scholarly journals Not toeing the number line for simple arithmetic: Two large-n conceptual replications of Mathieu et al. (Cognition, 2016, Experiment 1)

2021 ◽  
Vol 7 (3) ◽  
pp. 248-258 ◽  
Author(s):  
Jamie I. D. Campbell ◽  
Yalin Chen ◽  
Maham Azhar
Keyword(s):  
Number Line ◽  
Operation Condition ◽  
Single Digit ◽  
Simple Arithmetic ◽  
Position Effects ◽  
Large N ◽  
Addition And Subtraction ◽  
Mixed Operation ◽  
The Right ◽  
The University

We conducted two conceptual replications of Experiment 1 in Mathieu, Gourjon, Couderc, Thevenot, and Prado (2016, https://doi.org/10.1016/j.cognition.2015.10.002). They tested a sample of 34 French adults on mixed-operation blocks of single-digit addition (4 + 3) and subtraction (4 – 3) with the three problem elements (O1, +/-, O2) presented sequentially. Addition was 34 ms faster if O2 appeared 300 ms after the operation sign and displaced 5° to the right of central fixation, whereas subtraction was 19 ms faster when O2 was displaced to the left. Replication Experiment 1 (n = 74 recruited at the University of Saskatchewan) used the same non-zero addition and subtraction problems and trial event sequence as Mathieu et al., but participants completed blocks of pure addition and pure subtraction followed by the mixed-operation condition used by Mathieu et al. Addition RT showed a 32 ms advantage with O2 shifted rightward relative to leftward but only in mixed-operation blocks. There was no effect of O2 position on subtraction RT. Experiment 2 (n = 74) was the same except mixed-operation blocks occurred before the pure-operation blocks. There was an overall 13 ms advantage with O2 shifted right relative to leftward but no interaction with operation or with mixture (i.e., pure vs mixed operations). Nonetheless, the rightward RT advantage was statistically significant for both addition and subtraction only in mixed-operation blocks. Taken together with the robust effects of mixture in Experiment 1, the results suggest that O2 position effects in this paradigm might reflect task specific demands associated with mixed operations.

scholarly journals The relationship between problem size and fixation patterns during addition, subtraction, multiplication, and division

2016 ◽  
Vol 2 (2) ◽  
pp. 91-115 ◽  
Author(s):  
Evan T. Curtis ◽  
Matthew G. Huebner ◽  
Jo-Anne LeFevre
Keyword(s):  
Eye Movements ◽  
Eye Tracking ◽  
Cognitive Processing ◽  
Mental Arithmetic ◽  
Problem Size ◽  
Single Digit ◽  
Simple Arithmetic ◽  
Division Problems ◽  
The Right ◽  
The Relationship

Eye-tracking methods have only rarely been used to examine the online cognitive processing that occurs during mental arithmetic on simple arithmetic problems, that is, addition and multiplication problems with single-digit operands (e.g., operands 2 through 9; 2 + 3, 6 x 8) and the inverse subtraction and division problems (e.g., 5 – 3; 48 ÷ 6). Participants (N = 109) solved arithmetic problems from one of the four operations while their eye movements were recorded. We found three unique fixation patterns. During addition and multiplication, participants allocated half of their fixations to the operator and one-quarter to each operand, independent of problem size. The pattern was similar on small subtraction and division problems. However, on large subtraction problems, fixations were distributed approximately evenly across the three stimulus components. On large division problems, over half of the fixations occurred on the left operand, with the rest distributed between the operation sign and the right operand. We discuss the relations between these eye tracking patterns and other research on the differences in processing across arithmetic operations.

Time course of overt attentional shifts in mental arithmetic: Evidence from gaze metrics

2018 ◽  
Vol 71 (4) ◽  
pp. 1009-1019 ◽  
Author(s):  
Nicolas Masson ◽  
Clément Letesson ◽  
Mauro Pesenti
Keyword(s):  
Time Course ◽  
Mental Arithmetic ◽  
Number Line ◽  
Detection Task ◽  
Mental Number Line ◽  
Large Numbers ◽  
Attentional Shifts ◽  
Addition And Subtraction ◽  
The Right ◽  
Target Detection Task

Processing numbers induces shifts of spatial attention in probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. This has been interpreted as supporting the concept of a mental number line with number magnitudes ranging from left to right, from small to large numbers. Recently, the investigation of this spatial-numerical link has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems might induce attentional displacements, rightward or leftward, respectively. At the neurofunctional level, the activations elicited by the solving of additions have been shown to resemble those induced by rightward eye movements. However, the possible behavioural counterpart of these activations has not yet been observed. Here, we investigated overt attentional shifts with a target detection task primed by addition and subtraction problems (2-digit ± 1-digit operands) in participants whose gaze orientation was recorded during the presentation of the problems and while calculating. No evidence of early overt attentional shifts was observed while participants were hearing the first operand, the operator or the second operand, but they shifted their gaze towards the right during the solving step of addition problems. These results show that gaze shifts related to arithmetic problem solving are elicited during the solving procedure and suggest that their functional role is to access, from the first operand, the representation of the result.

Spatial Bias Induced by Simple Addition and Subtraction: From Eye Movement Evidence

Perception ◽  
2017 ◽  
Vol 47 (2) ◽  
pp. 143-157 ◽  
Author(s):  
Rongjuan Zhu ◽  
Yangmei Luo ◽  
Xuqun You ◽  
Ziyu Wang
Keyword(s):  
Spatial Attention ◽  
Time Window ◽  
Mental Arithmetic ◽  
Number Line ◽  
Mental Number Line ◽  
Spatial Bias ◽  
Semantic Link ◽  
Addition And Subtraction ◽  
The Right ◽  
Attention Shifts

The associations between number and space have been intensively investigated. Recent studies indicated that this association could extend to more complex tasks, such as mental arithmetic. However, the mechanism of arithmetic-space associations in mental arithmetic was still a topic of debate. Thus, in the current study, we adopted an eye-tracking technology to investigate whether spatial bias induced by mental arithmetic was related with spatial attention shifts on the mental number line or with semantic link between the operator and space. In Experiment 1, participants moved their eyes to the corresponding response area according to the cues after solving addition and subtraction problems. The results showed that the participants moved their eyes faster to the leftward space after solving subtraction problems and faster to the right after solving addition problems. However, there was no spatial bias observed when the second operand was zero in the same time window, which indicated that the emergence of spatial bias may be associated with spatial attention shifts on the mental number line. In Experiment 2, participants responded to the operator (operation plus and operation minus) with their eyes. The results showed that mere presentation of operator did not cause spatial bias. Therefore, the arithmetic–space associations might be related with the movement along the mental number line.

The Number Line And Mental Arithmetic

1990 ◽  
Vol 38 (4) ◽  
pp. 44-46
Author(s):  
Theodore E. Kurland
Keyword(s):  
Mental Arithmetic ◽  
Number Line ◽  
Single Digit ◽  
Addition And Subtraction

Some students have easily recognized difficulties with addition and subtraction. Some have no trouble adding or subtracting single-digit numbers when the sums are less than ten (7 + 2, 5 + 4, etc.) but have to resort to their fingers for sums greater than ten (7 + 5, 8 + 6, etc.). Other students have no difficulty adding numbers whose sums are greater than ten, such as 7 + 5, but have difficulty determining their differences, like 12 − 7. Finally, some students have no difficulty adding 7 + 5 or 8 + 4 but cannot mentall y add 17 + 5 or 18 + 4 or recognize the connection between the sum of singledigit numbers and numbers inc reased by orders of ten. Any one or a combination of these difficulties may appear when students compute; moreover, these problems will continue to plague them, curtailing their confidence and development in mathematics and mental arithmetic.

scholarly journals Finger Tracking Reveals the Covert Stages of Mental Arithmetic

Open Mind ◽  
2017 ◽  
Vol 1 (1) ◽  
pp. 30-41 ◽  
Author(s):  
Pedro Pinheiro-Chagas ◽  
Dror Dotan ◽  
Manuela Piazza ◽  
Stanislas Dehaene
Keyword(s):  
Mental Arithmetic ◽  
Number Line ◽  
Mental Number Line ◽  
Correct Result ◽  
Single Digit ◽  
Absolute Value ◽  
Transient Activation ◽  
Novel Method ◽  
Finger Tracking ◽  
The Right

We introduce a novel method capable of dissecting the succession of processing stages underlying mental arithmetic, thus revealing how two numbers are transformed into a third. We asked adults to point to the result of single-digit additions and subtractions on a number line, while their finger trajectory was constantly monitored. We found that the two operands are processed serially: the finger first points toward the larger operand, then slowly veers toward the correct result. This slow deviation unfolds proportionally to the size of the smaller operand, in both additions and subtractions. We also observed a transient operator effect: a plus sign attracted the finger to the right and a minus sign to the left and a transient activation of the absolute value of the subtrahend. These findings support a model whereby addition and subtraction are computed by a stepwise displacement on the mental number line, starting with the larger number and incrementally adding or subtracting the smaller number.

Low temperature x-ray microanalysis of frozen-hydrated tobacco leaves

1984 ◽  
Vol 42 ◽  
pp. 284-285
Author(s):  
S. Edith Taylor ◽  
Patrick Echlin ◽  
May McKoon ◽  
Thomas L. Hayes
Keyword(s):  
Low Temperature ◽  
Lemna Minor ◽  
Root Tips ◽  
Tobacco Leaves ◽  
X Ray ◽  
Whole Cells ◽  
Carbon Coated ◽  
The Right ◽  
Beam Currents ◽  
The University

Low temperature x-ray microanalysis (LTXM) of solid biological materials has been documented for Lemna minor L. root tips. This discussion will be limited to a demonstration of LTXM for measuring relative elemental distributions of P,S,Cl and K species within whole cells of tobacco leaves.Mature Wisconsin-38 tobacco was grown in the greenhouse at the University of California, Berkeley and picked daily from the mid-stalk position (leaf #9). The tissue was excised from the right of the mid rib and rapidly frozen in liquid nitrogen slush. It was then placed into an Amray biochamber and maintained at 103K. Fracture faces of the tissue were prepared and carbon-coated in the biochamber. The prepared sample was transferred from the biochamber to the Amray 1000A SEM equipped with a cold stage to maintain low temperatures at 103K. Analyses were performed using a tungsten source with accelerating voltages of 17.5 to 20 KV and beam currents from 1-2nA.

A Tracer Study of ICT Graduate Students at Mzuzu University, Malawi

Mousaion ◽  
2019 ◽  
Vol 36 (3) ◽  
Author(s):  
Chimango Nyasulu ◽  
Winner Chawinga ◽  
George Chipeta
Keyword(s):  
Language Processing ◽  
Mobile Application ◽  
First Century ◽  
Application Development ◽  
Job Requirements ◽  
Level Of Satisfaction ◽  
Information And Communication ◽  
Quantitative Design ◽  
The Right ◽  
The University

Governments the world over are increasingly challenging universities to produce human resources with the right skills sets and knowledge required to drive their economies in this twenty-first century. It therefore becomes important for universities to produce graduates that bring tangible and meaningful contributions to the economies. Graduate tracer studies are hailed to be one of the ways in which universities can respond and reposition themselves to the actual needs of the industry. It is against this background that this study was conducted to establish the relevance of the Department of Information and Communication Technology at Mzuzu University to the Malawian economy by systematically investigating occupations of its former students after graduating from the University. The study adopted a quantitative design by distributing an online-based questionnaire with predominantly closed-ended questions. The study focused on three key objectives: to identify key employing sectors of ICT graduates, to gauge the relevance of the ICT programme to its former students’ jobs and businesses, and to establish the level of satisfaction of the ICT curriculum from the perspectives of former ICT graduates. The key findings from the study are that the ICT programme is relevant to the industry. However, some respondents were of the view that the curriculum should be strengthened by revising it through an addition of courses such as Mobile Application Development, Machine Learning, Natural Language Processing, Data Mining, and LINUX Administration to keep abreast with the ever-changing ICT trends and job requirements. The study strongly recommends the need for regular reviews of the curriculum so that it is continually responding to and matches the needs of the industry.

IMAGERY AND EMOTIONS IN THE PIANO PIECE „THE SICK DOLL“ FROM CHILDREN’S ALBUM OF P . I TCHAIKOVSKY

2020 ◽  
Vol 11 (1) ◽  
pp. 110-113
Author(s):  
Smilena Smilkova ◽  
Keyword(s):  
At Risk ◽  
Social Work ◽  
Short Story ◽  
Special Educational Needs ◽  
Social Pedagogy ◽  
Sound Image ◽  
The Individual ◽  
The Right ◽  
The University ◽  
Art Pedagogy

The proposed material examines the creative task of students majoring in Social Pedagogy at the University „Prof. Dr. Assen Zlatarov“ in Burgas, and studying the discipline Art Pedagogy – Part 1 – Music. In the course of the lecture course students get acquainted with the elements of musical expression, as a means of figurative representations and impact of music, with different techniques concerning individual musical activities, with the endless and diverse opportunities that music provides in the use of art pedagogy for social work teachers.Verbal interpretation of music is a necessary component when working with children with special educational needs, at risk and in the norm. Looking at Tchaikovsky’s short and extremely figurative piano piece „The Sick Doll“ from his charming „Children’s Album“, in the form of a short story, tale or essay, students express their personal vision, feeling and transformation of the musical image. The aim of the task is to transcribe the sound image into a verbal one. This requires speed, flexibility and logic in thinking, through imagination and creativity in its manifestation. Children love to listen, especially when they are involved. In search of the right way to solve problems and situations, future social educators could successfully benefit from the conversion of sound into words, according to the needs and deficits of the individual or group.

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