Some quick arithmetic
TENNET XI
205
rather p r i v i l e g e d view o f the sources o f i n f o r m a t i o n p r o v i d e d by these two c o m p o nents o f the lexical p r o c e s s i n g system.
REFERENCES
Buchanan, L., Hildebrandt, N., & MacKinnon, G. E. (1999). Phonological processing in deep dyslexia
reconsidered. In R. Klein & P. McMullen (Eds.), Converging Methods for Understanding Reading
and Dyslexia (pp. 191-221). Cambridge, MA: MIT Press.
Butterworth, B. (1983). Lexical representation. In B. Bunerworth (Ed.), Language production (Vol. 2,
pp. 257-294). San Diego, CA: Academic Press.
Coltheart, M. (1980). Deep dyslexia: A review of the syndrome. In M. Coltheart, K. Patterson, & J.
Marshall (Eds.), Deep dvslexia (pp. 22-47). Boston: Routledge & Kegan Paul.
Jarema, G., Busson, C., Nikolova, R., Tsapkini, K., & Libben, G. (1999). Processing compounds: A
cross-linguistic study. Brain and Language, 68, 362-369.
Libben, G. (1993). A case of obligatory access to morphological constituents. Nordic Journal of Linguistics, 16, 111-121.
Libben, G. (1998). Semantic transparency in the processing of compounds: Consequences for representation, processing, and impairment. Brain and Language, 61, 30-44.
Libben, G., Gibson, M. Yoon, Y., & Sandra, D. (1997), Semantic transparency and compound fracture.
CLASNET Working Papers, 9, 1-13.
Marslen-Wilson, W., Tyler, L. K., Waksler, R., & Older, L. (1994). Morphology and meaning in the
English mental lexicon. Psychological Review, 101, 3-33.
Sandra, D. (1990). On the representation and processing of compound words: Automatic access to constituent morphemes does not occur. The Quarterly Journal of Experimental Psychology, 42a, 529567.
Taft, M., & Forster, K. I. (1975). Lexical storage and retrieval of prefixed words. Journal of Verbal
Learning and Verbal Behavior, 14, 638-647.
Some Quick Arithmetic
Vesna Mildner
UniversiO' of Zagreb, Croatia
Mathematical abilities for the four simple arithmetic operations were studied on a sample
of 53 female right-handers. True and false statements were presented auditorily and a manual
response was required as to the trueness of the statements. Response times, accuracy, and
laterality index showed no significant ear advantage, but the responses to true statements were
significantly faster than to the false ones. The shortest response times were found for addition
problems, and the longest for subtractions. The correlation between the size of the difference
between the two operands and response time was not conclusive but the trend was
unexpectedly positive. © 2001 AcademicPress
Introduction
M a t h e m a t i c a l abilities, as an integral part o f c o g n i t i v e processes, have been studied
in n o r m a l and clinical populations, w h i c h resulted in a b o d y o f frequently conflicting
data. A c a l c u l i a or anarithmetria was f o u n d most often to i n v o l v e lesions o f the posterior left h e m i s p h e r e ( G r a f m a n et al., 1982; M c C a r t h y & W a r r i n g t o n , 1990), i n c l u d i n g
left subcortical infarcts ( D e h a e n e & Cohen, 1998). On the other hand, B e n b o w (1988)
s u g g e s t e d that m a t h e m a t i c a l abilities were related to spatial abilities, indicating a
p r e d o m i n a n t l y right h e m i s p h e r e i n v o l v e m e n t .
206
TENNET XI
With respect to differential vulnerability of numerical abilities to deficits of various
etiologies, including degenerative deterioration, there have been reports of patients
who could do additions and multiplications, but not subtractions (Dehaene & Cohen,
1998), those with initial impairment limited to multiplication and division (Grafman
et al., 1989) or to multiplication and complex subtraction (Girelli et al., 1999).
Furthermore, it has been argued (Geary, 1996) that addition and subtraction are
biologically primary mathematical abilities and multiplication and division secondary
ones.
The aims of this work were (1) to check for possible ear advantage as an indicator
of functional cerebral asymmetry in solving simple arithmetic problems and (2) to
determine which arithmetic operations were the most difficult or the easiest.
Me~od
The subjects were 53 healthy right-handed and right-footed female university students, between 18 and 25 years of age (mean 20), without familial sinistrality, with
normal and symmetrical hearing, and with no history of neurological disorders, native
speakers of Croatian.
Recording and reproduction were done on a Sony MiniDisc recorder. Test material
was prepared on a 486 PC (Sound Blaster 16, Creative Wave Studio 2.01). Analogdigital conversion was at the l l,025-Hz (8-bit) sampling frequency. The apparatus
and software for computer-aided RT recording and measurement were designed at
the University of Zagreb. Rona Kern Type G stereophonic headphones were used.
Testing was performed individually, in a quiet but not specially sound-treated room
(ambient noise less than 40 dB).
The test material consisted of 32 arithmetic problems in the form of statements,
using the four basic operations: addition, multiplication, subtraction, and division on
integers from 1 to 10. The statements were pronounced at the rate of approximately
three syllables per second by a male speaker and presented at 75 dB. Half of the
solutions were correct (true statements) and the other half were incorrect (false statements) (e.g., 1 + 3 = 4 or 6 + 1 = 8). Half of the statements were presented to
the right ear, and the other half to the left, with the opposite ear masked by a murmur
-+ 5 dB representation level. This yielded four stimuli categories of eight statements
(two for each operation): true statements presented to the right ear, false statements
presented to the right ear, true statements presented to the left ear, and false statements presented to the left ear. The order and side of stimuli presentation were quasirandom. Three-hundred milliseconds before each statement a 1000-Hz pure tone was
presented simultaneously to both ears for 250 ms in order to bring the subject's attention back to the middle. The language of testing was Croatian.
Oral instructions and a training session were given before the test. The task was
to answer whether the statements were true or false. The responses were given manually, by pressing the response plate positioned on the table in the midline in front of
the subject, with both hands--thumbs for a positive answer (true statement) and
index fingers for a negative answer (false statement). The subjects were encouraged
to respond as fast as possible.
Response times (to the nearest ms) and accuracy were measured, recorded, and
calculated by a personal computer. Laterality index (LI) was calculated from the
accuracy measures: LI = (Rc - Lc/Re + Le) * 100. R and L stand for right and left
ear, respectively; c is correct responses, and e is incorrect responses.
Statgraphics package was used for statistical analysis.
TENNET Xl
207
600
500
400
RT (ms)
300
200
I00
0 - -
Left
[]
FIG. 1.
Right
EAR
true
[]
false
1
Response times for true and false statements for both ears.
Results and Discussion
Overall accuracy was very high: 99.32%. Mean response time for the entire sample
was 295 ms. LI for the whole test was positive (5.66), indicating right-ear advantage
(REA), i.e., left-hemisphere dominance. However, as many as 71.70% subjects,
showed no laterality (LI = 0), only 17% exhibited REA, and 11.30% actually exhibited left-ear advantage (LEA), indicative of right-hemisphere dominance.
Two-way analysis of variance has shown that the stimulated ear had no effect on
the accuracy or response time (p > .05) (Fig. 1). Mean RTs for left and right ear
were identical: 295 ms. Accuracy of responses to the stimuli presented to the left
ear (98.91%) was insignificantly lower than to the stimuli presented to the right ear
(99.73%).
The responses to true statements were significantly faster than those to the false
ones (p = .00), without significant interactions between the two independent variables (Fig. 1). Faster responses to true statements have been found in earlier studies
as well (e.g., Lemaire, Abdi, & Fayol, 1996) (but not in De Rammelaere, Stuyven, &
Vandierendonck, 1999) and the present results may be, in a broader sense, interpreted
along the lines of the findings that yes responses are in general faster than the no
responses.
The responses were further analyzed by type of operation. All results broken down
by type of operation (addition, subtraction, multiplication, division) and trueness of
statement (true, false) are summarized in Table 1.
Analysis of variance for response accuracy showed only main effect of type of
operation (p = .03) and no significant interactions (p > .05). As can be seen from
Table 1, the differences were very small, with subtraction problems yielding the least
accurate responses.
TABLE 1
Summary of Results for Response Times in ms (RT) and Accuracy (%)
Addition
Subtraction
Multiplication
Division
Statement
RT
%
RT
%
RT
%
RT
%
True
False
159
343
100
100
272
450
96.74
98.91
170
400
100
98.91
190
379
100
100
208
TENNET XI
Analysis of variance for response times showed main effects of trueness-of-statement and type-of-operation variables (p = .00), but no main effect of stimulated ear
or any significant interactions (p > .05).
If biologically primary mathematical abilities (addition and subtraction) are assumed to be automatic as opposed to the secondary ones (multiplication, division)
that are learned later in life, it would be reasonable to expect a REA. On the other
hand, simple addition and multiplication of single-digit numbers are considered to
be performed by rote (Dehaene & Cohen, 1998), such performance being also characteristic of the left hemisphere. However, the absence of any significant ear advantage
indicates lack of functional cerebral asymmetry, regardless of the operation type.
It was also reasonable to expect the biologically primary mathematical abilities to
have shorter RTs than the secondary ones. Furthermore, based on Grafman et al.'s
(1989) report on a patient whose dementia, with respect to numerical abilities, was
manifested initially as impairment in division and multiplication, it could be expected
that the 'robustness' of addition and subtraction would be manifested as yielding
better results than multiplication and division. The RTs for multiplication and division problems are indeed very similar, but it is not clear why subtraction should be
so much more difficult as indicated both by RTs and accuracy. Such results were
found within both the subset of true statements and the subset of false statements-the addition in both cases being on the average the fastest and the most accurate and
subtraction the slowest and the least accurate. This warrants further study with a
greater number of stimuli belonging to each type of operation, including better control
of the other factors that may influence responses, such as the odd-even effect or the
associative-confusion/interference effect (De Rammelaere, Stuyven, & Vandierendonck, 1999).
The combination of significant main effects showed that the shortest RTs were to
true statements involving addition problems (159 ms) and the longest RTs were to
false statements involving subtraction problems (450 ms).
In the subset of the fastest responses there was no effect of the size of the difference
between the two operands in the problem (p > .05). The analyzed differences were
2, 5, and 8. This result is contrary to that of De Rammelaere, Stuyven, & Vandierendonck (1999), who found a significant effect of difference size on response times.
In the subset of the slowest responses the effect of the size of the difference was
significant (p = .00). The analyzed differences were 2, 4, 5 and 9. However, Scheffe
test showed that the differences of 4, 5, and 9 belonged to a homogeneous group,
with only the difference of 2 eliciting significantly faster responses. This is an interesting result in itself, because it is contrary to the literature data. Namely, previous
studies have shown that the smaller the difference, the slower the response (Posner &
Raichle, 1997; De Rammelaere, Stuyven, & Vandierendonck, 1999), whereas in this
study the data for the 'slow' subgroup suggest a positive correlation of the betweenoperand difference and RT, i.e., the greater the difference, the slower the response
(with inconclusive data for the 'fast' subgroup).
Similarly to the results of De Rammelaere, Stuyven, and Vandierendonck (1999),
there was no tradeoff between accuracy and response time. In fact, there was a trend
for the fastest subjects to be the more accurate ones.
Conclusions
This study has shown that regardless of the type of operation, simple arithmetic
processing involves both cerebral hemispheres. The distinction between primary and
secondary mathematical abilities was not reflected in the accuracy or response time
to the simple arithmetic problems presented. The responses to true arithmetic state-
TENNET XI
209
ments were significantly faster than to the false ones. The shortest response times
were found for addition problems and the longest for subtractions. The correlation
between the size of the difference between the two operands and response time was
not conclusive but the trend was unexpectedly positive.
ACKNOWLEDGMENT
This research was supported by Grant 130721 of the Croatian Ministry for science and technology.
REFERENCES
Benbow, C. P. (1988). Sex differences in mathematical reasoning ability in intellectually talented preadolescents: Their nature, effects, and possible causes. Behavioral and Brain Sciences, 11, 169-232.
Dehaene, S., & Cohen, L. (1998). Levels of representation in number processing. In B. Stemmer & H.
Whitaker (Eds.), Handbook of neurolinguistics. San Diego: Academic Press.
De Rammelaere, S., Stuyven, E., & Vandierendonck, A. (1999). A contribution of working memory
resources in the verification of simple mental arithmetic sums. Psychological Research, 62, 7277.
Geary, D. C. (1996). Sexual selection and sex differences in mathematical abilities. Behavioral and
Brain Sciences, 19, 229-284.
Girelli, L., Luzzatti, C., Annoni, G., & Vecchi, T. (1999). Progressive decline of numerical skills in
Alzheimer-type dementia: A case study. Brain and Cognition, 40, 132-136.
Grafman, J., Passafiume, D., Faglioni, P., & Boller, F. (1982). Calculation disturbances in adults with
focal hemispheric damage. Cortex, 18, 37.
Grafman, J., Kampen, D., Rosenberg, J., Salazar, A. M., & Boiler, F. (1989). The progressive breakdown
of number processing and calculation ability: A case study. Cortex, 25, 121-133.
Lemaire, P., Abdi, H., & Fayol, M. (1996). The role of working memory resources in simple cognitive
arithmetic. European Journal of Cognitive Psychology, 8, 73-103.
McCarthy, R. A., & Warrington, E. K. (1990). Cognitive neuropsychology: A clinical introduction. New
York: Academic Press.
Posner, M. I., & Raichle, M. E. (1997). Images of mind. New York: Scientific American Library.
H a n d e d n e s s and Immune Function
N. S. Morfit and N. Y. Weekes
Department of Psychology, Pomona College
Geschwind, Galaburda, and Behan (GBG) have suggested that in utero levels of testosterone
influence both cerebral and immune system developments (Geschwind & Behan, 1982; Geschwind & Galaburda, 1984; Geschwind & Galaburda, 1985). According to this theory, high
levels of testosterone result in greater incidences of left-handedness, deviations from standard
distribution of cerebral functions (known as anomalous dominance), and increased autoimmune dysfunction. While the original data supported these assertions, more recent tests of the
hypothesis have been equivocal. One criticism of these studies is that the definition of both
handedness and anomalous dominance are too vague. It was one of the aims of this project
to investigate and clarify the GBG model by examining four different aspects of handedness
as well as a more direct measure of anomalous dominance. In order to extend the GBG model,
degree of left-handedness, general immune system functioning, and current testosterone levels
were also examined. First, it was predicted and found that left handers had a higher incidence
of autoimmune diseases in their immediate families than did right handers. Second, those left
handers with an incidence of at least one autoimmune disease were more strongly left-handed
than were those with no incidence of autoimmunity. Finally, it was observed that higher testos-
205
rather p r i v i l e g e d view o f the sources o f i n f o r m a t i o n p r o v i d e d by these two c o m p o nents o f the lexical p r o c e s s i n g system.
REFERENCES
Buchanan, L., Hildebrandt, N., & MacKinnon, G. E. (1999). Phonological processing in deep dyslexia
reconsidered. In R. Klein & P. McMullen (Eds.), Converging Methods for Understanding Reading
and Dyslexia (pp. 191-221). Cambridge, MA: MIT Press.
Butterworth, B. (1983). Lexical representation. In B. Bunerworth (Ed.), Language production (Vol. 2,
pp. 257-294). San Diego, CA: Academic Press.
Coltheart, M. (1980). Deep dyslexia: A review of the syndrome. In M. Coltheart, K. Patterson, & J.
Marshall (Eds.), Deep dvslexia (pp. 22-47). Boston: Routledge & Kegan Paul.
Jarema, G., Busson, C., Nikolova, R., Tsapkini, K., & Libben, G. (1999). Processing compounds: A
cross-linguistic study. Brain and Language, 68, 362-369.
Libben, G. (1993). A case of obligatory access to morphological constituents. Nordic Journal of Linguistics, 16, 111-121.
Libben, G. (1998). Semantic transparency in the processing of compounds: Consequences for representation, processing, and impairment. Brain and Language, 61, 30-44.
Libben, G., Gibson, M. Yoon, Y., & Sandra, D. (1997), Semantic transparency and compound fracture.
CLASNET Working Papers, 9, 1-13.
Marslen-Wilson, W., Tyler, L. K., Waksler, R., & Older, L. (1994). Morphology and meaning in the
English mental lexicon. Psychological Review, 101, 3-33.
Sandra, D. (1990). On the representation and processing of compound words: Automatic access to constituent morphemes does not occur. The Quarterly Journal of Experimental Psychology, 42a, 529567.
Taft, M., & Forster, K. I. (1975). Lexical storage and retrieval of prefixed words. Journal of Verbal
Learning and Verbal Behavior, 14, 638-647.
Some Quick Arithmetic
Vesna Mildner
UniversiO' of Zagreb, Croatia
Mathematical abilities for the four simple arithmetic operations were studied on a sample
of 53 female right-handers. True and false statements were presented auditorily and a manual
response was required as to the trueness of the statements. Response times, accuracy, and
laterality index showed no significant ear advantage, but the responses to true statements were
significantly faster than to the false ones. The shortest response times were found for addition
problems, and the longest for subtractions. The correlation between the size of the difference
between the two operands and response time was not conclusive but the trend was
unexpectedly positive. © 2001 AcademicPress
Introduction
M a t h e m a t i c a l abilities, as an integral part o f c o g n i t i v e processes, have been studied
in n o r m a l and clinical populations, w h i c h resulted in a b o d y o f frequently conflicting
data. A c a l c u l i a or anarithmetria was f o u n d most often to i n v o l v e lesions o f the posterior left h e m i s p h e r e ( G r a f m a n et al., 1982; M c C a r t h y & W a r r i n g t o n , 1990), i n c l u d i n g
left subcortical infarcts ( D e h a e n e & Cohen, 1998). On the other hand, B e n b o w (1988)
s u g g e s t e d that m a t h e m a t i c a l abilities were related to spatial abilities, indicating a
p r e d o m i n a n t l y right h e m i s p h e r e i n v o l v e m e n t .
206
TENNET XI
With respect to differential vulnerability of numerical abilities to deficits of various
etiologies, including degenerative deterioration, there have been reports of patients
who could do additions and multiplications, but not subtractions (Dehaene & Cohen,
1998), those with initial impairment limited to multiplication and division (Grafman
et al., 1989) or to multiplication and complex subtraction (Girelli et al., 1999).
Furthermore, it has been argued (Geary, 1996) that addition and subtraction are
biologically primary mathematical abilities and multiplication and division secondary
ones.
The aims of this work were (1) to check for possible ear advantage as an indicator
of functional cerebral asymmetry in solving simple arithmetic problems and (2) to
determine which arithmetic operations were the most difficult or the easiest.
Me~od
The subjects were 53 healthy right-handed and right-footed female university students, between 18 and 25 years of age (mean 20), without familial sinistrality, with
normal and symmetrical hearing, and with no history of neurological disorders, native
speakers of Croatian.
Recording and reproduction were done on a Sony MiniDisc recorder. Test material
was prepared on a 486 PC (Sound Blaster 16, Creative Wave Studio 2.01). Analogdigital conversion was at the l l,025-Hz (8-bit) sampling frequency. The apparatus
and software for computer-aided RT recording and measurement were designed at
the University of Zagreb. Rona Kern Type G stereophonic headphones were used.
Testing was performed individually, in a quiet but not specially sound-treated room
(ambient noise less than 40 dB).
The test material consisted of 32 arithmetic problems in the form of statements,
using the four basic operations: addition, multiplication, subtraction, and division on
integers from 1 to 10. The statements were pronounced at the rate of approximately
three syllables per second by a male speaker and presented at 75 dB. Half of the
solutions were correct (true statements) and the other half were incorrect (false statements) (e.g., 1 + 3 = 4 or 6 + 1 = 8). Half of the statements were presented to
the right ear, and the other half to the left, with the opposite ear masked by a murmur
-+ 5 dB representation level. This yielded four stimuli categories of eight statements
(two for each operation): true statements presented to the right ear, false statements
presented to the right ear, true statements presented to the left ear, and false statements presented to the left ear. The order and side of stimuli presentation were quasirandom. Three-hundred milliseconds before each statement a 1000-Hz pure tone was
presented simultaneously to both ears for 250 ms in order to bring the subject's attention back to the middle. The language of testing was Croatian.
Oral instructions and a training session were given before the test. The task was
to answer whether the statements were true or false. The responses were given manually, by pressing the response plate positioned on the table in the midline in front of
the subject, with both hands--thumbs for a positive answer (true statement) and
index fingers for a negative answer (false statement). The subjects were encouraged
to respond as fast as possible.
Response times (to the nearest ms) and accuracy were measured, recorded, and
calculated by a personal computer. Laterality index (LI) was calculated from the
accuracy measures: LI = (Rc - Lc/Re + Le) * 100. R and L stand for right and left
ear, respectively; c is correct responses, and e is incorrect responses.
Statgraphics package was used for statistical analysis.
TENNET Xl
207
600
500
400
RT (ms)
300
200
I00
0 - -
Left
[]
FIG. 1.
Right
EAR
true
[]
false
1
Response times for true and false statements for both ears.
Results and Discussion
Overall accuracy was very high: 99.32%. Mean response time for the entire sample
was 295 ms. LI for the whole test was positive (5.66), indicating right-ear advantage
(REA), i.e., left-hemisphere dominance. However, as many as 71.70% subjects,
showed no laterality (LI = 0), only 17% exhibited REA, and 11.30% actually exhibited left-ear advantage (LEA), indicative of right-hemisphere dominance.
Two-way analysis of variance has shown that the stimulated ear had no effect on
the accuracy or response time (p > .05) (Fig. 1). Mean RTs for left and right ear
were identical: 295 ms. Accuracy of responses to the stimuli presented to the left
ear (98.91%) was insignificantly lower than to the stimuli presented to the right ear
(99.73%).
The responses to true statements were significantly faster than those to the false
ones (p = .00), without significant interactions between the two independent variables (Fig. 1). Faster responses to true statements have been found in earlier studies
as well (e.g., Lemaire, Abdi, & Fayol, 1996) (but not in De Rammelaere, Stuyven, &
Vandierendonck, 1999) and the present results may be, in a broader sense, interpreted
along the lines of the findings that yes responses are in general faster than the no
responses.
The responses were further analyzed by type of operation. All results broken down
by type of operation (addition, subtraction, multiplication, division) and trueness of
statement (true, false) are summarized in Table 1.
Analysis of variance for response accuracy showed only main effect of type of
operation (p = .03) and no significant interactions (p > .05). As can be seen from
Table 1, the differences were very small, with subtraction problems yielding the least
accurate responses.
TABLE 1
Summary of Results for Response Times in ms (RT) and Accuracy (%)
Addition
Subtraction
Multiplication
Division
Statement
RT
%
RT
%
RT
%
RT
%
True
False
159
343
100
100
272
450
96.74
98.91
170
400
100
98.91
190
379
100
100
208
TENNET XI
Analysis of variance for response times showed main effects of trueness-of-statement and type-of-operation variables (p = .00), but no main effect of stimulated ear
or any significant interactions (p > .05).
If biologically primary mathematical abilities (addition and subtraction) are assumed to be automatic as opposed to the secondary ones (multiplication, division)
that are learned later in life, it would be reasonable to expect a REA. On the other
hand, simple addition and multiplication of single-digit numbers are considered to
be performed by rote (Dehaene & Cohen, 1998), such performance being also characteristic of the left hemisphere. However, the absence of any significant ear advantage
indicates lack of functional cerebral asymmetry, regardless of the operation type.
It was also reasonable to expect the biologically primary mathematical abilities to
have shorter RTs than the secondary ones. Furthermore, based on Grafman et al.'s
(1989) report on a patient whose dementia, with respect to numerical abilities, was
manifested initially as impairment in division and multiplication, it could be expected
that the 'robustness' of addition and subtraction would be manifested as yielding
better results than multiplication and division. The RTs for multiplication and division problems are indeed very similar, but it is not clear why subtraction should be
so much more difficult as indicated both by RTs and accuracy. Such results were
found within both the subset of true statements and the subset of false statements-the addition in both cases being on the average the fastest and the most accurate and
subtraction the slowest and the least accurate. This warrants further study with a
greater number of stimuli belonging to each type of operation, including better control
of the other factors that may influence responses, such as the odd-even effect or the
associative-confusion/interference effect (De Rammelaere, Stuyven, & Vandierendonck, 1999).
The combination of significant main effects showed that the shortest RTs were to
true statements involving addition problems (159 ms) and the longest RTs were to
false statements involving subtraction problems (450 ms).
In the subset of the fastest responses there was no effect of the size of the difference
between the two operands in the problem (p > .05). The analyzed differences were
2, 5, and 8. This result is contrary to that of De Rammelaere, Stuyven, & Vandierendonck (1999), who found a significant effect of difference size on response times.
In the subset of the slowest responses the effect of the size of the difference was
significant (p = .00). The analyzed differences were 2, 4, 5 and 9. However, Scheffe
test showed that the differences of 4, 5, and 9 belonged to a homogeneous group,
with only the difference of 2 eliciting significantly faster responses. This is an interesting result in itself, because it is contrary to the literature data. Namely, previous
studies have shown that the smaller the difference, the slower the response (Posner &
Raichle, 1997; De Rammelaere, Stuyven, & Vandierendonck, 1999), whereas in this
study the data for the 'slow' subgroup suggest a positive correlation of the betweenoperand difference and RT, i.e., the greater the difference, the slower the response
(with inconclusive data for the 'fast' subgroup).
Similarly to the results of De Rammelaere, Stuyven, and Vandierendonck (1999),
there was no tradeoff between accuracy and response time. In fact, there was a trend
for the fastest subjects to be the more accurate ones.
Conclusions
This study has shown that regardless of the type of operation, simple arithmetic
processing involves both cerebral hemispheres. The distinction between primary and
secondary mathematical abilities was not reflected in the accuracy or response time
to the simple arithmetic problems presented. The responses to true arithmetic state-
TENNET XI
209
ments were significantly faster than to the false ones. The shortest response times
were found for addition problems and the longest for subtractions. The correlation
between the size of the difference between the two operands and response time was
not conclusive but the trend was unexpectedly positive.
ACKNOWLEDGMENT
This research was supported by Grant 130721 of the Croatian Ministry for science and technology.
REFERENCES
Benbow, C. P. (1988). Sex differences in mathematical reasoning ability in intellectually talented preadolescents: Their nature, effects, and possible causes. Behavioral and Brain Sciences, 11, 169-232.
Dehaene, S., & Cohen, L. (1998). Levels of representation in number processing. In B. Stemmer & H.
Whitaker (Eds.), Handbook of neurolinguistics. San Diego: Academic Press.
De Rammelaere, S., Stuyven, E., & Vandierendonck, A. (1999). A contribution of working memory
resources in the verification of simple mental arithmetic sums. Psychological Research, 62, 7277.
Geary, D. C. (1996). Sexual selection and sex differences in mathematical abilities. Behavioral and
Brain Sciences, 19, 229-284.
Girelli, L., Luzzatti, C., Annoni, G., & Vecchi, T. (1999). Progressive decline of numerical skills in
Alzheimer-type dementia: A case study. Brain and Cognition, 40, 132-136.
Grafman, J., Passafiume, D., Faglioni, P., & Boller, F. (1982). Calculation disturbances in adults with
focal hemispheric damage. Cortex, 18, 37.
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H a n d e d n e s s and Immune Function
N. S. Morfit and N. Y. Weekes
Department of Psychology, Pomona College
Geschwind, Galaburda, and Behan (GBG) have suggested that in utero levels of testosterone
influence both cerebral and immune system developments (Geschwind & Behan, 1982; Geschwind & Galaburda, 1984; Geschwind & Galaburda, 1985). According to this theory, high
levels of testosterone result in greater incidences of left-handedness, deviations from standard
distribution of cerebral functions (known as anomalous dominance), and increased autoimmune dysfunction. While the original data supported these assertions, more recent tests of the
hypothesis have been equivocal. One criticism of these studies is that the definition of both
handedness and anomalous dominance are too vague. It was one of the aims of this project
to investigate and clarify the GBG model by examining four different aspects of handedness
as well as a more direct measure of anomalous dominance. In order to extend the GBG model,
degree of left-handedness, general immune system functioning, and current testosterone levels
were also examined. First, it was predicted and found that left handers had a higher incidence
of autoimmune diseases in their immediate families than did right handers. Second, those left
handers with an incidence of at least one autoimmune disease were more strongly left-handed
than were those with no incidence of autoimmunity. Finally, it was observed that higher testos-