Intuition in Mathematical and Probabilistic Reasoning

Author(s):  
Kinga Morsanyi ◽  
Denes Szucs

Many people have a fragmented knowledge and understanding of the rules of mathematics and probability. As a consequence, they struggle with selecting the appropriate strategies to solve problems, and they often rely on intuitive solutions instead of normative rules. The purpose of this chapter is to introduce some typical intuitive strategies that people might apply when they solve mathematical or probability problems. Then the chapter describes the notions of primary and secondary intuitions, and gives an overview of the factors that might affect the selection of a particular intuitive strategy (such as certain individual differences variables and task characteristics). Finally, the chapter discusses the implications of these findings for researchers and educators.

Author(s):  
Elizabeth L. Fox ◽  
Joseph W. Houpt

The type and amount of task demands that humans must simultaneously process and respond to influences how efficient they are in completing the tasks. Capturing how and to what degree human efficiency changes in different task environments is crucial to inform an appropriate system design. An individual-based analytic approach is necessary to accurately capture performance changes and lend practical suggestions. We can provide designers with the amount and type of task demands that we expect a person to sustain adequate performance given their unique underlying cognitive properties. We develop a metric, multi-tasking throughput (MT), that provides the extent to which a person processes tasks more efficiently, the same, or less efficiently when required to complete several different types of tasks at once. This is a cognitive-based, standardized metric; meaning it yields the relative degree of change from a baseline model that is created to accommodate to unique individual differences, numbers of tasks, and task characteristics. We quantify MT by using transformations of RTs to predict the extent that external demands of multi-tasking exceeds what the cognitive system can accommodate to thereby hindering performance. We use a real world dual-task application to highlight the apparent differences in strategy and ability across individuals and alternative task environments.


1995 ◽  
Vol 18 (1) ◽  
pp. 165-176
Author(s):  
Warren O. Eaton ◽  
Mark E. Speed

It was hypothesised that physically mature children would exceed their less mature classmates on two standardised tests of phonological ability, one measuring the repetition of aurally presented pseudowords and the other, the reading of pseudowords. Phonological skills were assessed for 94 5to 11-year-old children, and physical maturities were estimated from relative stature (RS), the percentage of estimated adult height each had attained. After the effects of chronological age had been removed, individual differences in physical maturity positively predicted pseudoword repetition, although this effect was largely limited to males. The results provide partial support for the hypothesis and suggest that individual differences in physical maturation are associated with phonological skills, but such linkage is likely mediated by gender and task characteristics.


Author(s):  
Nina M. van Mastrigt ◽  
Katinka van der Kooij ◽  
Jeroen B. J. Smeets

AbstractWhen learning a movement based on binary success information, one is more variable following failure than following success. Theoretically, the additional variability post-failure might reflect exploration of possibilities to obtain success. When average behavior is changing (as in learning), variability can be estimated from differences between subsequent movements. Can one estimate exploration reliably from such trial-to-trial changes when studying reward-based motor learning? To answer this question, we tried to reconstruct the exploration underlying learning as described by four existing reward-based motor learning models. We simulated learning for various learner and task characteristics. If we simply determined the additional change post-failure, estimates of exploration were sensitive to learner and task characteristics. We identified two pitfalls in quantifying exploration based on trial-to-trial changes. Firstly, performance-dependent feedback can cause correlated samples of motor noise and exploration on successful trials, which biases exploration estimates. Secondly, the trial relative to which trial-to-trial change is calculated may also contain exploration, which causes underestimation. As a solution, we developed the additional trial-to-trial change (ATTC) method. By moving the reference trial one trial back and subtracting trial-to-trial changes following specific sequences of trial outcomes, exploration can be estimated reliably for the three models that explore based on the outcome of only the previous trial. Since ATTC estimates are based on a selection of trial sequences, this method requires many trials. In conclusion, if exploration is a binary function of previous trial outcome, the ATTC method allows for a model-free quantification of exploration.


2019 ◽  
Vol 51 (5) ◽  
pp. 622-665 ◽  
Author(s):  
Saskia F. Kuliga ◽  
Benjamin Nelligan ◽  
Ruth C. Dalton ◽  
Steven Marchette ◽  
Amy L. Shelton ◽  
...  

This article focuses on the interactions between individual differences and building characteristics that may occur during multilevel wayfinding. Using the Seattle Central Library as our test case, we defined a series of within-floor and between-floor wayfinding tasks based on different building analyses of this uniquely designed structure. Tracking our 59 participants while they completed assigned tasks on-site, we examined their wayfinding performance across tasks and in relation to a variety of individual differences measures and wayfinding strategies. Both individual differences and spatial configuration, as well as the organization of the physical space, were related to the wayfinding challenges inherent to this library. We also found wayfinding differences based on other, nonspatial features, such as semantic expectations about destinations. Together, these results indicate that researchers and building planners must consider the interactions among building, human, and task characteristics in a more nuanced fashion.


2020 ◽  
Vol 16 (1) ◽  
pp. 87-121
Author(s):  
Bárbara Eizaga-Rebollar ◽  
Cristina Heras-Ramírez

AbstractThe study of pragmatic competence has gained increasing importance within second language assessment over the last three decades. However, its study in L2 language testing is still scarce. The aim of this paper is to research the extent to which pragmatic competence as defined by the Common European Framework of Reference for Languages (CEFR) has been accommodated in the task descriptions and rating scales of two of the most popular Oral Proficiency Interviews (OPIs) at a C1 level: Cambridge’s Certificate in Advanced English (CAE) and Trinity’s Integrated Skills in English (ISE) III. To carry out this research, OPI tests are first defined, highlighting their differences from L2 pragmatic tests. After pragmatic competence in the CEFR is examined, focusing on the updates in the new descriptors, CAE and ISE III formats, structure and task characteristics are compared, showing that, while the formats and some characteristics are found to differ, the structures and task types are comparable. Finally, we systematically analyse CEFR pragmatic competence in the task skills and rating scale descriptors of both OPIs. The findings show that the task descriptions incorporate mostly aspects of discourse and design competence. Additionally, we find that each OPI is seen to prioritise different aspects of pragmatic competence within their rating scale, with CAE focusing mostly on discourse competence and fluency, and ISE III on functional competence. Our study shows that the tests fail to fully accommodate all aspects of pragmatic competence in the task skills and rating scales, although the aspects they do incorporate follow the CEFR descriptors on pragmatic competence. It also reveals a mismatch between the task competences being tested and the rating scale. To conclude, some research lines are proposed.


Author(s):  
Derek Brock ◽  
Deborah Hix ◽  
Lynn Dievendorf ◽  
J. Gregory Trafton

Software user interfaces that provide users with more than one device, such as a mouse and keyboard, for interactively performing tasks, are now commonplace. Concerns about how to represent individual differences in patterns of use and acquisition of skill in such interfaces led the authors to develop modifications to the standard format of the User Action Notation (UAN) that substantially augment the notation's expressive power. These extensions allow the reader of an interface specification to make meaningful comparisons between functionally equivalent interaction techniques and task performance strategies in interfaces supporting multiple input devices. Furthermore, they offer researchers a new methodology for analyzing the behavioral aspects of user interfaces. These modifications are documented and their benefits discussed.


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