@misc{FischerWinterFelisattietal.2021,
  author    = {Fischer, Martin and Winter, Bodo and Felisatti, Arianna and Myachykov, Andriy and Jeglinski-Mende, Melinda A. and Shaki, Samuel},
  title     = {More Instructions Make Fewer Subtractions},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  volume    = {12},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Humanwissenschaftliche Reihe},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {1866-8364},
  doi       = {10.25932/publishup-55008},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-550086},
  pages     = {1 -- 3},
  year      = {2021},
  abstract  = {Research on problem solving offers insights into how humans process task-related information and which strategies they use (Newell and Simon, 1972; {\"O}llinger et al., 2014). Problem solving can be defined as the search for possible changes in one's mind (Kahneman, 2003). In a recent study, Adams et al. (2021) assessed whether the predominant problem solving strategy when making changes involves adding or subtracting elements. In order to do this, they used several examples of simple problems, such as editing text or making visual patterns symmetrical, either in naturalistic settings or on-line. The essence of the authors' findings is a strong preference to add rather than subtract elements across a diverse range of problems, including the stabilizing of artifacts, creating symmetrical patterns, or editing texts. More specifically, they succeeded in demonstrating that "participants were less likely to identify advantageous subtractive changes when the task did not (vs. did) cue them to consider subtraction, when they had only one opportunity (vs. several) to recognize the shortcomings of an additive search strategy or when they were under a higher (vs. lower) cognitive load" (Adams et al., 2021, p. 258). Addition and subtraction are generally defined as de-contextualized mathematical operations using abstract symbols (Russell, 1903/1938). Nevertheless, understanding of both symbols and operations is informed by everyday activities, such as making or breaking objects (Lakoff and N{\´u}{\~n}ez, 2000; Fischer and Shaki, 2018). The universal attribution of "addition bias" or "subtraction neglect" to problem solving activities is perhaps a convenient shorthand but it overlooks influential framing effects beyond those already acknowledged in the report and the accompanying commentary (Meyvis and Yoon, 2021). Most importantly, while Adams et al.'s study addresses an important issue, their very method of verbally instructing participants, together with lack of control over several known biases, might render their findings less than conclusive. Below, we discuss our concerns that emerged from the identified biases, namely those regarding the instructions and the experimental materials. Moreover, we refer to research from mathematical cognition that provides new insights into Adams et al.'s findings.},
  language  = {en}
}
@article{FischerWinterFelisattietal.2021,
  author    = {Fischer, Martin and Winter, Bodo and Felisatti, Arianna and Myachykov, Andriy and Jeglinski-Mende, Melinda A. and Shaki, Samuel},
  title     = {More Instructions Make Fewer Subtractions},
  series = {Frontiers in Psychology},
  volume    = {12},
  journal   = {Frontiers in Psychology},
  publisher = {Frontiers Media SA},
  address   = {Lausanne, Schweiz},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2021.720616},
  pages     = {1 -- 3},
  year      = {2021},
  abstract  = {Research on problem solving offers insights into how humans process task-related information and which strategies they use (Newell and Simon, 1972; {\"O}llinger et al., 2014). Problem solving can be defined as the search for possible changes in one's mind (Kahneman, 2003). In a recent study, Adams et al. (2021) assessed whether the predominant problem solving strategy when making changes involves adding or subtracting elements. In order to do this, they used several examples of simple problems, such as editing text or making visual patterns symmetrical, either in naturalistic settings or on-line. The essence of the authors' findings is a strong preference to add rather than subtract elements across a diverse range of problems, including the stabilizing of artifacts, creating symmetrical patterns, or editing texts. More specifically, they succeeded in demonstrating that "participants were less likely to identify advantageous subtractive changes when the task did not (vs. did) cue them to consider subtraction, when they had only one opportunity (vs. several) to recognize the shortcomings of an additive search strategy or when they were under a higher (vs. lower) cognitive load" (Adams et al., 2021, p. 258). Addition and subtraction are generally defined as de-contextualized mathematical operations using abstract symbols (Russell, 1903/1938). Nevertheless, understanding of both symbols and operations is informed by everyday activities, such as making or breaking objects (Lakoff and N{\´u}{\~n}ez, 2000; Fischer and Shaki, 2018). The universal attribution of "addition bias" or "subtraction neglect" to problem solving activities is perhaps a convenient shorthand but it overlooks influential framing effects beyond those already acknowledged in the report and the accompanying commentary (Meyvis and Yoon, 2021). Most importantly, while Adams et al.'s study addresses an important issue, their very method of verbally instructing participants, together with lack of control over several known biases, might render their findings less than conclusive. Below, we discuss our concerns that emerged from the identified biases, namely those regarding the instructions and the experimental materials. Moreover, we refer to research from mathematical cognition that provides new insights into Adams et al.'s findings.},
  language  = {en}
}
@article{FischerShaki2018,
  author    = {Fischer, Martin H. and Shaki, Samuel},
  title     = {Repeating Numbers Reduces Results: Violations of the Identity Axiom in Mental Arithmetic},
  series = {Frontiers in psychology},
  volume    = {9},
  journal   = {Frontiers in psychology},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {1664-1078},
  doi       = {10.3389/fpsyg.2018.02453},
  pages     = {9},
  year      = {2018},
  abstract  = {Even simple mental arithmetic is fraught with cognitive biases. For example, adding repeated numbers (so-called tie problems, e.g., 2 + 2) not only has a speed and accuracy advantage over adding different numbers (e.g., 1 + 3) but may also lead to under-representation of the result relative to a standard value (Charras et al., 2012, 2014). Does the tie advantage merely reflect easier encoding or retrieval compared to non-ties, or also a distorted result representation? To answer this question, 47 healthy adults performed two tasks, both of which indicated under-representation of tie results: In a result-to-position pointing task (Experiment 1) we measured the spatial mapping of numbers and found a left-bias for tie compared to non-tie problems. In a result-to-line-length production task (Experiment 2) we measured the underlying magnitude representation directly and obtained shorter lines for tie-compared to non-tie problems. These observations suggest that the processing benefit of tie problems comes at the cost of representational reduction of result meaning. This conclusion is discussed in the context of a recent model of arithmetic heuristics and biases.},
  language  = {en}
}