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

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None of the participants showed clinical signs of dementia or degenerative processes and all had good to perfect numerical and mathematical abilities, so that the EC 301 R showed no sign of acalculia in any one patient. Table 2 summarizes the test results of the NET, EC 301 R and SIDAM. For detailed results of the subtests of the NET (e.g. line crossing: patient M.M. correctly marked 17 out of 36 lines) and EC 301 R (e.g. dot counting: patient M.M. was not able to count the presented dots) see Appendix A. Stimuli and design: 160 triplets of two-digit numbers (ranging from 11 to 99) were used in this study. The triplets were presented in Arabic notation. Overall distance, problem size, average parity, parity homogeneity, decade-crossing, the inclusion of decade numbers as well as tie numbers were matched between the respective stimuli groups. 80 non-bisected triplets were organized in a fully crossed 2 x 2 design incorporating the factors distance to the arithmetical middle (close vs. far) and size relative to the arithmetical middle (smaller or larger than the arithmetical middle). Distance to the middle refers to the distance of the presented middle number to the true arithmetical middle of the interval. In the triplet 21_22_35, the presented central number 22 has a far distance to the arithmetical middle (i.e. 28 - 22 = 6) while in 21_27_35, 27 is close to the arithmetical middle (i.e. 28 - 27 = 1). Size relative to the arithmetical middle refers to the position of the central number in relation to the arithmetical middle of the given interval. For the triplet 33_34_47 the presented middle number 34 is smaller than the arithmetical middle 40, while in 21_34_35 the number 34 is larger than the arithmetical middle 28. 210
Table 1: Demographic and clinical data of all participants Neglect patients M.M. K.R. S.I. S.G. H.E. R.R. Mean(SD) Sex Male Male Female Male Female Male Age 57 46 45 62 55 63 54.7(7.7) Education 8 13 9 8 9 9 9.3(1.9) Time post lesion (weeks) 12 3 6 17 14 10 10(5.2) Median 12 Lesion etiology IS IS HS(SAH) HS IS IS Lesion site RH; PO RH;TP RH; RH; BN RH; FP RH; TP Affected blood vessel Middle cerebral artery Middle cerebral artery Middle cerebral artery Middle cerebral artery Middle cerebral artery Middle cerebral artery Control patients H.G. F.C. B.R. B.H. O.H. G.D. Sex Male Male Female Male Female Male Age 58 46 46 60 54 69 55.5(8.8) Education 9 9 10 9 10 9 9.3(0.5) Time post lesion (weeks) 10 6 5 44 17 200 47(76.3)Median 14 Lesion etiology IS IS IS IS SAH IS Lesion site LH; P RH; BS RH; T LH; Pons Bilat. F RH;FP Affected blood vessel Middle cerebral artery Artery vertibralis Cerebral posterior artery Arteria pontis Middle cerebral artery Healthy controls R.M. Z.R. L.H. F.K. S.G. B.H. Sex Male Male Female Male Female Male Age 57 47 48 63 55 67 56.2(7.3) Education 12 9 8 9 9 13 10(2) 1 This patient was tested four years post lesion and could not be matched for the parameter time post lesion HS - hemorrhagic stroke, IS - ischemic stroke, SAH - subarachnoidal hemorrhagic LH - left hemisphere, RH - right hemisphere BN - basal nuclei, BS - brain stem, F - frontal, O - occipital, P - parietal, T - temporal 211
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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
Page 185 and 186: A word on the validity of the curre
Page 187 and 188: e adapted for the results of the pr
Page 189 and 190: Non-monotonous Model of the Relatio
Page 191 and 192: of the probes unit and/or decade di
Page 193 and 194: the place-value structure of the Ar
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: Visual field assessment showed no s
Page 239 and 240: For 80 bisected triplets the factor
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
Page 279 and 280: 236) = 417.38, p < .001] and incorp
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
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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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