GENERAL INTRODUCTION ........................................... 11
The Triple Code Model of numerical cognition ................ 12
Research questions driving the studies enclosed ............. 13
Section 1: Basic number processing ....................... 13
Section 2: Complex number processing on the example of
mental addition ............................... 14
Section 3: Number processing on the example of
multiplication ................................ 18
Section 4: Connections of number magnitude processing
and fact retrieval ............................ 19
SECTION 1: BASIC NUMBER PROCESSING ............................. 20
Study 1: On the neuro-cognitive foundations of basic
auditory number processing ............................... 21
BACKGROUND ............................................... 22
METHODS .................................................. 27
DISCUSSION ............................................... 36
REFERENCES ............................................... 42
SECTION 2: COMPLEX NUMBER PROCESSING FOR MENTAL ADDITION ....... 46
Study 2: To carry or not to carry - is this the question?
Disentangling the carry effect in multi-digit addition ... 47
INTRODUCTION ............................................. 48
METHODS .................................................. 55
RESULTS .................................................. 57
DISCUSSION ............................................... 60
References ............................................... 67
Appendix A ............................................... 70
Appendix В ............................................... 72
Appendix C ............................................... 73
Study 3: Three processes underlying the carry effect in
addition - Evidence from eye-tracking .................... 75
INTRODUCTION ............................................. 76
METHOD ................................................... 81
RESULTS .................................................. 83
DISCUSSION ............................................... 95
REFERENCES .............................................. 101
Study 4: (No) small adults - Children's processing of
carry addition problems ................................. 105
INTRODUCTION ............................................ 106
METHODS ................................................. 110
RESULTS ................................................. 114
DISCUSSION .............................................. 118
REFERENCES .............................................. 125
Study 5: Categorical and continuous - disentangling the
neural correlates of the carry effect in multi-digit
addition ................................................ 129
INTRODUCTION ............................................ 130
METHODS ................................................. 132
RESULTS ................................................. 136
DISCUSSION .............................................. 147
REFERENCES .............................................. 154
Appendix A .............................................. 159
SECTION 3: NUMBER PROCESSING FOR MULTIPLICATION ............... 160
Study 6: Rehabilitation of arithmetic fact retrieval via
extensive practice: A combined fMRI and behavioural
case-study .............................................. 161
INTRODUCTION ............................................ 162
CASE DESCRIPTION ........................................ 166
EXPERIMENTAL INVESTIGATION .............................. 170
RESULTS ................................................. 171
DISCUSSION .............................................. 176
REFERENCES .............................................. 181
SECTION 4: CONNECTIONS OF NUMBER MAGNITUDE PROCESSING AND
FACT RETRIEVAL ............................................. 185
Study 7: Dorsal and ventral processing in mental
arithmetic .............................................. 186
INTRODUCTION ............................................ 187
MATERIALS AND METHODS ................................... 193
DISCUSSION .............................................. 205
REFERENCES .............................................. 213
GENERAL DISCUSSION ............................................ 218
Integration of the individual studies in terms of the
Triple Code model (TCM) .................................... 218
Section 1: Basic number processing ...................... 218
Section 2: Complex number processing on the example of
mental addition .............................. 219
Section 3: Number processing on the example of
multiplication ............................... 221
A recommended update for the Triple-Code model (TCM) ....... 222
Magnitude related processing ............................ 224
Verbally mediated fact retrieval processes .............. 227
Interplay between both networks ......................... 229
Future directions .......................................... 233
REFERENCES .................................................... 238
DANKSAGUNG .................................................... 244
ERKLÄRUNG ..................................................... 246
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