Content uploaded by Oliver Lindemann

Author content

All content in this area was uploaded by Oliver Lindemann on Jul 27, 2014

Content may be subject to copyright.

This article was downloaded by: [Universitaetsbibliothek Potsdam]

On: 27 July 2014, At: 04:28

Publisher: Routledge

Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office:

Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

The Quarterly Journal of Experimental

Psychology

Publication details, including instructions for authors and subscription

information:

http://www.tandfonline.com/loi/pqje20

Spatial interferences in mental arithmetic:

Evidence from the motion–arithmetic

compatibility effect

Michael Wiemersa, Harold Bekkeringa & Oliver Lindemannab

a Donders Institute for Brain, Cognition and Behaviour, Radboud University

Nijmegen, Nijmegen, The Netherlands

b Division of Cognitive Science, University of Potsdam, Potsdam, Germany

Accepted author version posted online: 31 Jan 2014.Published online: 05

Mar 2014.

To cite this article: Michael Wiemers, Harold Bekkering & Oliver Lindemann (2014) Spatial interferences

in mental arithmetic: Evidence from the motion–arithmetic compatibility effect, The Quarterly Journal of

Experimental Psychology, 67:8, 1557-1570, DOI: 10.1080/17470218.2014.889180

To link to this article: http://dx.doi.org/10.1080/17470218.2014.889180

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”)

contained in the publications on our platform. However, Taylor & Francis, our agents, and our

licensors make no representations or warranties whatsoever as to the accuracy, completeness, or

suitability for any purpose of the Content. Any opinions and views expressed in this publication

are the opinions and views of the authors, and are not the views of or endorsed by Taylor &

Francis. The accuracy of the Content should not be relied upon and should be independently

verified with primary sources of information. Taylor and Francis shall not be liable for any

losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities

whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or

arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial

or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or

distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use

can be found at http://www.tandfonline.com/page/terms-and-conditions

Spatial interferences in mental arithmetic: Evidence from

the motion–arithmetic compatibility effect

Michael Wiemers

1

, Harold Bekkering

1

, and Oliver Lindemann

1,2

1

Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen, Nijmegen,

The Netherlands

2

Division of Cognitive Science, University of Potsdam, Potsdam, Germany

Recent research on spatial number representations suggests that the number space is not necessarily

horizontally organized and might also be affected by acquired associations between magnitude and

sensory experiences in vertical space. Evidence for this claim is, however, controversial. The present

study now aims to compare vertical and horizontal spatial associations in mental arithmetic. In

Experiment 1, participants solved addition and subtraction problems and indicated the result verbally

while moving their outstretched right arm continuously left-, right-, up-, or downwards. The analysis of

the problem-solving performances revealed a motion–arithmetic compatibility effect for spatial actions

along both the horizontal and the vertical axes. Performances in additions was impaired while making

downward compared to upward movements as well as when moving left compared to right and vice

versa in subtractions. In Experiment 2, instead of being instructed to perform active body movements,

participants calculated while the problems moved in one of the four relative directions on the screen. For

visual motions, only the motion–arithmetic compatibility effect for the vertical dimension could be

replicated. Taken together, our ﬁndings provide ﬁrst evidence for an impact of spatial processing on

mental arithmetic. Moreover, the stronger effect of the vertical dimension supports the idea that

mental calculations operate on representations of numerical magnitude that are grounded in a vertically

organized mental number space.

Keywords: Mental arithmetic; Numerical cognition; Spatial–numerical associations; Embodied

cognition.

Classical research on mathematical cognition has

emphasized the importance of spatial codes

for the representation of numerical magnitude

(see e.g., Fias & Fischer, 2005; Hubbard, Piazza,

Pinel, & Dehaene, 2005). Very recently, the idea

of spatial–numerical associations has been utilized

to formulate theories of mental arithmetic, which

basically hold that adding or subtracting numbers

involves a cognitive process that can be described

as right- or leftward attentional shifts on a spatial

representation of numerical magnitude (Knops,

Viarouge, & Dehaene, 2009; McCrink, Dehaene,

& Dehaene-Lambertz, 2007; Pinhas & Fischer,

2008).

Studies on spatial associations in number

processing have traditionally focused on numerical

judgements and interference effects between

numerical information and horizontal space. The

most prominent example of this coupling is the

effect of spatial–numerical association of response

codes (SNARC; Dehaene, Bossini, & Giraux,

1993), which reﬂects the tendency to react faster

Correspondence should be addressed to: Michael Wiemers, Donders Institute for Brain, Cognition and Behaviour, P.O. Box 9104,

6500 HE Nijmegen, The Netherlands. E-mail: m.wiemers@donders.ru.nl

© 2014 The Experimental Psychology Society 1557

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014

Vol. 67, No. 8, 1557–1570, http://dx.doi.org/10.1080/17470218.2014.889180

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

with right-side responses to large numbers and

with left-side responses to small numbers. This

number–response compatibility effect indicates

that numerical magnitudes are associated with pos-

itions along the horizontal axis with small numbers

on the left and large number on the right (so-called

mental number line hypothesis; Dehaene et al.,

1993; Fias & Fischer, 2005).

Interestingly, research has shown that the inter-

action between number and space also extends to

the vertical dimension (Holmes & Lourenco,

2012; Ito & Hatta, 2004; Schwarz & Keus, 2004;

Shaki & Fischer, 2012). Schwarz and Keus (2004)

were amongst the ﬁrst to report a vertical number–

response compatibility effect and demonstrated

that upward saccades were initiated faster in

response to large numbers, while downwardsaccades

were initiated faster in response to small numbers.

However, studies on number representation that

compared vertical and horizontal spatial–numerical

couplings provide so far no consistent evidence on

whether the vertical or horizontal organization is

predominant (Holmes & Lourenco, 2012; Sell &

Kaschak, 2012; Shaki & Fischer, 2012; Winter &

Matlock, 2013). One the one hand, Shaki and

Fischer (2012) reported that Hebrew-speaking

participants who do not show a SNARC effect

with horizontally aligned responses due to incon-

sistent processing habits for words and numbers

exhibit a vertical SNARC effect. This ﬁnding

suggests a more robust and culturally independent

mapping between vertical space and magnitude.

Also, Winter and Matlock (2013) provided

support in favour of a strong vertical organization

of number space by showing that the production

of random numbers is affected stronger by vertical

than by horizontal head movements. On the

other hand, a predominance of vertical number

associations has been challenged by Holmes and

Lourenco (2012). The authors tested SNARC-

like effects in a parity judgement task with different

spatial response button layouts and found that

when pitting both dimensions directly against

each other, only a horizontal but not a vertical

number–space mapping could be observed.

Although the empirical evidence for a predomi-

nantly vertical organization of number space is

ambiguous at this point, we argue that this idea is

in line with recent theoretical developments in psy-

chology of knowledge representations and the

general hypothesis that any conceptual represen-

tation is somehow grounded in sensorimotor

experiences (e.g., Barsalou, 2008; Lakoff, 1987).

Following such an embodied view on cognition,

Fischer and Brugger (2011) pointed out that

especially sensorimotor experience in vertical

space play a crucial role in the development of

abstract number concepts. They stated that due to

a strong correlation between vertical space and

numerical magnitude in the world—for example,

through piling objects when comparing the numer-

osity of two sets of objects and the fact that stacks

extend upwards as they grow—an association

between these two dimensions emerges from early

life on. However, in the action of piling objects,

numerical magnitude is confounded with stack

height. As a consequence, vertical space should

become associated with numerical magnitude and

magnitude at an abstract level. Therefore, it is

more accurate to speak of an association of vertical

space and magnitude. Crucially, no systematic

relationship between horizontal space and

numerical magnitude exists when arranging

objects horizontally. One might therefore assume

that mappings of numbers onto vertical space

provide the grounding for any type of spatial–

numerical mapping (henceforth referred to as

the “grounding hypothesis of spatial–numerical

associations”).

As mentioned above, the activation of spatial

codes is not restricted to the representation of

single numbers but also seems to play a crucial

role for mental arithmetic (McCrink et al.,

2007; Pinhas & Fischer, 2008). Until now,

studies of the interplay between mental arithmetic

and spatial processing have merely focused on the

horizontal dimension. McCrink et al. (2007) were

amongst the ﬁrst to discuss the interaction

between spatial processing and mental arithmetic.

The authors reported that when adding or sub-

tracting the numerosities of two dot clouds, par-

ticipants tend to overestimate the result of

additions and underestimate the result of subtrac-

tions (see also Knops, Viarouge, et al., 2009).

1558 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8)

WIEMERS ET AL.

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

This so-called operational momentum effect has

been interpreted as evidence for the idea that

addition and subtraction are accompanied by

attentional shifts to the right (addition) and left

(subtraction) on the mental number line, inducing

an over- or underestimation, respectively (Knops,

Viarouge, et al., 2009; McCrink et al, 2007).

Similar effects of the operation have also been

observed in symbolic arithmetic. For instance,

Pinhas and Fischer (2008), who instructed par-

ticipants to indicate the outcome of symbolic

additions and subtractions by pointing to the cor-

responding location on the horizontal number

line, found a systematic response bias towards

larger numbers (i.e., the right side) after adding

and towards smaller numbers (i.e., the left side)

after subtracting.

The notion that shifts on a spatial or spatial–

numerical continuum are causing the operational

momentum effect received so far only support

from two ﬁndings. First, Knops, Viarouge, et al.

(2009) reported a space-to-arithmetic mapping.

That is, participants preferred to choose the upper

right dot cloud for additions and the upper left

dot cloud for subtractions. Second, neuroimaging

research (Knops, Thirion, Hubbard, Michel, &

Dehaene, 2009) demonstrated that activity in the

posterior superior parietal cortex related to horizon-

tal eye movements was correlated with mental

additions and subtractions. This evidence is

however rather indirect, and a strong test of the

coupling of space and arithmetic, such as an effect

of spatial processes on the performances in arith-

metic tasks, is still missing.

Taken together, the grounding hypothesis of

spatial–numerical associations predicts predomi-

nant vertical organization of number space and

stronger interference effects for vertical rather

than horizontal spatial information in number pro-

cessing. Since research on number representations

provided only inconclusive evidence for this idea

and since vertical mappings have been neglected

in studies on mental arithmetic so far, the present

study aims to compare vertical and horizontal

spatial associations while solving addition and

subtraction problems.

We addressed these issues by employing a dual-

task-like paradigm, in which participants per-

formed slow continuous arm movements in the

horizontal (left- or rightward) or vertical dimen-

sion (up- or downwards) while solving addition

or subtraction problems. We expected an effect

of the compatibility between the performed move-

ment and the mental arithmetic task (motion–

arithmetic compatibility effect). That is, based on

studies on the operational momentum effect

(e.g., Knops, Viarouge, et al., 2009), a motion–

arithmetic compatibility effect should be reﬂected

in the horizontal dimension by better performance

for addition for a rightward movement than for a

leftward movement and better performance in sub-

traction for leftward than for rightward move-

ments. Importantly, the grounding hypothesis of

spatial–numerical associations predicts further-

more a stronger motion–arithmetic compatibility

effect along the vertical dimension, with facilitated

processing of additions while moving upward and

facilitated processing of subtractions for downward

movements.

EXPERIMENT 1

Participants were instructed to perform constant-

speed arm movements with the fully extended

right arm, starting pointing straight forward and

moving left-, right-, up-, or downwards. Arm

movements had to be initiated at the presentation

of an arithmetic (addition or subtraction) problem

on the screen and had to be continued until an

answer was given verbally. Assuming that the

spatial coding of numerical magnitudes is function-

ally involved in mental arithmetic, it is expected

that the execution of arm movements in space has

a systematic impact on solving simple additions

and subtraction problems. In particular, we expect

that the processing of arithmetic problems is

more efﬁcient while performing a compatible

action than while performing an incompatible

action (motion–arithmetic compatibility effect).

Moreover, we expect the motion–arithmetic

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8) 1559

SPATIAL INTERFERENCE IN MENTAL ARITHMETIC

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

compatibility effect for vertical arm movements to

be stronger than that for horizontal arm

movements.

METHOD

Participants

A total of 38 students from the Radboud University

Nijmegen (11 males, mean age of 20.49 years, 20

native Dutch and 18 native German speakers)

with normal or corrected-to-normal vision, naive

to the purpose of the study, took part in the study

in exchange for 15 euros or credit points.

Experimental set-up and apparatus

Participants were standing at approximately 3 m

distance from a 17′′ CRT monitor holding the

Wii®-controller (Nintendo) in their right hand,

which was used to record the hand position with

a sampling rate of 100 Hz. To detect the voice

onset, a microphone was placed in front of the

head of the subject. The set-up consisted of two

interconnected computers, one for the recording

of the Wii controller position data and one for pre-

sentations of the stimuli and the voice onset detec-

tion. The experiment was controlled using the

Python software package Expyriment (Krause &

Lindemann, 2013). The experimenter registered

the verbally given answers and the correctness of

the executed movements.

Stimuli

All problems consisted of two operands and one

operator (plus or minus) and were presented cen-

trally in black Arial font on a light grey background

(see Table 1). At a viewing distance of 3 metres, the

problems were spanning approximately 4° (hori-

zontal) ×2° (vertical) in visual angle. Subtraction

and addition problems were matched for overall

problem size (i.e., average of all numbers in the

correct equation) by inverting addition into sub-

traction problems (e.g., 34 +58 =92, 92 −58 =

34). The arithmetic problems in the experimental

block consisted of 15 small-size addition and sub-

traction problems (problem size ranging from 22

to 34, mean result: 13.2 for additions and 6.73

for subtractions) and 15 large-size addition and

Table 1. Arithmetic problems used for the experimental phase

Problem number Operand 1 Operation Operand 2 Result

19+817

27+916

39+615

45+914

59+413

63+912

78+715

86+814

98+513

10 3 +811

11 7 +613

12 5 +712

13 7 +411

14 6 +511

15 9 +211

16 27 +36 63

17 39 +25 64

18 29 +38 67

19 27 +44 71

20 49 +23 72

21 28 +53 81

22 37 +45 82

23 44 +39 83

24 56 +28 84

25 47 +38 85

26 57 +29 86

27 25 +66 91

28 38 +54 92

29 26 +67 93

30 36 +59 95

31 17 −89

32 16 −97

33 15 −69

34 14 −95

35 13 −49

36 12 −93

37 15 −78

38 14 −86

39 13 −58

40 11 −83

41 13 −67

42 12 −75

43 11 −47

44 11 −56

45 11 −29

46 63 −36 27

47 64 −25 39

48 67 −38 29

49 71 −44 27

50 72 −23 49

(Continued overleaf)

1560 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8)

WIEMERS ET AL.

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

subtraction problems (problem size ranging 124 to

190, mean result: 80.60 for additions and 37.67 for

subtractions). A different set of arithmetic pro-

blems was used in the training phase.

A black square frame of 2° ×2° in visual angle

was used as a starting position of each arm move-

ment. Block arrows pointing to the left, to the

right, up, or down served as movement cues. A

black diamond (3° by 3° visual angle) indicated

that no movement had to be executed.

Procedure

The experiment started with two practice blocks.

First, participants were required to verbally report

the correct result of visually presented arithmetic

problems. The second practice block was identical

to the subsequent experimental block (see below).

The experiment started when participants were

able to perform both tasks correctly simultaneously.

In the experimental block, every trial started

with a movement instruction, indicated by an

arrow pointing in one of the four relative directions

or a black ﬁlled diamond symbol indicating that no

movement had to be performed in this trial.

Participants had to bring the arm to a centre pos-

ition by moving a red dot into a centrally presented

square frame (2° ×2°of visual angle). After a

random interval of 1000–1500 ms, the arithmetic

problem was presented. With problem onset, par-

ticipants were required to start the instructed arm

movement and to continue with a steady speed of

approximately 10° angle/s until an answer was

given.

If the arm movement did not start within 1000

ms, an error signal was presented, and the trial was

interrupted. Participants were instructed to report

the result of the presented problem as soon as poss-

ible by ﬁrst saying “is”followed by the result (in

their native language). The experimenter moni-

tored the movements and the verbal response and

entered both into the computer. If a movement

was stopped before an answer was given or the

answer was not given in the instructed manner,

the trial was scored as erroneous. After every trial,

feedback messages were presented saying “Correct

Movement”or “Correct Answer”with green font

colour or “Wrong Movement”or “Wrong

Answer”in red font colour. Afterwards, the exper-

imenter started the next trial.

Design

The experimental block comprised 30 addition and

30 subtraction problems each presented once in

each of the ﬁve movement conditions (left, right,

up, down, no movement), resulting in 300 trials

in total. All trials were presented in a randomized

order. The experiment lasted approximately

90 min.

Data analysis

The response time (RT) was deﬁned as the time

between problem presentation and onset of the

vocal response.

For the analysis, all trials with anticipation

responses (RTs ,400 ms), missing responses (no

responses and RTs .10,000 ms), trials in which

triggering of the voice key was not due to the

verbal response of the participant, and trials with

incorrectly performed arm movements (e.g., move-

ments in the wrong direction, movements that

stopped before verbal response, very slowly per-

formed movements) were excluded (7.8% of the

trials).

To control for a possible trade-off between

speed and accuracy of responding or different strat-

egies of the participant—that is, an emphasis on

speed or accuracy depending on the experimental

condition—we analysed efﬁciency scores.

Efﬁciency scores integrate the two performance

Table 1. Continued.

Problem number Operand 1 Operation Operand 2 Result

51 81 −53 28

52 82 −45 37

53 83 −39 44

54 84 −28 56

55 85 −38 47

56 86 −29 57

57 91 −66 25

58 92 −54 38

59 93 −67 26

60 95 −59 36

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8) 1561

SPATIAL INTERFERENCE IN MENTAL ARITHMETIC

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

indices speed and accuracy of responding by divid-

ing the accuracy rate by response time in seconds.

Motion–arithmetic compatibility was deﬁned as

follows. In addition trials, right- and upward

motions were deﬁned as motion–arithmetic com-

patible. Left- and downward movements were con-

sidered as incompatible. For subtractions,

compatible and incompatible motions were in the

opposite direction to that for additions.

Results

The average error rate was 3.23% for problems

with small size and 17.67% for large-size problems,

t(41) =−10.02, p,.001.

Efﬁciency scores (ES) were submitted to a four-

way repeated measures analysis of variance

(ANOVA) with the within-subject factors problem

size (small, large), operation (addition, subtraction),

spatial dimension (horizontal, vertical), and motion–

arithmetic compatibility (compatible, incompatible).

The analysis revealed two main effects of the factors

problem size, F(1, 37) =344.20, MSE =0.10,

p,.001, η

2

=.90, and operation, F(1, 37) =

129.59, MSE =0.02, p,.001, η

2

=.78. That is,

performance was better for additions (0.575 effect

size, ES) than for subtraction problems (0.453 ES)

and better for small-size problems (0.749 ES) than

for large-size problems (0.279 ES). Both effects

reﬂect two well-established ﬁndings in the ﬁeld of

mental arithmetic. Moreover, there was a signiﬁcant

interaction between the factors operation and

problem size, F(1, 37) =37.03, MSE =0.01,

p,.001, η

2

=.50, reﬂecting that the difference in

performance between addition and subtraction

trials was more pronounced for small- (0.176 ES)

than for large-size problems (0.072 ES).

Importantly, there was a signiﬁcant effect of

motion–arithmetic compatibility, F(1, 37) =8.43,

MSE =0.03, p,.01, η

2

=.19, suggesting that

problem-solving performance was better when

adding and moving up or to the right or subtracting

and moving down or to the left (motion–arithmetic

compatible; 0.521 ES) than when adding and

moving down or left or subtracting and moving up

or right (motion–arithmetic incompatible; 0.507

ES). Interestingly, there was no interaction

between the factors motion–arithmetic compatibility

and spatial dimension, F(1, 37) =1.14, MSE =

0.003, p=.29, η

2

=.03, suggesting that the

motion–arithmetic compatibility effects for the hori-

zontal and vertical dimensions did not differ from

each other. However, post hoc ttests revealed that

only for the vertical dimension was the interaction

between movement direction and arithmetic

operation signiﬁcant, t(37) =2.00, p,.05. The

motion–arithmetic compatibility effect for the hori-

zontal dimension did not reach signiﬁcance, t(37) =

1.10, p=.14 (see Figure 1). This pattern suggests a

predominant role of vertical space for numerical pro-

cessing in the context of mental arithmetic.

In order to specify whether the vertical motion–

arithmetic compatibility effect reﬂects an interfer-

ence and/or facilitation effect, the compatible and

incompatible conditions were compared with the

no-movement condition. The ttests indicated sig-

niﬁcantly lower performance in both the motion–

arithmetic compatible (0.523 ES) and incompatible

conditions (0.505 ES) than in the no-movement

condition (0.534 ES), t(37) =2.81, p,.05, and

t(37) =3.57,p,.01. This pattern suggests inter-

ference of motion, which is incompatible with the

arithmetic operation, as well as greater overall cog-

nitive demands for the movement than for the no-

movement conditions.

Since the average result size in additions was

larger than that in subtractions (13.2 for additions

and 6.73 for subtractions in small-size problems

and 80.60 for additions and 37.67 for subtractions

in large-size problems), it might be objected that

Figure 1.Efﬁciency scores (accuracy rate/response time, acc/RT, in s)

as a function of the factors spatial dimension and motion–arithmetic

compatibility in Experiment 1. The asterisk indicates a signiﬁcant

difference between conditions, p,.05.

1562 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8)

WIEMERS ET AL.

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

the interaction between movement direction and

arithmetic operation is driven by a difference in

result size and a sort of effect of spatial–numerical

compatibility (larger results might be associated

with right- and upward motions and smaller with

left- and downward motions). In order to rule out

that the difference in result size for additions and

subtractions is driving the compatibility effects,

we performed an additional three-way repeated

measures ANOVA with the within-subject

factors problem size (small, large), spatial dimen-

sion (horizontal, vertical), and spatial–numerical

compatibility (compatible, incompatible). The

analysis did not reveal a main effect of spatial–

numerical compatibility, F(1, 37) ,1, an inter-

action between spatial–numerical compatibility

and spatial dimension, F(1, 37) ,1, an interaction

between spatial–numerical compatibility and

problem size, F(1, 37) =1.14, MSE =0.002,

p=.29,η

2

=.03, or a three-way interaction

between spatial–numerical compatibility, spatial

dimension, and problem size, F(1, 37) ,1.

To further explore the effects from the efﬁciency

analyses, we performed repeated measures

ANOVAs for mean RT data and error rates with

the factors operation (Table 3) (addition, subtrac-

tion), spatial dimension (horizontal, vertical), and

motion–arithmetic compatibility (compatible,

incompatible). For the analysis of RT data, all

trials with a RT 2.5 standard deviations below or

above the grand mean were excluded. Similar to

the efﬁciency score data, the analyses revealed a sig-

niﬁcant effect for motion–arithmetic compatibility,

F(1, 37) =8.36, MSE =0.43, p,01, η

2

=.18,

and no interaction between spatial dimension and

motion–arithmetic compatibility, F(1, 37) ,1.

The analyses of error rates did not show a signiﬁ-

cant effect for motion–arithmetic compatibility or

an interaction between motion–arithmetic compat-

ibility and another factor.

Discussion

Experiment 1 provides evidence for an impact of

spatial processing on mental arithmetic by

showing a systematic effect of movement direction

on problem-solving performance of arithmetic

problems. That is, participants’arithmetic perform-

ance was impaired while moving the arm in an

incompatible direction with respect to the required

arithmetic operation (i.e., adding while moving left

or down, or subtracting while moving right or up)

as compared to the compatible movement con-

dition (adding while moving right or up, or sub-

tracting while moving left or down). The data

support the notion that spatial representations are

functionally involved in mental arithmetic (cf.

McCrink et al., 2007; Pinhas & Fischer, 2008).

Most importantly, the demonstration that arith-

metic operations are systematically affected by

movements along the vertical axis indicates that a

vertically organized number space is involved in

mental arithmetic (Fischer & Brugger, 2011).

It has to be emphasized that the grounding

hypothesis of spatial–numerical association predicts

a predominant role for the vertical associations.

While Experiment 1 revealed clear evidence for a

coupling of arithmetic operations and vertical

space, it provided only mixed support for a difference

in the motion–arithmetic compatibility effects along

the horizontal and vertical dimensions. The lack of

interaction between the factors motion–arithmetic

compatibility and spatial dimension in the

ANOVA suggests that compatibility effects are

not modulated by the spatial dimension.

The simple effects analysis, however, is in line

with the grounding hypothesis and supports our

assumption that motion–arithmetic compatibility

effects emerge predominantly for vertical move-

ments. The results of Experiment 1 are thus not

fully conclusive, and we interpret the outcome

therefore parsimoniously as a failure to ﬁnd evi-

dence for a difference between horizontal and ver-

tical motion–arithmetic compatibility effects.

Another problem of Experiment 1 relates to the

physical effort associated with arm movements in

different directions. Due to the forces of gravity,

moving the arm upwards is more effortful than

moving it downwards. This difference in effort

for vertical arm movements has a potentially con-

founding effect, since the motion–arithmetic com-

patibility for the vertical dimension could also be

due to a “more-is-more”mapping (i.e., linking

physical effort with arithmetic operations, cf.

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8) 1563

SPATIAL INTERFERENCE IN MENTAL ARITHMETIC

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

Stavy & Tirosh, 2000) instead of a grounding in

terms of mental space. In contrast, horizontal

arm movements do not suffer from the same

confound.

We conducted a second experiment in order to

address the issue of an asymmetry in the required

energy for up- and downward arm movements

and to provide a more conclusive additional test

of a potential difference between the effect of hori-

zontal and vertical spatial representations on arith-

metic problem-solving performance.

EXPERIMENT 2

Experiment 2 further investigated the two motion–

arithmetic compatibility effects and aimed to rule

out the potential confound of a difference in effort

for the upward compared to the downward move-

ment condition being responsible for the compat-

ibility between vertical motion and arithmetic.

Whereas a difference in the effort for up- and

downward arm movements is clearly noticeable by

the participant, we believe that the difference in

the effort of up- and downward smooth pursuit

eye movements is only marginal and will not be

mentally represented. As a study by Collewijn,

Erkelens, and Steinman (1988) indicates, the brain

does not sufﬁciently take into account gravity and

the related difference in inertial forces for the plan-

ning of vertical eye movements. The authors

showed that upward saccades undershoot, while

downward saccades systematically overshoot relative

to target position. This ﬁnding supports our

assumption that the difference in the applied

energy for eye movements is small and negligible.

Experiment 2 also served to provide an

additional test of a difference between the impact

of horizontal and vertical spatial information on

arithmetic problem-solving performance, since the

results from Experiment 1 were inconclusive in

this regard.

In order to induce slow smooth pursuit eye

movements, we presented arithmetic problems

moving from screen centre in one of the four

relative directions with a rate of about 1.7° visual

angle/s.

Method

Participants

A total of 44 students of the Radboud University

Nijmegen (10 males, mean age of 21.77 years) par-

ticipated in the experiment in return for 10 euros or

course credits.

Experimental set-up and apparatus

Participants were sitting at about 70 cm viewing

distance from a 17′′ CRT monitor. As in

Experiment 1, response onset was detected via

voice key. Responses were classiﬁed and scored by

the experimenter.

Stimuli

The same arithmetic problems as those in

Experiment 1 were presented. Problems were

moving after appearance at the screen centre to

the left, to the right, up, or down at approximately

1.7° visual angle/s. The problems were presented in

smaller size, spanning only 4° ×2° visual angle.

A black square (1° ×1° of visual angle) served as a

ﬁxation point.

Procedure

Again, the experiment started with a practice block.

In the experimental block, each trial started with a

central presentation of the ﬁxation point. After a

random interval of 1,000 to 1,500 ms, the addition

or subtraction problem was presented at the centre

of the screen and started moving in one of the four

directions or remained at screen centre. The par-

ticipants’task was to indicate the correct result as

fast as possible by ﬁrst saying “is”followed by the

result. If an answer was not provided before

the arithmetic problem reached the border of the

screen, or within 6 s in the no-motion condition,

the trial was counted as erroneous. Messages

saying either “Correct Answer”in a green font or

“Wrong Answer”in a red font were presented at

the end of each trial as feedback.

Design and data analysis

The experimental design and data analysis were

identical to those in Experiment 1. The experiment

lasted about 60 min.

1564 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8)

WIEMERS ET AL.

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

Results

The average error rate was 3.22% for small-size

problems and 17.46% for large-size problems,

t(41) =−10.05, p,.001.

Efﬁciency scores were submitted to a repeated

measures ANOVA with the within-subject factors

problem size (small/large), operation (addition/sub-

traction), spatial dimension (horizontal/vertical),

and motion–arithmetic compatibility (compatible/

incompatible). As in the previous analyses, the

same pattern of effects for problem size, operation,

and the interaction between operation and problem

size was shown. The effect of motion–arithmetic

compatibility was not signiﬁcant, F(1, 42) =2.63,

MSE =0.02, p=.11, η

2

=.06.

Most importantly, there was a signiﬁcant

interaction between spatial dimension and

motion–arithmetic compatibility, F(1, 42) =4.50,

MSE =0.04, p,.05, η

2

=.10 (see Figure 2).

Post hoc ttests revealed that only vertical spatial

motion showed a signiﬁcant motion–arithmetic

compatibility effect, with higher efﬁciency scores

for compatible (0.504 ES) than for incompatible

(0.493 ES) visual motion, t(42) =7.48, p,.01.

For the horizontal dimension, movement direction

did not modulate the performance in the

mental arithmetic task (0.498 ES vs. 0.500 ES),

t(42) ,1. Thus, arithmetic problem-solving per-

formance was better when adding and moving up

or subtracting and moving down (0.504 ES) than

when adding and moving down or subtracting

and moving up (0.493 ES). In order to further

specify the compatibility effect for the vertical

dimension, the compatible and incompatible con-

ditions were compared against the no-movement

condition. The ttests indicated signiﬁcantly lower

performance in the motion–arithmetic incompati-

ble (0.493 ES) than in the no-movement condition

(0.510 ES), t(41) =3.70, p,.01. The motion–

arithmetic compatible condition did not differ

from the no-movement condition,t(41) =1.29,

p=.20, which suggests an interference of motion,

which is incompatible with the arithmetic

operation.

In order to rule out that differences in result size

for additions and subtractions are underlying the

motion–arithmetic compatibility effect, we per-

formed an additional ANOVA with the within-

subject factors problem size (small, large), spatial

dimension (horizontal, vertical), and spatial–

numerical compatibility (compatible, incompati-

ble). As in Experiment 1, the analysis revealed

neither a signiﬁcant effect of spatial–numerical

compatibility nor a signiﬁcant interaction between

spatial–numerical compatibility and any other

factor, all Fs,1.

As a supplement to the efﬁciency score analysis,

we also performed analyses for RT and error data

with the factors operation (addition/subtraction),

spatial dimension (horizontal/vertical), and motion–

arithmetic compatibility (compatible/incompatible)

(see Table 4).

For Experiment 2 the analyses of mean RTs

merely revealed a trend for an effect of motion–

arithmetic compatibility, F(1, 41) =1.06, MSE =

0.012, p=.06.

The error rate analyses showed a trend for an

interaction between spatial dimension and

motion–arithmetic compatibility, F(1, 41) =3.73,

MSE =226.19, p=.06, with a descriptive differ-

ence in the a motion–arithmetic compatibility for

the vertical dimension (9.87%, compatible vs.

11.07%, incompatible) and an inverted difference

for the horizontal dimension (10.99%, compatible

vs. 9.87%, incompatible). However, further ttests

failed to prove the signiﬁcance of these differences

[t(41) =1.61, p=.06, and t(41) =1.56, p=.06,

for the vertical and horizontal spatial dimension,

respectively].

Figure 2.Efﬁciency scores (accuracy rate/response time, acc/RT, in s)

as a function of the factors spatial dimension and motion–arithmetic

compatibility in Experiment 2. The double asterisk indicates a

signiﬁcant difference between conditions, p,.01.

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8) 1565

SPATIAL INTERFERENCE IN MENTAL ARITHMETIC

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

Discussion

Experiment 2 addressed the problem of a potential

confound of a difference of effort or required energy

for upward compared to downward movements,

underlying the compatibility between vertical

motion and arithmetic. In order to control for

this, we presented addition and subtraction pro-

blems moving from screen centre in one of the

four directions. The continuous motion induced

smooth pursuit eye movements, for which the

asymmetry in effort for up- and downward move-

ments is marginal or not even taken into account

by the brain (Collewijn et al., 1988). Importantly,

we found a compatibility between vertical motion

and mental arithmetic—that is, performance was

impaired for additions when moving downwards

(compared to upward movements) and for subtrac-

tions when moving upwards (compared to down-

ward movements). The replication of the vertical

motion–arithmetic compatibility effect in this

setting suggests that representations of space are

driving the compatibility effect in the vertical

dimension. Moreover, as in Experiment 1, the

motion–arithmetic compatibility for the horizontal

dimension was not signiﬁcant, suggesting a stron-

ger coupling of vertical space and mental arithmetic

than the linkage with horizontal space. Together,

Experiment 2 supports our hypothesis of a stronger

coupling between mental arithmetic and the verti-

cal than with the horizontal dimension and sup-

ports the notion that mental addition and

Table 2. Mean efﬁciency scores in Experiment 2 as a function of the factors problem size, operation, spatial dimension, and motion–arithmetic

compatibility

Spatial dimension MAC

Problems

Small-size Large-size

Addition Subtraction Addition Subtraction

Horizontal dimension Compatible 0.8045 0.6469 0.2900 0.2524

Incompatible 0.8019 0.6512 0.2907 0.2550

Vertical dimension Compatible 0.8126 0.6602 0.2907 0.2469

Incompatible 0.7988 0.6419 0.2857 0.2436

Note: MAC =motion–arithmetic compatibility.

Table 3. Mean response time and error rates in Experiment 1 as a function of the factors problem size, operation, spatial dimension, and

motion–arithmetic compatibility

Dependent variable Spatial dimension MAC compatibility

Problems

Small-size Large-size

Addition Subtraction Addition Subtraction

Response time (s) Horizontal Compatible 1.235 1.602 3.095 3.483

Incompatible 1.282 1.581 3.125 3.652

Vertical Compatible 1.230 1.531 3.110 3.568

Incompatible 1.277 1.619 3.083 3.587

Error rate (%) Horizontal Compatible 2.76 3.67 8.43 13.91

Incompatible 2.90 3.10 7.87 12.65

Vertical Compatible 2.96 4.68 8.20 10.72

Incompatible 3.37 2.58 7.29 15.23

Note: MAC =motion–arithmetic compatibility.

1566 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8)

WIEMERS ET AL.

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

subtraction are grounded in vertical spatial–

numerical associations.

GENERAL DISCUSSION

Two experiments investigated the involvement of

spatial representations in mental arithmetic and

demonstrated for the ﬁrst time an impact of

spatial information on the performances to solve

addition and subtraction problems. Interestingly,

the observed motion–arithmetic compatibility

effect is more reliable for the vertical than for the

horizontal dimension, supporting the idea that

the mapping between numbers and vertical space

has a predominant function in mental arithmetic.

If participants were required to move their arm

while solving arithmetic problems (Experiment

1), we observed impaired performance in addition

when moving left- or downwards than when

moving right- or upwards and vice versa in subtrac-

tion. Experiment 1 furthermore revealed a descrip-

tive difference between the compatibility effects

along the two dimensions, suggesting a stronger

association for the vertical dimension. However,

the interaction between the factors motion–arith-

metic compatibility and dimension did not reach

signiﬁcance. The second experiment provided an

additional test of differences in the impact of verti-

cal and horizontal spatial information and

controlled for the potential confound of higher

effort associated with upward than with downward

arm movements as an alternative explanation for

the motion–arithmetic compatibility effect for the

vertical dimension. Experiment 2 revealed only a

vertical but not a horizontal motion–arithmetic

compatibility effect and this way conﬁrmed our

hypothesis that the coupling of mental arithmetic

is more robust for the vertical dimension.

Together our data support the idea that spatial pro-

cesses are functionally linked to mental arithmetic

(Pinhas & Fischer, 2008) and indicate that both

horizontal and vertical spatial information are

involved in mental arithmetic. Importantly, the

greater robustness of the motion–arithmetic com-

patibility effect for the vertical than for the horizon-

tal dimension argues for a predominant role of the

vertical dimension in the coupling of space and

arithmetic operations.

The observed motion–arithmetic compatibility

effect is in line with the idea that mental arithmetic

is accompanied by attentional shifts in mental

number space (McCrink et al., 2007; Pinhas &

Fischer, 2008). The previous support for a spatial

origin of the operational momentum effect in

approximate arithmetic was exclusively based on

spatial response biases for symbolic and nonsym-

bolic arithmetic (Knops, Viarouge, et al., 2009;

Pinhas & Fischer, 2008) and the predictability of

addition and subtraction from neural correlates of

Table 4. Mean response time and error rates in Experiment 2 as a function of the factors problem size, operation, spatial dimension, and

motion–arithmetic compatibility

Dependent variable Spatial dimension MAC compatibility

Problems

Small-size problems Large-size problems

Addition Subtraction Addition Subtraction

Response time (s) Horizontal Compatible 1.300 1.650 3.106 3.518

Incompatible 1.330 1.628 3.168 3.497

Vertical Compatible 1.299 1.622 3.162 3.526

Incompatible 1.330 1.646 3.153 3.555

Error rate (%) Horizontal Compatible 3.23 4.28 16.50 19.95

Incompatible 2.23 3.64 13.64 19.98

Vertical Compatible 2.71 2.97 12.68 21.11

Incompatible 2.25 4.51 15.42 22.11

Note: MAC =motion–arithmetic compatibility.

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8) 1567

SPATIAL INTERFERENCE IN MENTAL ARITHMETIC

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

horizontal saccades (Knops, Thirion et al., 2009).

Motor response biases, however, do not provide a

strict test for the spatial processes and can be alter-

natively explained by the simple response heuristic

to point more toward smaller numbers after sub-

tracting and more towards large numbers after

additions in situations of uncertainty (see e.g.,

Knops, Zitzmann, & McCrink, 2013 for a discus-

sion of a similar alternative account). The present

study now sheds new light on the origin of the

operational momentum effect by showing that the

mere activation of spatial codes affects the overall

efﬁciency to solve arithmetic problems. The non-

spatial accounts of response heuristics predict a

systematic over- or underestimation or distortions

in pointing trajectories but do not account for the

inﬂuence reported here of spatial codes on arith-

metic performances. Therefore, the present

ﬁnding of an impact of spatial information on

arithmetic problem-solving performance also pro-

vides support for the previously made notions that

biases in nonsymbolic (McCrink et al., 2007) and

symbolic arithmetic (Pinhas & Fischer, 2008) orig-

inate from attentional shifts in mental numerical

space (Knops, Thirion, et al., 2009).

The present study substantially extends the lit-

erature on number processing by showing that

associations with vertical space are not restricted

to the processing of single numbers (Sell &

Kaschak, 2012; Shaki & Fischer, 2012; Winter &

Matlock, 2013) but are also present in mental arith-

metic. Importantly, the greater impact of vertical

spatial information on arithmetic provides direct

empirical support for the grounding hypothesis of

spatial–numerical associations (cf. Fischer &

Brugger, 2011; Lakoff, 1987). According to this

notion, sensory experiences with numbers will be

primarily associated with the vertical dimension

due to a correlation between vertical space and

magnitude in the world. Therefore, vertical space

becomes an important and maybe even the predo-

minant dimension in the organization of number

space. Following this line of reasoning, it has also

been argued that vertical spatial associations

provide the conceptual basis for the development

of any numerical knowledge (Fischer & Brugger,

2011). The presented motion arithmetic

compatibility effect and more robust effect of verti-

cal spatial information can therefore also be con-

ceived as support for the recently discussed

general hypothesis that sensorimotor experiences

shape the development of any kind of conceptual

knowledge (Barsalou, 2008).

One fundamental question concerning the

interference between spatial processing and

mental arithmetic is the direction of the inﬂuence.

Importantly, in Experiment 2 participants merely

had to follow the moving problem with their eyes.

We regard it as rather unlikely that mental arith-

metic has a strong impact on the control of eye

movements, since previous studies could show

that the control of such movements is highly auto-

matized and robust against cognitive interferences

(e.g., Kathmann, Hochrein, & Uwer, 1999;

Theeuwes, 2010). The motion–arithmetic compat-

ibility effect for visual motions therefore most likely

reﬂects an impact of spatial processing on mental

arithmetic. However, more research is needed to

determine the causality between space and

arithmetic.

Since problem size was controlled between

addition and subtraction trials by matching overall

numerical size (i.e., the sum of the operands and

the correct solution), it might be objected that

our ﬁndings are confounded by a difference in the

size of solutions for addition and subtraction

trials. If this was true, an interaction between

motion direction and problem size would be

expected. That is, independent of the arithmetic

operation performance should be enhanced for

large-solution trials when moving right- or

upwards compared to when moving left- or down-

wards. Similarly, small-solution problems should

be facilitated when moving left- or downwards

compared to when moving right- or upwards.

Additional analyses demonstrated that the data

provided no evidence for such an interaction

effect, which demonstrates that the effect of the

motion direction was driven by the compatibility

with the arithmetic operation.

As discussed above, vertical movements per

deﬁnition suffer from a confound of effort, since a

movement working against gravity requires more

energy than a movement going with the forces of

1568 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8)

WIEMERS ET AL.

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

gravity. This difference is, however, marginal for

smooth pursuit eye movements and not even fully

taken into account by the brain (see Collewijn

et al., 1988). We therefore argue that asymmetries

in effort do not account for the predominance of

the vertical mapping in the present study.

Nevertheless we acknowledge that in principle it

cannot be exclude that the stronger vertical

motion arithmetic compatibility effect is the result

of a “more-is-more”association (Stavy & Tirosh,

2000) between effort and numerical size, since a

difference in physically required energy for up and

downward eye movements does clearly exist.

The present ﬁnding of a motion–arithmetic

compatibility effect for horizontal and vertical

space might have implications for maths education

in elementary school or for remedial educational

programmes for dyscalculic individuals. As it has

already been shown that gestures can increase

mathematical learning (Goldin-Meadow, Cook,

& Mitchell, 2009), a systematic involvement of

both horizontal and vertical spatial mappings

might support the learning of numerical concepts

and arithmetic.

In conclusion, the present study shows that both

horizontal and vertical organizations of mental

numerical space are activated during mental arith-

metic and suggests a functional involvement of

both dimensions. Our ﬁnding of a more robust

effect of vertical space furthermore suggests a pre-

dominant role of the vertical organization of the

mental number space in mental calculations.

Original manuscript received 13 August 2013

Accepted revision received 19 December 2013

First published online 6 March 2014

REFERENCES

Barsalou, L. W. (2008). Grounded cognition. Annual

Review of Psychology,59, 617–645.

Collewijn, H., Erkelens, C. J., & Steinman, R. (1988).

Binocular Co-ordination of human vertical saccadic

eye movements. Journal of Physioloogy,404, 183–197.

Dehaene, S., Bossini, S., & Giraux, P. (1993). The

mental representation of parity and number

magnitude. Journal of Experimental Psychology:

Genera,122, 371–396.

Fias, W., & Fischer, M. H. (2005). Spatial represen-

tation of numbers. In J. I. D. Campbell (Ed.),

Handbook of mathematical cognition (pp. 43–54).

New York: Psychology Press.

Fischer, M., & Brugger, P. (2011). When digits help

digits: Spatial–numerical associations point to ﬁnger

counting as prime example of embodied cognition.

Frontiers in Psychology,2, 260

Goldin-Meadow, S., Cook, S. W., & Mitchell, Z. A.

(2009). Gesturing gives children new ideas about

math. Psychological Science,20(3), 267–272.

Holmes, K. J., & Lourenco, S. F. (2012). Orienting

numbers in mental space: Horizontal organization

trumps vertical. The Quarterly Journal of

Experimental Psychology,65, 1044–1051.

Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S.

(2005). Interactions between number and space in par-

ietal cortex. Nature Reviews Neuroscience,6,435–448.

Ito, Y., & Hatta, T. (2004). Spatial structure of quanti-

tative representation of numbers: Evidence from the

SNARC effect. Memory & Cognition,32, 662–673.

Kathmann, N., Hochrein, A., & Uwer, R. (1999).

Effects of dual task demands on the accuracy of

smooth pursuit eye movements. Psychophysiology,36

(2), 158–163.

Knops, A., Thirion, B., Hubbard, E. M., Michel, V., &

Dehaene, S. (2009). Recruitment of an area involved

in eye movements during mental arithmetic. Science,

324, 1583–1585.

Knops, A., Viarouge, A., & Dehaene, S. (2009).

Dynamic representations underlying symbolic and

nonsymbolic calculation: Evidence from the oper-

ational momentum effect. Attention Percepion &

Psychophysics,71, 803–821.

Knops, A., Zitzmann, S., & McCrink, K. (2013).

Examining the presence and determinants of oper-

ational momentum in childhood. Frontiers in

Psychology,4, 325.

Krause, F., & Lindemann, O. (2013). Expyriment: A

Python library for cognitive and neuroscientiﬁc exper-

iments. Behavior Research Methods.doi: 10.3758/

s13428-013-0390-6

Lakoff, G. (1987). Women, ﬁre, and dangerous things:

What categories reveal about the mind. Chicago:

University of Chicago Press.

McCrink, K., Dehaene, S., & Dehaene-Lambertz, G.

(2007). Moving along the number line: Operational

momentum in nonsymbolic arithmetic. Perception

and Psychophysics,69(8), 1324–1333.

THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8) 1569

SPATIAL INTERFERENCE IN MENTAL ARITHMETIC

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014

Pinhas, M., & Fischer, M. H. (2008). Mental movements

without magnitude? A study of spatial biases in sym-

bolic arithmetic. Cognition,109,408–415.

Schwarz, W., & Keus, I. (2004). Moving the eyes along

the mental number line: Comparing SNARC effects

with manual and saccadic responses. Perception &

Psychophysics,66, 651–664.

Sell, A. J., & Kaschak, M. P. (2012). The comprehension

of sentences involving quantity information affects

responses on the up–down axis. Psychonomic Bulletin

and Review,19, 708–714.

Shaki, S., & Fischer, M. (2012). Multiple spatial mappings

in numerical cognition. Journal of Experimental

Psychology: Human Perception and Performance,38(3),

804–809.

Stavy, R., & Tirosh, D. (2000). How students (mis-)

understand science and mathematics: Intuitive rules.

New York: Teachers College Press.

Theeuwes, J.(2010). Top-down and bottom-up control of

visual selection. Acta Psychologica,135(2), 77–99.

Winter, B., & Matlock, T. (2013). More is up…and

right: Random number generation along two axes.

In M. Knauff, M. Pauen, N. Sebanz, & I.

Wachsmuth (Eds.), Proceedings of the 35th Annual

Conference of the Cognitive Science Society (pp. 3789–

3974). Austin, TX: Cognitive Science Society.

1570 THE QUARTERLY JOURNAL OF EXPERIMENTAL PSYCHOLOGY, 2014, 67 (8)

WIEMERS ET AL.

Downloaded by [Universitaetsbibliothek Potsdam] at 04:28 27 July 2014