use it to clarify theoretical debates on biases and facilitation effects in Bayesian reasoning and to integrate the scientific measures from various semantic domains within a unifying framework. A better understanding of problem structures, representational transparency, and the role of perspectives in the scientific process yields both theoretical insights and practical applications.
Why read this paper?
This paper is quite long and covers a wide array of concepts and topics. So what can you expect to gain from reading it?
Paper: The echo in flu-vaccination echo chambers
Helge Giese, Hansjörg Neth, Mehdi Moussaïd, Cornelia Betsch, Wolfgang Gaissmaier
The echo in flu-vaccination echo chambers: Selective attention trumps social influence
Abstract
Background
Online discussions may impact the willingness to get vaccinated. This experiment tests how groups of individuals with consistent and inconsistent attitudes towards flu vaccination attend to and convey information online, and how they alter their corresponding risk perceptions.
Methods
Out of 1859 MTurkers, we pre-selected 208 people with negative and 221 people with positive attitudes towards flu vaccinations into homogeneous or heterogeneous 3-link experimental diffusion chains. We assessed (i) which information about flu vaccinations participants conveyed to the subsequent link, (ii) how flu-vaccination related perceptions were altered by incoming messages, and (iii) how participants perceived incoming information.
Results
Participants (i) selectively conveyed attitude-consistent information, but exhibited no overall anti-vaccination bias, (ii) were reluctant to alter their flu-vaccination related perceptions in response to messages, and (iii) evaluated incoming information consistent with their prior attitudes as more convincing.
Discussion
Flu-vaccination related perceptions are resilient against contradictions and bias online communication. Contrary to expectations, there was no sign of amplification of anti-vaccine attitudes by online communication.
Keywords: Amplification of risk; Diffusion chain; Opinion dynamics; Vaccine hesitancy; Social media; Polarization
Press release
- in English: https://www.campus.uni-konstanz.de/en/science/immune-to-influence
- auf Deutsch: https://www.campus.uni-konstanz.de/wissenschaft/immun-gegen-informationen
Reference: Giese, H., Neth, H., Moussaïd, M., Betsch, C., & Gaissmaier, W. (2020). The echo in flu-vaccination echo chambers: Selective attention trumps social influence. Vaccine, 38 (8), 2070–2076. doi: 10.1016/j.vaccine.2019.11.038
Related: Social influence and collective opinion formation
Resources: Download_PDF | Google Scholar
Paper: FFTrees: An R toolbox to create, visualize, and evaluate FFTs
is nevertheless totally incomprehensible to a human expert, can it
be described as knowledge? Under the common-sense definition of this term
as material that might be assimilated and used by human beings, it is not…
An example of an FFT predicting the risk of having heart disease.
Nathaniel Phillips, Hansjörg Neth, Jan Woike, Wolfgang Gaissmaier
FFTrees: A toolbox to create, visualize, and evaluate fast-and-frugal decision trees
Abstract: Fast-and-frugal trees (FFTs) are simple algorithms that facilitate efficient and accurate decisions based on limited information. But despite their successful use in many applied domains, there is no widely available toolbox that allows anyone to easily create, visualize, and evaluate FFTs. We fill this gap by introducing the R package FFTrees.