The intuitiveness of the law of large numbers

Lem, Stephanie

doi:10.1007/s11858-015-0676-5

Cited by 16 publications

(14 citation statements)

References 26 publications

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“…The suggestion that inhibitory control is specifically required in the use of mathematics concepts when they are inconsistent with an irrelevant but salient perceptual stimulus or with an initial mathematical concept (whole number reasoning) has been made by several researchers working in the area of numerical cognition (e.g., Obersteiner, Bernhard, & Reiss, 2015;Lem, 2015;Van Dooren & Inglis, 2015). These authors argued that this result can be interpreted in the light of dual process theories (Evans, 2008;Evans & Stanovich, 2013;Kahneman, 2011).…”

Section: Conclusion Limitations and Implications For Cognitive Thementioning

confidence: 99%

The Recruitment of Shifting and Inhibition in On‐line Science and Mathematics Tasks

et al. 2018

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Prior research has investigated the recruitment of inhibition in the use of science/mathematics concepts in tasks that require the rejection of a conflicting, nonscientific initial concept. The present research examines if inhibition is the only EF skill recruited in such tasks and investigates whether shifting is also involved. It also investigates whether inhibition and/or shifting are recruited in tasks in which the use of science/mathematics concepts does not require the rejection of an initial concept, or which require only the use of initial concepts. One hundred and thirty-three third- and fifth-grade children participated in two inhibition and shifting tasks and two science and mathematics conceptual understanding and conceptual change (CU&C) tasks. All the tasks were on-line, and performance was measured in accuracy and RTs. The CU&C tasks involved the use of initial concepts and of science/mathematics concepts which required conceptual changes for their initial formation. Only in one of the tasks the use of the science/mathematics concepts required the concurrent rejection of an initial concept. The results confirmed that in this task inhibition was recruited and also showed that the speed of shifting was a significant predictor of performance. Shifting was a significant predictor of performance in all the tasks, regardless of whether they involved science/mathematics or initial concepts. It is argued that shifting is likely to be recruited in complex tasks that require multiple comparisons of stimuli and the entertainment of different perspectives. Inhibition seems to be a more selective cognitive skill likely to be recruited when the use of science/mathematics concepts requires the rejection of a conflicting initial concept.

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Section: Conclusion Limitations and Implications For Cognitive Thementioning

confidence: 99%

The Recruitment of Shifting and Inhibition in On‐line Science and Mathematics Tasks

et al. 2018

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“…We have discussed several examples where intuition may conflict with reason in mathematical thinking (and other examples exist, see for example Lem 2015, this issue, on the law of large numbers). In each case, Type 1 processing leads to a response that is not always appropriate, and Type 2 thinking is necessary to override this response.…”

Section: Cases Of Conflict In Mathematical Thinkingmentioning

confidence: 99%

Increasing cognitive inhibition with a difficult prior task: implications for mathematical thinking

Attridge

Inglis

2014

ZDM Mathematics Education

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Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing in order to apply new skills or knowledge that require Type 2 processing. In two studies we demonstrate that giving participants a difficult task (Raven's Matrices) before a task that requires the inhibition of intuitive responses (the Cognitive Reflection Test) significantly improves performance. Our findings suggest that encountering a difficult task that requires Type 2 processing before completing a task that requires inhibition of Type 1 processing may encourage an enduring 'Type 2' mind-set, whereby participants are more likely to spontaneously use Type 2 processing for a period of time. Implications for mathematics education are discussed. Increasing cognitive inhibition with a difficult prior task: Implications for mathematical thinking.

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“…Meanwhile, at a high FOR level, IR is generated in system 1 in the first stage and is directly selected as the final response without going through the second and third stages. This condition can occur in two possibilities, firstly because the stimulus faced is salience so that it attracts attention unconcious and a response is directly generated (Babai et al, 2015;Lamy et al, 2004;Lem, 2015;Zink et al, 2004 ). The second possibility is a familiar feeling towards the stimulus that is being faced so that the response is generated emotionally without analyzing (Fu et al, 2010;Mihaela & Voica, 2008).…”

Section: Discussionmentioning

confidence: 99%

“…In other words, students only give attention to certain information, and ignore information that is considered insignificant. This is triggered by the salience of the attention given information (Babai et al, 2015;Lamy et al, 2004;Lem, 2015;Zink et al, 2004) or because of familiar feelings students towards that information (Fu et al, 2010;Mihaela & Voica, 2008).…”

Section: Studentmentioning

confidence: 99%

The Levels of Students’ Feeling of Rightness (FOR) in Solving Polygon Perimeter Problems

Darmawan¹,

Purwanto²,

Parta³

et al. 2020

INT J INSTRUCTION

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This research aimed to describe the levels of feeling of rightness (FOR) of students. This research used a qualitative method with an explorative type. The subjects of this research were 3 students of 5th grade selected from 77 other students in Indonesia. In uncovering FOR subject of this research, instruments were used in the form of problems about the open-ended polygon perimeter and interview guidelines. The data of this research were the subjects' answers to the problems of polygon perimeter and the results of interviews with subjects related to these answers. The data were analyzed using the FOR subject level indicator rubric. There were three levels of FOR which were the findings in this research, namely low, medium, and high. Low FOR level was indicated by the answers crossed out and the objectives or goal changed. Medium FOR level was indicated by crossed out answers, objectives or goals changed, problems text read repeatedly, indecisive statements about the truth of the answers that have been generated, and doubts in determining the steps to be taken. High FOR level was indicated by answers that were not crossed and goals that were not changed.

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The intuitiveness of the law of large numbers

Cited by 16 publications

References 26 publications

The Recruitment of Shifting and Inhibition in On‐line Science and Mathematics Tasks

The Recruitment of Shifting and Inhibition in On‐line Science and Mathematics Tasks

Increasing cognitive inhibition with a difficult prior task: implications for mathematical thinking

The Levels of Students’ Feeling of Rightness (FOR) in Solving Polygon Perimeter Problems

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