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Book cover for The Oxford Handbook of Numerical Cognition The Oxford Handbook of Numerical Cognition
Roi Cohen Kadosh (ed.), Ann Dowker (ed.)
https://doi.org/10.1093/oxfordhb/9780199642342.001.0001
Published online:
03 March 2014
Published in print:
30 July 2015
Online ISBN:
9780191750878
Print ISBN:
9780199642342

Contents

Book cover for The Oxford Handbook of Numerical Cognition The Oxford Handbook of Numerical Cognition
Front Matter

List of Figures

https://doi.org/10.1093/oxfordhb/9780199642342.002.0006
Pages
xv–xx
  • Published:
    March 2014
Subject
Psychology
Series
Oxford Library of Psychology
Collection: Oxford Handbooks Online
1.1

(a) A Circular Celtic Knot. (b) The Chased Chicken Sona pattern.  15

4.1

An illustration of the typically found modulation of the SiCE by the task-irrelevant intrapair numerical distance.  49

4.2

SiCE is larger for unit-decade compatible versus incompatible trials, but is unaffected by the decade size.  51

4.3

Congruency effect indicating automating processing of the irrelevant dimension of place-value.  52

4.4

SiCE in comparisons of a set of natural numbers to a given fraction (black lines) increases with the magnitudes of the natural numbers.  54

4.5

Mean RTs as a function of comparison type, congruency and (absolute) distance.  59

B5.1

Grip aperture during the grasping of wooden blocks with small or large numbers printed on their visible face.  69

B5.2

A finger-based method to multiply any pair of numbers between 5 and 10.  71

B5.3

A finger-based method to prove that 9 × n = 10(n – 1) + (10 – n).  72

B5.4

Finger-based method to subtract 1 from 5.  74

5.1

A fMRI experiment where a wooden block was placed in each hand of the participant.  81

6.1

Schematic depiction of the SNARC effect.  91

6.2

Schematic depiction of the number interval bisection task.  94

6.3

Depiction of the magnitude comparison distance effect in neglect patients.  96

6.4

Results of the Principal Component Analyses (PCA) of the association between numbers and space.  101

8.1

Illustration of the abstract-code model.  141

8.2

Illustration of triple-code theory.  142

8.3

Illustration of the encoding-complex model.  143

9.1

Each part of the Change situation.  173

9.2

Initial total amount of objects portioned into two parts.  174

10.1

Examples for symmetric and asymmetric dot patterns.  184

10.2

Examples for ratio bias task.  186

10.3

Illustration of rectangle task.  187

11.1

Monkeys show ratio dependence when ordering numerosities.  204

11.2

Infant numerical change detection tasks demonstrates ratio dependence.  205

12.1

Laboratory studies have shown the existence of quantity abilities in mammals, birds, basal vertebrates, and invertebrates.  216

12.2

Preferential looking time was recorded to assess whether dogs can spontaneously add numerical information.  220

12.3

Compared guppies and humans in small and large number discrimination.  227

12.4

Ordinal information seems to be already processed at birth in birds.  230

13.1

Example stimulus cards from the investigation of number concept formation in rhesus monkeys.  238

13.2.

Stimuli used to show that squirrel monkeys could make relative numerousness judgments between polygons.  239

13.3

A macaque monkey is given an array of numerals and must select them in descending order using a cursor to contact the numerals in sequence.  243

13.4

Systematically controlled tests of relative numerousness judgment in rhesus monkeys.  244

15.1

Path model of development of SFON and mathematical skills from the age of 3.5 years to the age of 6 years.  281

15.2

Model illustrating significant direct effects between subitizing-based enumeration, verbal-counting skills, SFON, and mathematics achievement.  282

16.1

Aggregate data from 641 2–4-year-old children tested on the Give-N task.  297

16.2

Relations among expressive vocabulary, receptive vocabulary, and knower-level variables.  299

16.3

Heat map of data from 65 bilingual children tested on the Give-N task in each of their languages separately.  300

16.4

Blocks and Water task design.  302

16.5

Example of a Match-to-Sample trial where the correct response picture matches the sample picture on number.  303

17.1

Example of an animated sequence showing addition of dot arrays.  312

17.2

Example of an animated sequence for a non-canonical problem.  320

18.1

Two examples of the stimuli used in the non-symbolic number comparison task.  332

18.2

A schematic representation of the neural representation of number.  334

19.1

Age-related changes in number sense acuity with age.  346

19.2

Numerical distance effects in children, young and older adults, and in MCI patients.  347

19.3

Age-related changes in SNARC effects.  348

19.4

Age-related changes in counting and subitizing speed per item.  349

19.5

Age-related changes in arithmetic problem size effects.  351

19.6

Effects of arithmetic problem complexity with age.  352

19.7

Age-related changes in strategy repertoire.  354

19.8

Strategy selection in young and older adults’ strategy selection in a computational estimation task.  356

19.9

Strategy execution and strategy distribution in older adults compared to younger adults.  357

20.1

A 27-body part counting system.  373

21.1

A canonical Collecting gesture.  393

21.2

A canonical Path gesture.  394

21.3

Participants spontaneously produced Path and Collecting gestures.  395

22.1

Compressed 0–100 number scale and logarithmic estimation curve.  408–9

23.1

A test item assessing children’s place value understanding.  419

26.1

Representation of visual cardinality in rhesus monkeys.  458

26.2

Numerosity-selective neurons in the monkey.  460

26.3

Coding of sequentially presented numerosity.  462

26.4

Relation between monkey behaviour and numerosity-selective neurons.  464

26.5

Implementation of numerosity detectors.  466

26.6

Neuronal coding of continuous and discrete quantity.  469

26.7

Neuronal coding of proportions.  470

26.8

Semantic associations between signs and numerical categories by single neurons.  472

26.9

Temporal ordering task and single cell responses from the PFC.  476

26.10

Numerical rule coding.  478

27.1

Four-step-developmental model of numerical cognition.  488

27.2

Tentative developmental calculation model emphasizing the dynamic nature of numerical development.  489

27.3

Schematic representation depicting neural networks supporting the acquisition of number skills.  491

28.1

Schematic circuit diagram of basic neurocognitive processes involved in arithmetic.  503

28.2

Canonical brain areas involved in arithmetic problem solving.  506

28.3

Neuroanatomy of posterior parietal cortex regions involved in arithmetic.  507

28.4

Brain regions that showed significant differences in activation between arithmetic operations.  512

28.5

Neurodevelopmental changes in arithmetic.  515

28.6

Developmental changes in causal network interactions during arithmetic problem solving.  518

28.7

Comparison of ventral visual stream responses in 2nd and 3rd grade children.  520

28.8

Strategy differences in arithmetic problem solving.  522

29.1

Numerals 1–9 in the Thai script.  532

29.2

The three fields in the first phase of the neural network experiment.  535

29.3

Illustration of the second phase of the neural network experiment.  536

29.4

Brain regions commonly involved in number processing.  541

31.1

Illustration of the pathway for the processing of number from visual input to a number-selective code.  568

31.2

Activation of three different contrasts.  573

32.1

Reported brain sites whose stimulation through TMS has led to disruption in quantity.  592

32.2

Reported brain sites whose stimulation through TMS has led to disruption in spatial-numerical processes.  596

32.3

Scheme of the localization of calculation and language interference.  600

32.4

Examples of two patients showing the proximity of sites where Gerstmann symptoms were observed.  601

35.1

Causal model of possible interrelationships between biological, cognitive, and simple behavioural levels.  651

35.2

Structural abnormalities in young dyscalculic brains suggesting the critical role for the IPS.  653

35.3

Remediation using learning technology.  656

36.1

Deficits in IPS and AG leading to difficulties both in language and DD.  664

40.1

Summary of deficient brain function, gray matter, white matter, and brain metabolism in children with DD.  735

42.1

Fluency scores on the Number Sets Test comparing typically achieving children to children with mathematical learning disability.  772

42.2

Procedural competence scores for complex addition and the percentage of the simple addition problems that were correctly solved using retrieval.  774

43.1

Illustration of the effect of adaptation on numerosity perception as a function of the number of dots in the probe.  789

43.2

ERSP results illustrating the topography of electrode sites showing the distance effect in phase 1 and in phase 2.  793

43.3

Illustration of the experimental design.  794

43.4

Blind and sighted participants’ accuracy scores in the key press estimation task and in the auditory events estimation tasks.  797

43.5

Blind and sighted participants’ accuracy scores in the footstep estimation task and in the oral verbal estimation tasks.  799

45.1

Speed and accuracy improvements in complex multiplication and subtraction following training.  844

45.2

Schematic illustration of brain activation changes in complex calculation following training.  845

49.1

The working memory tasks.  923

55.1

The related MD&A diagrams for addition and multiplication.  1044

55.2

Mathematically-desirable and accessible algorithms and diagrams.  1045

55.3

Using the multiplication table for teaching and learning ratio and proportion.  1047

56.1

Scissors tool for creating doubles.  1066

56.2

Grouping boxes and number line.  1067

56.3

The Ghost Box grouping tool.  1068

56.4

Four pedagogical agents.  1068

58.1

Entry standardized score and number age gain.  1110

59.1

Potential components of an information-processing model for the relations between conceptual and procedural knowledge.  1128

60.1.

The number and colour linear board games.  1144

60.2

Performance of preschoolers from low-income backgrounds on four numerical tasks.  1145

60.3

The circular number board games.  1146

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