The influence of the place-value structure of the Arabic number ...

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Table 2: Scores of each participant in the NET, SIDAM and EC 301 R; Individual mean RT and error rate Neglect Group M.M. K.R. S.I. S.G. H.E. R.R. NET Standard value 78 163 136 99.5 147 71 Diagnosis Considerable Low Considerable - low Considerable Low Very Considerable SIDAM Raw data 43/55 1 54/55 50/55 37/55 1 44/55 1 52/55 EC301R Raw data 84/135 2 130/135 115/135 2 Missing data. 3 123/135 2 103/135 2 NBT (RT) ms 8493 2425 7133 6436 5660 7452 NBT (Errors) % 15.00 5.60 7.50 21.30 26.90 10.00 Patient group H.G. F.C. B.R. B.H. O.H. G.D. NET Diagnosis No Negelct No Negelct No Negelct No Negelct No Negelct No Negelct SIDAM Raw data 54/55 53/55 55/55 55/55 46/55 50/55 EC301R Raw data 135/135 134/135 134/135 135/135 133/135 123/135 NBT (RT) ms 2190 3332 2954 2738 3467 4421 NBT (Errors) % 1.30 1.90 1.90 5.60 10.60 4.40 Healthy group R.M. Z.R. L.H. F.K. S.G. B.H. NET Diagnosis No Negelct No Negelct No Negelct No Negelct No Negelct No Negelct SIDAM Raw data 55/55 51/55 49/55 46/55 54/55 54/55 EC301R Raw data 133/135 134/135 130/135 133/135 135/135 135/135 NBT (RT) ms 3778 3336 5800 2860 5061 6387 NBT (Errors) % 2.50 11.30 6.30 1.30 1.30 3.80 1 Due to neglect symptoms some items of the SIDAM could not be successfully processed (e.g. copying shapes) 2 Due to neglect symptoms some items of the EC310R could not be successfully processed (e.g. counting dots) 3 This patient was tested on the following numerical and mathematical abilities: comparing single- and multi-digit Arabic numbers, mental arithmetic (addition, subtraction, multiplication, division) and written arithmetic (addition and subtraction). The patient’s tested abilities were intact. 212
For 80 bisected triplets the factors multiplicativity (yes vs. no) and decade crossing (yes vs. no) were manipulated. Bisected triplets could not be fully crossed, as triplets which are part of a multiplication table larger than three would always cross into the next decade. Therefore, the factors decade-crossing (yes vs. no) and multiplicativity (yes vs. no) were assessed in distinct item sets. The three numbers were presented above each other in the centre of the screen’s right half. Each two-digit number extended 7 cm horizontally and 4.5 cm vertically. The numbers were vertically separated by 4.5 cm. The stimuli were presented in bold Arial font (size 48), white on black background. In this study neglect patients’ performance in the verification version of the NBT was compared to that of non-neglect controls. Procedure: The experiment was run on a 1.6 GHz laptop and participants were seated approximately 50 cm in front of a 15´´ screen driven at a resolution of 1024x768 pixels. The left and right arrow keys located at the bottom right-hand corner of the keyboard functioned as response buttons: bright orange stickers with the letters “J” for “yes” (in German “Ja”) and “N” for “no” (in German “Nein”) covered the left and right arrow keys, respectively. All other keys were covered up with white cardboard. Participants were instructed to indicate their decision by pressing one of the two response buttons as fast and as accurately as possible. The instruction was followed by 20 practice trials incorporating one- and two-digit numbers. To ensure that patients perceived the presented numbers correctly all participants were asked to read out the numbers of the first four practice trials aloud. All patients were able to do so without mistakes. Participation in the critical experiment was only allowed when more than 2/3 (14 out of 20) practice trials were classified correctly. The experiment involved 213
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The influence of the place-value st
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Ich möchte mich an dieser Stelle b
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ZUSAMMENFASSUNG Das wissenschaftlic
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Study 5: All for one but not one fo
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Classification performance ........
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The Arabic place-value structure an
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Large problem size > small problem
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ABSTRACT ..........................
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Study 2: On the cognitive instantia
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LIST OF FIGURES Section 1: General
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Section 4: The neurocognitive under
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LIST OF TABLES Section 1: General I
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Section 5: A computational model of
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Number, the simplest and most unive
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limited set of symbols. To achieve
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interexponential structuring princi
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(i) separating power and base dimen
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Abstract Code Model Verbal number C
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of the Arabic number system within
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previous studies on two-digit numbe
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eview), questions concerning repres
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esponses are easier (i) for problem
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2009c). Based on the framework of t
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scarce (but see Domahs et al., 2006
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y Studies 5 and 6 of the current th
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OVERVIEW OVER THE STUDIES INCORPORA
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a view was corroborated by a variet
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would indicate influences of verbal
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2. Study 6: Impairments of the ment
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eplicate processes of unit-decade i
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determinants shall be reviewed. Mor
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Study 6: Hoeckner, S., Moeller, K.,
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Section 2 Task invariant influences
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ABSTRACT Over the last years, evide
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The authors used a magnitude compar
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Such congruency is important as mos
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Procedure: After ten randomly chose
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compatibility effect for large unit
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2004). So, increasing the maximum u
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proportions in earlier studies. The
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CONCLUSIONS In summary, the conclus
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Study 2 On the cognitive instantiat
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INTRODUCTION One of the probably mo
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eye fixation behaviour for the eval
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(see Rayner, 1998 for a review). Tr
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Procedure: After being seated with
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adjustment of the degrees of freedo
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Eye fixation behaviour TRT in ms To
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or the decade digits was found (393
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egressions were directed to the sec
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the requirement of a carry is deter
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In line with this prediction, total
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Instead, it seems to involve differ
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Section 3 On the importance of plac
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ABSTRACT The mental number line of
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preschoolers aged 4). However, the
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still represented even when only th
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specificity. Yet, in adults it has
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METHOD The reported experiment was
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child separately to obtain estimati
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indicated that Italian children’s
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striking similarity between the ori
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Inversion influences on estimation
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% overall Estimation Error 25 20 15
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seem to be the origin of the perfor
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this system. In this case no langua
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two-linear model with one linear re
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and 40 is 10 times as large as the
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APPENDIX A A remark on how to evalu
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Splitting the overall interval in t
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much closer to the proposed breakpo
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the individual approach may be more
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Contrarily, data produced by a two-
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Study 4 Early place-value understan
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INTRODUCTION Dealing with (multi-di
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has been shown that other represent
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number system as formalized by its
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124 10024, see Deloche & Seron, 19
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Please note that in contrast to Miu
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Roid, Prifitera, & Weiss, 1993; see
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effect-based approach has never bee
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(ii) In the magnitude comparison ta
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problem of capitalizing on differen
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Error rate in % Error Categories (c
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positively correlated with overall
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(ii) Effect approach analyses of pr
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whether the carry effect for additi
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Non-carry problems: For the percent
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from basic numerical concepts to ar
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transcoding and/or who showed relat
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A word on the validity of the curre
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Page 189 and 190: Non-monotonous Model of the Relatio
Page 191 and 192: of the probes unit and/or decade di
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Page 195 and 196: Therefore, we believe that this stu
Page 197 and 198: APPENDIX A: Correlation tables of s
Page 199 and 200: Section 4 The neurocognitive underp
Page 201 and 202: ABSTRACT Mental arithmetic and calc
Page 203 and 204: manipulations cannot be distinguish
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Page 207 and 208: correctly bisected by the second nu
Page 209 and 210: Table 1: Behavioural performance in
Page 211 and 212: were found bilaterally in the dorso
Page 213 and 214: Table 3: Brain areas activated by b
Page 215 and 216: portion of the superior frontal gyr
Page 217 and 218: Figure 3: fMRI signal for parametri
Page 219 and 220: The fronto-parietal network and the
Page 221 and 222: Finally, increased activation in th
Page 223 and 224: Inferior parietal cortex, the angul
Page 225 and 226: primarily necessary for solving the
Page 227 and 228: Tippet (1996) have shown that patie
Page 229 and 230: Study 6 Impairments of the mental n
Page 231 and 232: INTRODUCTION Patients suffering fro
Page 233 and 234: 2005), triplets in which the interv
Page 235 and 236: Visual field assessment showed no s
Page 237: Table 1: Demographic and clinical d
Page 241 and 242: Factorial Analyses (ANOVA and t-tes
Page 243 and 244: Errors: The ANOVA revealed a main e
Page 245 and 246: DISCUSSION The effects of neglect o
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Page 249 and 250: strategic value of retrieving this
Page 251 and 252: APPENDIX A Test results of patients
Page 253 and 254: the middle the beneficial effect of
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Page 257 and 258: Study 7 Two-digit number processing
Page 259 and 260: INTRODUCTION The internal represent
Page 261 and 262: all numbers the overlap for larger
Page 263 and 264: digit numbers were engaged. Additio
Page 265 and 266: single node in an ordered sequence
Page 267 and 268: modelling to evaluate the plausibil
Page 269 and 270: A Output Layer 11 99 11 #1 #2 99 In
Page 271 and 272: expected considering their magnitud
Page 273 and 274: the output of the right node would
Page 275 and 276: advantages for these numbers (see a
Page 277 and 278: Finally, a regression analysis only
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Page 281 and 282: Regression The stepwise regression
Page 283 and 284: compared numbers, unit distance, lo
Page 285 and 286: RT in ms 780 770 Compatible Number
Page 287 and 288: esponse latencies increased as dist
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Table 5: Predictors included in the
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Taken together, these results revea
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of overall distance necessarily req
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most important predictor in a multi
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activation of the output layer is a
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The nature of the representation of
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Thereby, possible interactions and
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decomposed model did not include an
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APPERNDIX B Development of connecti
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Figure C: Development of connection
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Figure E: Development of connection
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Interestingly, one might infer from
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Section 6 Summary 287
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may be determined by the presentati
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tens and units: German-speaking chi
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Study 6 examined the influence of t
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295
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GENERAL DISCUSSION In the last sect
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to-be-evaluated triplet crossed a d
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specific processing of place-value
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explanation of the decade consisten
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verbal recoding of tens and units d
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system and the ordinality of the me
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epresentation itself as well as its
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Furthermore, converging evidence is
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methodological problems. In most of
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jittering the positions of the sequ
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numbers within the triplets, proces
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Pollatsek, 1989) states that an obj
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computational models were programme
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The developmental influence of plac
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correspond to the order of tens and
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Asian languages (e.g., Japanese, Ko
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indicating that decomposed processi
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REFERENCES Banks, W. P. (1977). Enc
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Karmiloff-Smith, Annette (1996). Be
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Pixner, S. (2009). How do children
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