scholarly journals Symbolic Fractions Elicit an Analog Magnitude Representation in School-age Children

2019 ◽  
Author(s):  
Priya B. Kalra ◽  
John Binzak ◽  
Percival G. Matthews ◽  
Edward M. Hubbard ◽  
Percival G Matthews
Keyword(s):  
Formal Education ◽  
Response Times ◽  
Second Graders ◽  
Error Rates ◽  
Fifth Grade ◽  
School Age Children ◽  
Whole Numbers ◽  
Magnitude Processing ◽  
Formal Instruction ◽  
Analog Magnitude

A fundamental question about fractions is whether they are grounded in an abstract non-symbolic magnitude code, similar to those postulated for whole numbers. Mounting evidence suggests that symbolic fractions could be grounded in mechanisms for perceiving non-symbolic ratio magnitudes. However, systematic examination of such mechanisms in children has been lacking. We asked second and fifth grade children (prior to and after formal instructions with fractions, respectively) to compare pairs of symbolic fractions, non-symbolic ratios and mixed symbolic/non-symbolic pairs. This paradigm allowed us to test three key questions: 1) whether children show an analog magnitude code for rational numbers, 2) whether that code is compatible with mental representations of symbolic fractions, and 3) how formal education with fractions affects the symbolic-non-symbolic relation. We examined distance effects as a marker of analog ratio magnitude processing and notation effects as a marker of converting across numerical codes. Second and fifth grade children’s response times and error rates showed classic distance and notation effects. Non-symbolic ratios were processed most efficiently, with mixed and symbolic notations being relatively slower. Children with more formal instruction in symbolic fractions had a significant advantage in comparing symbolic fractions, but a smaller advantage for non-symbolic ratio stimuli. Supplemental analyses showed that second graders relied on numerator distance more than holistic distance, and fifth graders relied on holistic fraction magnitude distance more than numerator distance. These results suggest that children have a non-symbolic ratio magnitude code, and that symbolic fractions can be translated into that magnitude code.

scholarly journals Taking the Relational Structure of Fractions Seriously: Relational Reasoning Predicts Fraction Knowledge in Elementary School Children

2019 ◽  
Author(s):  
Priya B. Kalra ◽  
Edward M. Hubbard ◽  
Percival G Matthews
Keyword(s):  
Second Graders ◽  
Fifth Grade ◽  
Second Grade ◽  
Relational Reasoning ◽  
Reasoning Ability ◽  
Verbal Iq ◽  
Relational Structures ◽  
Fifth Grade Students ◽  
Magnitude Processing ◽  
General Test

Understanding and using symbolic fractions in mathematics is critical for access to advanced STEM concepts. However, children and adults consistently struggle with fractions. Here, we take a novel perspective on symbolic fractions, considering them within the framework of relational structures in cognitive psychology, such as those studied in analogy research. We tested the hypothesis that relational reasoning ability is important for reasoning about fractions by examining the relation between scores on a domain-general test of relational reasoning (TORR Jr.) and a test of fraction knowledge consisting of various types of fraction problems in 201 second grade and 150 fifth grade students. We found that relational reasoning was a significant predictor of fractions knowledge, even when controlling for non-verbal IQ and fractions magnitude processing for both grades. The effects of relational reasoning also remained significant when controlling for overall math knowledge and skill for second graders, but was attenuated for fifth graders. These findings suggest that this important subdomain of mathematical cognition is integrally tied to relational reasoning and opens the possibility that instruction targeting relational reasoning may prove to be a viable avenue for improving children’s fractions skills.

The Latin Square Task as a Measure of Relational Reasoning

2020 ◽  
Vol 36 (2) ◽  
pp. 296-302 ◽  
Author(s):  
Luke J. Hearne ◽  
Damian P. Birney ◽  
Luca Cocchi ◽  
Jason B. Mattingley
Keyword(s):  
Brain Imaging ◽  
Response Times ◽  
Latin Square ◽  
Error Rates ◽  
Functional Brain Imaging ◽  
Inspection Time ◽  
Relational Reasoning ◽  
Validity And Reliability ◽  
The Stability ◽  
Test Retest Reliability

Abstract. The Latin Square Task (LST) is a relational reasoning paradigm developed by Birney, Halford, and Andrews (2006) . Previous work has shown that the LST elicits typical reasoning complexity effects, such that increases in complexity are associated with decrements in task accuracy and increases in response times. Here we modified the LST for use in functional brain imaging experiments, in which presentation durations must be strictly controlled, and assessed its validity and reliability. Modifications included presenting the components within each trial serially, such that the reasoning and response periods were separated. In addition, the inspection time for each LST problem was constrained to five seconds. We replicated previous findings of higher error rates and slower response times with increasing relational complexity and observed relatively large effect sizes (η2p > 0.70, r > .50). Moreover, measures of internal consistency and test-retest reliability confirmed the stability of the LST within and across separate testing sessions. Interestingly, we found that limiting the inspection time for individual problems in the LST had little effect on accuracy relative to the unconstrained times used in previous work, a finding that is important for future brain imaging experiments aimed at investigating the neural correlates of relational reasoning.

Current Task Activation Predicts General Effects of Advance Preparation in Task Switching

2006 ◽  
Vol 53 (4) ◽  
pp. 260-267 ◽  
Author(s):  
Edita Poljac ◽  
Ab de Haan ◽  
Gerard P. van Galen
Keyword(s):  
Task Performance ◽  
Task Switching ◽  
Shape Matching ◽  
Response Times ◽  
Error Rates ◽  
Matching Task ◽  
Task Switch ◽  
Current Task ◽  
Within Subjects ◽  
And Task

Two experiments investigated the way that beforehand preparation influences general task execution in reaction-time matching tasks. Response times (RTs) and error rates were measured for switching and nonswitching conditions in a color- and shape-matching task. The task blocks could repeat (task repetition) or alternate (task switch), and the preparation interval (PI) was manipulated within-subjects (Experiment 1) and between-subjects (Experiment 2). The study illustrated a comparable general task performance after a long PI for both experiments, within and between PI manipulations. After a short PI, however, the general task performance increased significantly for the between-subjects manipulation of the PI. Furthermore, both experiments demonstrated an analogous preparation effect for both task switching and task repetitions. Next, a consistent switch cost throughout the whole run of trials and a within-run slowing effect were observed in both experiments. Altogether, the present study implies that the effects of the advance preparation go beyond the first trials and confirms different points of the activation approach ( Altmann, 2002) to task switching.

The effects of language impairment on the use of direct object pronouns and verb inflections in heritage Spanish speakers: A look at attrition, incomplete acquisition and maintenance

2011 ◽  
Vol 15 (1) ◽  
pp. 22-38 ◽  
Author(s):  
PEGGY F. JACOBSON
Keyword(s):  
Language Impairment ◽  
Error Rates ◽  
School Age Children ◽  
Gender Assignment ◽  
Verb Inflection ◽  
Heritage Spanish Speakers ◽  
Third Person ◽  
And Gender ◽  
Verb Inflections ◽  
Incomplete Acquisition

This study examined object clitic pronouns (OCPs) and verb inflections in twenty-five school-age children with typical development (TD) and twenty children with bilingual language impairment (BLI). MANOVA and ANOVA were used to explore differences according to grade level and language status (TD vs. BLI). Although children with BLI produced higher rates of grammatical errors overall, accuracy on number and gender assignment for OCPs was better for both groups in the higher grades. Although the rate of verb inflection errors did not differ for children with TD and BLI in the lower grades, a significant interaction yielded higher error rates on subject–verb agreement for third person singular and plural inflections in the later grades for children with BLI. Greater accuracy on OCP use in later grades weakens claims that bilingualism exacerbates language impairment. For BLI, whether incomplete acquisition or delayed development is the determining factor for verb inflection errors remains undetermined.

Traffic Signal Color Recognition Is a Problem for Both Protan and Deutan Color-Vision Deficients

2003 ◽  
Vol 45 (3) ◽  
pp. 495-503 ◽  
Author(s):  
David A. Atchison ◽  
Carol A. Pedersen ◽  
Stephen J. Dain ◽  
Joanne M. Wood
Keyword(s):  
Color Vision ◽  
Response Times ◽  
Reaction Times ◽  
Error Rates ◽  
Traffic Signal ◽  
White Background ◽  
Signal Design ◽  
Traffic Light ◽  
Light Signals ◽  
Signal Color

We investigated the effect of color-vision deficiency on reaction times and accuracy of identification of traffic light signals. Participants were 20 color-normal and 49 color-deficient males, the latter divided into subgroups of different severity and type. Participants performed a tracking task. At random intervals, stimuli simulating standard traffic light signals were presented against a white background at 5° to right or left. Participants identified stimulus color (red/yellow/green) by pressing an appropriate response button. Mean response times for color normals were 525, 410, and 450 ms for red, yellow, and green lights, respectively. For color deficients, response times to red lights increased with increase in severity of color deficiency, with deutans performing worse than protans of similar severity: response times of deuteranopes and protanopes were 53% and 35% longer than those of color normals. A similar pattern occurred for yellow lights, with deuteranopes and protanopes having increased response times of 85% and 53%, respectively. For green lights, response times of all groups were similar. Error rates showed patterns similar to those of response times. Contrary to previous studies, deutans performed much worse than protans of similar severity. Actual or potential applications of this research include traffic signal design and driver licensing.

Leadership Role of Adult Education Departments in the Practice of Adult Education in Nigeria

2015 ◽  
pp. 23-50
Author(s):  
Idowu Biao
Keyword(s):  
Adult Education ◽  
Formal Education ◽  
Leadership Role ◽  
School Age Children ◽  
School Age ◽  
Girl Child ◽  
University Departments ◽  
Academic Personnel

This chapter briefly describes the challenges faced by the Nigerian education system as from 1983 after it had performed well between 1960 and 1980. It follows this description with the discussion of the innovative and ingenious educational devise that kept about one third of the number of school age children and youths in school between 1990 and the early part of the 21st century. That innovative educational sub-system was known as non-formal education for the Girl-Child, the out-of-school boy and Quranic school learners and it was developed, nurtured and implemented by academic personnel drawn from the eight existing university departments of adult education in Nigeria at the time. The chapter finally discusses how these departments of adult education worked for the establishment of national structures of adult education which ultimately came to promote both the visibility and popularisation of the modern practice of adult education in Nigeria from the 1980s.

scholarly journals Human Cognition in Interaction With Robots: Taking the Robot’s Perspective Into Account

2020 ◽  
pp. 001872082093376
Author(s):  
Sophia von Salm-Hoogstraeten ◽  
Jochen Müsseler
Keyword(s):  
Production Process ◽  
Response Times ◽  
Error Rates ◽  
Human Robot Interaction ◽  
Human Cognition ◽  
Robot Interaction ◽  
Shared Workspace ◽  
Stimulus Response ◽  
Processing Times ◽  
Shared Workspaces

Objective The present study investigated whether and how different human–robot interactions in a physically shared workspace influenced human stimulus–response (SR) relationships. Background Human work is increasingly performed in interaction with advanced robots. Since human–robot interaction often takes place in physical proximity, it is crucial to investigate the effects of the robot on human cognition. Method In two experiments, we compared conditions in which humans interacted with a robot that they either remotely controlled or monitored under otherwise comparable conditions in the same shared workspace. The cognitive extent to which the participants took the robot’s perspective served as a dependent variable and was evaluated with a SR compatibility task. Results The results showed pronounced compatibility effects from the robot’s perspective when participants had to take the perspective of the robot during the task, but significantly reduced compatibility effects when human and robot did not interact. In both experiments, compatibility effects from the robot’s perspective resulted in statistically significant differences in response times and in error rates between compatible and incompatible conditions. Conclusion We concluded that SR relationships from the perspective of the robot need to be considered when designing shared workspaces that require users to take the perspective of the robot. Application The results indicate changed compatibility relationships when users share their workplace with an interacting robot and therefore have to take its perspective from time to time. The perspective-dependent processing times are expected to be accompanied by corresponding error rates, which might affect—for instance—safety and efficiency in a production process.

Sex Differences in Mental Rotation Performance Through Holding Weights By the Hands

2020 ◽  
pp. 027623662095233
Author(s):  
Hiroyuki Muto ◽  
Soyogu Matsushita ◽  
Kazunori Morikawa
Keyword(s):  
Sex Differences ◽  
Embodied Cognition ◽  
Mental Rotation ◽  
Response Times ◽  
Error Rates ◽  
Female Students ◽  
Mental Rotation Task ◽  
Hands On ◽  
Sensorimotor Processes

Mental rotation is known to be mediated by sensorimotor processes. To deepen our understanding of the role of somatosensory inputs in mental rotation, we investigated the effects of holding weight by the hands on mental rotation performance. In an experiment, 22 male and 22 female students performed a chronometric mental rotation task while holding either light or heavy bags in both hands. Results showed that females holding heavy bags were quicker and more accurate at mental rotation than females holding light bags, as evidenced by shallower slopes for response times (RTs) and error rates. In contrast, males showed no such heavy-bag-induced improvement. Unlike slopes, intercepts for RTs and error rates were equivalent regardless of sex and bag weight. Consistent with previous research on embodied cognition, the present findings demonstrated the facilitatory role of somatosensory cues by weight in mental rotation and suggested sex differences in embodied processes in mental rotation.

scholarly journals Stroop Interference and Facilitation Effects in Kinesthetic and Haptic Tasks

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
David Hecht ◽  
Miriam Reiner
Keyword(s):  
Response Times ◽  
Error Rates ◽  
Stroop Interference ◽  
Mechanical Force ◽  
Computer Interface ◽  
Human Computer Interactions ◽  
Virtual Objects ◽  
Specific Direction ◽  
Multisensory Systems ◽  
Computer Interactions

Stroop interference and facilitation effects were documented in the visual, auditory, olfactory, and gustatory modalities. This study extends the Stroop phenomena also for kinesthetic and haptic tasks. In a touch-enabled computer interface, participants touched and manipulated virtual objects (cylinders, cubes, and tiles), through a pen-like stylus, and identified their haptic qualities (weight, firmness, vibrations). Similarly, participants were stimulated with a mechanical force pushing their hands lightly towards a specific direction which they had to identify. While performing these identification tasks, participants were simultaneously presented with words or symbols that were congruent, neutral, or incongruent with the experienced kinesthetic/haptic sensations. Error rates and response times were affected in the following order: congruent < neutral < incongruent. As technologies advance into multisensory systems, engineers and designers can improve human-computer interactions by ensuring optimal congruence between all the inter- and intra-sensory elements in the display.

scholarly journals Proactive interference in aging: A model-based study

2019 ◽  
Vol 27 (1) ◽  
pp. 130-138 ◽  
Author(s):  
Kim Archambeau ◽  
Birte Forstmann ◽  
Leendert Van Maanen ◽  
Wim Gevers
Keyword(s):  
Older Adults ◽  
Proactive Interference ◽  
Response Times ◽  
Error Rates ◽  
Motor Execution ◽  
Memory Decline ◽  
Fine Grained ◽  
New Information ◽  
Processing Mechanisms ◽  
Diffusion Decision Model

AbstractProactive interference occurs when previously learned information interrupts the storage or retrieval of new information. Congruent with previous reports, traditional analyses dealing with response times and error rates separately have indicated an increase in sensitivity to proactive interference in older adults. We reanalyzed the same data using diffusion decision model (DDM). Such models enable a more fine-grained interpretation concerning the latent processing mechanisms underlying performance. Now a different picture emerged. The DDM results showed that older adults needed more evidence than young adults before responding. The results also clearly indicated that peripheral processes (encoding time and motor execution), as well as recognition memory, decline with age. However, the drift rates, reflecting proactive interference, were similar, suggesting—contrary to earlier reports—that the inhibitory processes observed with this paradigm remain intact in older adults.

Sign in / Sign up

Export Citation Format

Share Document