2012. Vol.3, No.1, 57-61
Published Online January 2012 in SciRes (
Copyright © 2012 SciRes. 57
The Reversed Neighborhood Effects in Mental Arithmetic of
Spoken Mandarin Number Words
Mingliang Zhang1, Jiwei Si2, Xiaowen Zhu1
1Shandong Administration Institute, Jinan, China
2School of Psychology, Shandong No rmal University, Jinan, China
Email: {mingliang1, sijiwei1974, allay}
Received October 3rd, 2011; revised November 6th, 2011; accepted November 8th, 2011
In the present study, under the spoken Mandarin number words format, we employed verification tasks to
investigate the neighborhood effects in single-digit multiplication. The results revealed that, in the Arabic
digits format condition, the neighborhood effects like as the former studies discovered is natural, however,
the unexpected reversed neighborhood effects were found in the spoken Mandarin number words format.
Specifically, RTs of higher neighborhood effects multiplication problems were longer than lower neigh-
borhood effects.
Keywords: Single-Digit Multiplication; Neighborhood Effects; Reversed; The Spoken Mandarin Number
Words Format
How are mental arit hme tic proble ms solv ing? Direct ret rieva l
is an important way by which to come to a solution, and many
theories have been proposed to describe the underlying mecha-
nism of arithmetical fact retrieval (e.g., Groen, 1972; Siegler,
1988). How, then, are multiplication solutions stored and re-
trieved? An influential viewpoint is that problems are stored in
an associative network (e.g., Campbell, 1995). However, there
is no consensus on internal organization of this network. It is
worth notice that interacting neighbors (IN) model provided a
new meritorious feature (Frank et al., 2007; Verguts & Fias,
2005a, 2005b).
What IN model propose is that answers to multiplication pro-
blems are retrieved by the dual processes of cooperation and
competition. If a particular problem is presented, a number of
neighboring nodes in a semantic associative network are acti-
vated, each corresponding to a particular problem. For example,
upon presentation of 4 × 8, the representation of the problems 4
× 9, 4 × 7, 5 × 8, and 3 × 8 will also be activated to some de-
gree. Furthermore, if the different candidate solutions converge
on the same unit or decade part of the answer, cooperation will
occur between these answers, and retrieval will be compara-
tively easy. For instance, the answer “36” points in the correct
direction for the decade part of the problem 4 × 8, but “28”
does not. On the other hand, if many candidates point in a dif-
ferent direction (as “28” does for both decades and units),
competition will ensue, and the retrieval process will be slowed
Tom Verguts and Wim Fias (2005b) subsequently proposed
neighborhood effects in mental arithmetic. Specifically, neigh-
borhood effect is the sum of tens and units’ err form level. The
tens’ err form refers to the ten-digit of direct neighborhood-
answer in the problem presented (e.g., 6 × 4) aggregate the nu-
mber of ten-digit of correct answers and minus the number of
ten-digit of the answers far from the correct answers. The units’
err form is similar. The neighborhood effect level is the digits
for tens add the digits for units. In the present study, both direct
and arisen neighbor problems were employed.
On the other hand, the crucial assumption of the IN model is
that not all problems is represented, rather, for each commuta-
tive pair of problems (e.g., 9 × 4 and 4 × 9), there is only one
representational unit. The assumption that problems are stored
in max × min order is not critical, as long as only one order is
stored systematically (i.e., max × min or min × max).
In summary, IN model provided a novel perspective to reveal
the mechanism of mental arithmetic semantic processing. Do-
mahs et al. (2006; 2007) provided direct behavioral and neuro-
scientific evidence for the presence of neighborhood-consis-
tency effects. They found that neighborhood consistency effects
in simple multiplication stem at least partly from central (le-
xico-semantic’) stages of processing. Domahs et al. (2007) ex-
panded the task dimensions of the IN model, however, this mo-
del still needs to be improved or verified in many aspects since
it is a new model. Verguts and Fias (2005b), IN model’s foun-
ders, suggested that it is necessary to expand this model in the
following three aspects: 1) The expression of mathematical for-
mula in the “semantic field” in this model is simple and clear,
but it is also too static and single, since it is not consistent to the
main points of widely recognized encoding complex model.
Because the individual’s mathematical knowledge is a complex
system, which contains many components and levels, and it
constantly and dynamically changes along with the individual
experience. 2) Previous findings were based on the study of A-
rabic numerals form, but the number has multiple surface forms,
such as Arabic numbers, Roman numbers, spoken Mandarin
numbers, and dot-matrix digits, etc., and many studies have fo-
und that numerical surface form not only affects the encoding
stage, but also affect the retrieval phase and the production
stage (e.g., Campbell & Metcalfe, 2008; Kadosh, 2008; Kadosh,
Henik, & Rubinsten, 2008; Metcalfe & Campbell, 2008), that is,
after stimulate the coding, problem in different numerical sur-
face form remain its specificity and process in different paths,
therefore, it is particularly important to expand the interacting
neighbors model across numerical surface form. 3) Most stu-
dies suggest that most simple knowledge of the multiplication
was stocked and retrieved from the interconnected network of
memory (e.g., Rickard, 2005). Part of the activation on the
problem still remained in the network when the problem was
solved (e.g., Galfano, Rusconi, & Umiltà, 2003). Therefore, it
is necessary to use priming paradigms to expand the IN model
(neighborhood effects).
Based on this, the purpose of this study is: to expand on the
cross numerical surface form of interacting neighbors model, in
other words, to investigate whether the neighborhood-consis-
tency effects are harmonious in form of spoken Mandarin num-
ber words or Arabic digits. The logic of this study is: If the re-
sponse of high-consistency problem is shorter than low-consis-
tency one, which indicates neighborhood-consistency effect is
significant, so as to provide evidences to IN model’s cross nu-
merical surface form universals, otherwise, it couldn’t provide
Experiment One Neighborhood Effects
in Arabic Digits
Fifty healthy non-psychology-major college students (23 ma-
les, 27 females) participated in the current study. The age range
was 19 - 23, and five participants were left-handed. All were
Mandarin speakers with normal hearing who had not previously
participated in our lab’s experiments. Each subject was paid a
small fee for participating.
The present study adopted a 4 × 2 × 2 within-subject design.
The three independent variables were SOA (0 ms, 200 ms, 500
ms, 800 ms), neighborhood effects (Low: –6, –4; High: 0, 2),
and operand-order effects (smaller-operand-first entries, larger-
operand-first entries). The dependent variable was reaction time
for solutions.
Materials consisted of single-digit multiplication problems wi-
th a × b = c form. Solutions to each problem were classed as
correct or incorrect. We used a total of 30 multiplication prob-
Stimulus materials were presented using Arabic digits forms
which appeared on a computer monitor as white characters
approximately 6 mm high × 4 mm wide against a black back-
The experiment used a group-testing format. The formal ex-
periment was preceded by twenty practice trials. Participants
were asked to remain relaxed and natural during the whole
experiment. The procedure was programmed by E-Prime soft-
At the beginning of the trial, a white “+”was presented at the
center of a computer screen for 800 ms. Then, the first stimulus
“Op1” (multiplicand) appeared on the screen for 500 ms. After
a blank period of 500 ms, the second stimulus “Op2” (multipli-
cator) appeared for another 500 ms. The third stimulus “Sol”
(product) was presented either 0 ms or 800 ms after onset of the
second stimulus 1 cm below the position of the Op2. Data from
trials where the reaction time exceeded 1500 ms were not used.
The subjects were asked to judge whether Sol was true or false.
To balance the frequency of occurrence of a specific number
as a correct probe or error lure, each multiplication problem
was presented twice (once per SOA). Altogether, each partici-
pant’s data set consisted of 120 items error lures and 120 cor-
rect probes. The problems were presented in pseudo-randomi-
zed order such that the same problem could only be repeated
after at least four distinct intervening problems. No more than
four correct probes or lures was presented consecutively.
Using pseudo-randomized order, 240 trials were presented in
8 blocks, each containing 30 trials. During one block, the “yes”
response had to be given with the left hand, and the “no” re-
sponse with the right hand. During the other block, the respon-
se-hand assignment was reversed. The order of response-hand
assignments was counterbalanced across participants and blo-
cks. A short break was provided every 30 trials. Ten blocks
together lasted approximately 25 minutes.
Data from trials with incorrect responses and correct res-
ponses with RTs more than three standard deviations from the
mean (3.9%) were eliminated.
RTs of neighborhood effects in different SOA conditions are
listed in Table 1 and Figure 1.
Table 1.
Reaction time (M ± SD) of neighborhood effects in different SOA
conditions in Arabic digits format.
Effects 0 ms 200 ms 500 ms 800 ms
Low (–4, –6)742.22 ± 3.88529.64 ± 3.88 444.72 ± 3.90 423 .98 ± 4.02
High (0, 2) 717.93 ± 3.26513.68 ± 3.15 434.95 ± 3.20 420 .03 ± 3.16
Figure 1.
RTs of neighborhood effects in different
SOA conditions in Arabic digits format.
Copyright © 2012 SciRes.
A 4 × 2 × 2 repeated-measures ANOVA was conducted with
SOA, neighborhood effects, and operand-order effects inde-
pendent variables and RTs as the dependent variable. Statistical
results revealed signicant main effects of SOA (F (3, 147) =
3106.00, p < .001), neighborhood effects (F (1, 49) = 28.52, p
< .001), and operand-order effect (F (1, 49) = 60.45, p < .001).
That is, RTs at the smaller SOA level was significantly longer
than that at the bigger SOA level (M = 730 ms, SD = 2.53; M =
522 ms, SD = 2.50; M = 440 ms, SD = 2.52; M = 422 ms, SD =
2.56. SOA = 0 ms, 200 ms, 500 ms, 800 ms, respectively). We
response to the multiplication faster in the condition of small
number firstly presented (M = 519 ms, SD = 1.78) than the
large number firstly presented (M = 538 ms, SD = 1.79; p
< .001). RTs at high-consistency problem (M = 522 ms, SD =
1.60) is shorter than low-consistency one (M = 535 ms, SD =
1.96; p < .001). Some interactions were signicant (FSOA × oper-
and-order (3, 147) = 18.37, p < .001; FSOA × neighborhood effects (3, 147)
= 2.94, p < .05).
Experiment Two Neighborhood Effects in
Spoken Mandarin Number Words
The same as experiment one in “Participants”, “Design”, and
“Procedur”. Stimulus materials were presented using spoken
Mandarin number words which were read aloud by a female
voice. DJ-301MV outdoor-type ear headphones were used to
present auditory stimuli at a moderate volume. Auditory stimu-
lus was recorded by WaveCN1.70 sound-editing software. Each
stimulus was recorded into a separate file in PCM audio form.
The average data rate was 44,100 kb/s, the sampling rate was
22.50 kHz, and the audio sampling size was 16 bits with a sin-
gle voice channel.
The data from trials with incorrect responses and correct re-
sponses with RTs more than three standard deviations from the
mean (4.3%) were eliminated.
RTs of neighborhood effects in different SOA conditions are
listed in Table 2 and Figure 2.
A 4 × 2 × 2 repeated-measures ANOVA was conducted with
SOA, neighborhood effects, and operand-order effects as inde-
pendent variables and RTs as the dependent variable. Statistical
results revealed significant main effects of SOA (F (3, 147) =
1209.43, p < .001), neighborhood effects (F (1, 49) = 22.85, p
< .001), and operand-order effect (F (1, 49) = 422.64, p < .001).
That is, RTs at the smaller SOA level was significantly longer
than that at the bigger SOA level (M = 907 ms, SD = 4.50; M =
695 ms, SD = 4.45; M = 589 ms, SD = 4.35; M = 566 ms, SD =
4.36. SOA = 0 ms, 200 ms, 500 ms, 800 ms, respectively). We
response to the multiplication faster in the condition of small
number firstly presented (M = 644 ms, SD = 3.07) than the
large number firstly presented (M = 735 ms, SD = 3.18; p
< .001). The neighborhood effect was also significant, but it
was modified by an interesting inversion phenomenon. RTs at a
high-consistency problem (M = 700 ms, SD = 2.82) is signifi-
cantly longer than low-consistency one (M = 679 ms, SD = 3.41;
p < .001). Some interactions were signicant (FSOA × operand-order
(3, 147) = 24.85, p < .001; Foperand-order × neighborhood effects (1, 49) =
6.78, p < .01; FSOA × operand-order × neighborhood effects (3, 147) = 7.22, p
< .001).
General Discussion
Under the condition of spoken Mandarin number words, nei-
ghborhood-consistency effects has a “reversal phenomenon”,
which is a high-consistency problem’s reaction time is longer
than the low-consistency problem’s, and this phenomenon has
been observed in all levels of SOA, these indicated that the task
difficulty didn’t impact the “reversal phenome non”, which is the
opposite to the previous results in using Arabic numeral surface
forms. Of course, whether there will be “reverse phenomenon”
in neighborhood-consistency effects under other digital forms
(such as Roman numeral form, dot matrix digital form, etc.)
needs to be further investigated. Researchers have reported a si-
milar inversion phenomenon for several numerical-processing
effects, such as the SNARC effect (Zebian, 2005) and the dis-
tance effect (Turconi, Campbell, & Seron, 2006).
The differences of neighborhood-consistency effects in Ara-
bic numeral surface form and in spoken Mandarin number wo-
rds might be explained by the specificity of audio-visual sen-
sory channel, because the presence of digital information re-
sides longer in the visual channel than the auditory channel,
therefore, digital information can easily be totally and instanta-
neously accepted without the impact of overlapping stimuli.
While in auditory channels, the numerical information present
is relatively short, and the digital information is only partial and
non-instantaneously presented with the impact of overlapping
(Anderson & Holcomb, 1995). T his “reversal phenomeno n” que-
stioned the recent proposed IN model, indicated that the model
does have a lot of aspects to be verified and to be corrected.
Differences of neighborhood-consistency effects in the Ara-
bic numeral form and spoken Mandarin number words provide
Table 2.
Reaction time (M ± SD) of neighborhood effects in different SOA
conditions in spoken mandarin number words form at.
Effects 0 ms 200 ms 500 ms 800 ms
Low (–4, –6)885.59 ± 6 .85688.93 ± 6.88 581.28 ± 6.72559.12 ± 6.85
High (0, 2) 927.62 ± 5.93702.05 ± 5.65 596.04 ± 5.52573.78 ± 5.40
Figure 2.
RTs of neighborhood effects in different SOA
conditions in spoken mandarin number words
Copyright © 2012 SciRes. 59
evidence to support the hypothesis that the numerical surface
form affects the specific pathways of cognitive processing. The
specific pathway hypothesis assumes that the numerical surface
form affects not only the encoding phase, but also the retrieval
phase and the production stage. In other words, after stimulate
the coding, problems in discrete numerical surface form remain
its specificity and process in different paths (e.g., Campbell &
Clark, 1988). A substantial body of research supports the sepa-
rate-pathway hypothesis (e.g., Campbell, 1994; Campbell, 1999;
Campbell & Clark, 1992; Campbell & Fugelsang, 2001; Camp-
bell, Parker, & Doetzel, 2004; Metcalfe & Campbell, 2008).
The core hypothesis of interacting neighbors model is that “7
× 4” and “4 × 7” have only one representational unit, Butter-
worth et al. (2001) proposed the core assumptions of the COMP
model took a similar view, However, Robert and Campbell’s
(2008) study found, “7 × 4” and “4 × 7” problems didn’t have
significant difference in reaction time in addition and multipli-
cation tasks, thus demonstrated that “7 × 4” and “4 × 7” prob-
lems didn't have inherent comparison and have not been con-
verted into a common internal representational unit, which also
indicated that the “7 × 4” and “4 × 7” may have a different kind
of problem representation. This discovery questioned the core
assumptions of the IN model and the COMP model. The nature
of the query is actually the controversy of the nature of the
operand order effects. When we calculate a simple multiplica-
tion problem, the Chinese and Occidental showed the opposite
effect of the operand order. The Chinese response to the multi-
plication faster with lower error rates in the condition of small
number firstly presented (e.g., 3 × 8 = 24) than the large num-
ber firstly presented (8 × 3 = 24) when they calculate a simple
multiplication problem. While the Occidental response in an
opposing way. In the present study, we found that, the operand
order effect is significant in the form of spoken Mandarin nu-
mber words, which correspond to the COMP model and IN mo-
del, that is, supports the standpoint of “7 × 4” and “4 × 7” has
only one representational unit.
Robert and Campbell (2008) found that people reaction were
not significantly different in “7 × 4” and “4 × 7” problems in
addition and multiplication tasks. But this “not significantly di-
fferent” does not guarantee the internal mechanism of identity,
and coupled with the study subjects were Canadians who
learned the full multiplication table (containing both “7 × 4”
and “4 × 7” problem). Maybe for the reason of their learning
experiences, the perceptual transformation toward the “7 × 4”
and “4 × 7” problems seem be automatic for them. Refer to the
reaction, there may have slight differences, and this difference
can’t be detected at a statistically significant level.
In the present study, the similar neighborhood effects were
found in the Arabic digit format like as the former studies dis-
covered, however, the unexpected reversed neighborhood ef-
fects were found in the spoken Mandarin number word format.
The present study was supported by grants from the Humani-
ties and Social Sciences Project of the People’s Republic of Chi -
na Ministry of Education (09YJAXLX014. 2010-2012), Shan-
dong Province Social Science Foundation (11CSHJ11. 2011-2012),
Shandong Province Natural Science Foundation (ZR2010C,
059. 2011-2013), the Humanities and Social Sciences Project of
Shandong Province Institute (J11WH72. 2011-2012), and the
Key Subject Funds of Shandong Province, P. R. China (2011-
2015). Thank the two anonymous reviewers for their valuable
suggestions on the manuscript.
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