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Does Chess Instruction Enhance Mathematical Ability in Children?

A Three-Group Design to Control for Placebo Effects

Giovanni Sala (giovanni.sala@liv.ac.uk)

Department of Psychological Sciences, University of Liverpool, Bedford Street South, Liverpool, UK

Fernand Gobet (fernand.gobet@liv.ac.uk)

Department of Psychological Sciences, University of Liverpool, Bedford Street South, Liverpool, UK

Roberto Trinchero (roberto.trinchero@unito.it)

Department of Philosophy and Education, University of Turin, Via Gaudenzio Ferrari 9, Turin, ITA

Salvatore Ventura (salvatore.ventura@unimi.it)

University of Milan, ITA

Abstract

Pupils’ poor achievement in mathematics has recently been a

concern in many Western countries. In order to address this is-

sue, it has been proposed to teach chess in schools. However,

in spite of optimistic claims, no convincing evidence of the ac-

ademic benefits of chess instruction has ever been provided,

because no study has ever controlled for possible placebo ef-

fects. In this experimental study, a three-group design (i.e., ex-

perimental, placebo, and control groups) was implemented to

control for possible placebo effects. Measures of mathematical

ability and metacognitive skills were taken before and after the

treatment. We were interested in metacognitive skills because

they have been claimed to be boosted by chess instruction, in

turn positively influencing the enhancement of mathematical

ability. The results show that the experimental group (partici-

pants attending a chess course) achieved better scores in math-

ematics than the placebo group (participants attending a Go

course) but not than the control group (participants attending

regular school lessons). With regard to metacognition, no dif-

ferences were found between the three groups. These results

suggest that some chess-related skills generalize to the mathe-

matical domain, because the chess lessons compensated for the

hours of school lessons lost, whereas the Go lessons did not.

However, this transfer does not seem to be mediated by meta-

cognitive skills, and thus appears to be too limited to offer ed-

ucational advantages.

Keywords: chess; mathematics; transfer; education.

Introduction

Recently, pupils’ poor achievement in mathematics has been

the subject of debate both in the United States (Hanushek,

Peterson & Woessmann, 2012; Richland, Stigler, & Holyoak,

2012) and in Europe (Grek, 2009). Policy makers and re-

searchers have investigated several alternative methods and

activities with the aim of improving the effectiveness of

mathematical teaching. Teaching chess in schools is one of

these activities. Chess has recently become part of the school

curriculum in several countries, and several large studies and

educational projects involving chess are currently ongoing in

Germany, Italy, Spain, Turkey, the United Kingdom, and the

United States. Moreover, the European Parliament has ex-

pressed its positive opinion on using chess courses in schools

as an educational tool (Binev, Attard-Montalto, Deva,

Mauro, & Takkula, 2011).

Chess as Educational Tool: The available Evidence

Several studies have tried to demonstrate the potential bene-

fits of chess training on various cognitive abilities such as at-

tention (Scholz et al., 2008), development of spatial concepts

(Sigirtmac, 2012), general intelligence (Hong & Bart, 2007),

and metacognition (Kazemi, Yektayar, & Abad, 2012). Other

studies focused on academic variables, such as reading and

mathematics (Christiaen & Verhofstadt-Denève, 1981).

Recently, several studies have investigated the positive in-

fluence that chess could exert on children’s mathematical

abilities (Barrett & Fish, 2011; Kazemi et al., 2012; Sala,

Gorini, & Pravettoni, 2015; Scholz et al., 2008; Trinchero,

2012; Trinchero & Sala, in press). Barrett and Fish (2011)

examined the effect of chess instruction on adolescents re-

ceiving special education services, using TAKS (Texas As-

sessment of Knowledge and Skills) scores in mathematics.

The chess-treatment group showed an overall better perfor-

mance than the control group. In Kazemi et al. (2012), the

same pattern occurred with a sample of typically developing

male students from primary and secondary schools. Scholz et

al. (2008) examined the possible benefits of chess instruction

on a sample of primary school children with learning disabil-

ities (IQ between 70 and 85), with disappointing results. Fi-

nally, Sala’s and Trinchero’s studies (Sala, Gorini, & Pra-

vettoni, 2015; Trinchero, 2012; Trinchero & Sala, in press)

focused on the effect of chess instruction on primary school

children’s mathematical problem-solving ability. In these

studies the chess-treatment groups systematically outper-

formed the control groups.

The Lack of a Placebo Group

Following the above overall positive results, the view of the

chess community has been that chess practice increases aca-

demic performance because chess is an intellectually de-

manding and stimulating game (Bart, 2014; Garner, 2012;

Root, 2006). Such optimistic view has been challenged, ante

litteram, by Gobet and Campitelli’s (2006) review of the lit-

Sala, G., Gobet, F., Trinchero, R., & Ventura, S. (2016). Does chess instruction

enhance mathematical ability in children? A three-group design to control for placebo

effects. Proceedings of the 38th Annual Meeting of the Cognitive Science Society.

erature regarding the effectiveness of chess instruction in en-

hancing children’s academic and cognitive abilities. Gobet

and Campitelli highlighted that – in spite of some the prom-

ising results reported in the reviewed experiments – the ben-

efits of chess practice were yet to be clearly established, be-

cause of the poor experimental design used in most studies.

In particular, most studies did not control for placebo effects

– that is, effects that are not due to the treatment per se but

that are due to other, uncontrolled aspects of the experimental

design. Potential mechanisms behind placebo effects include

instructors’ motivation, the state of excitement and attention

induced by a novel activity, and teachers’ expectations.

More recently, a meta-analysis (Sala & Gobet, 2016) has

lent further support to Gobet and Campitelli’s conclusions. In

that meta-analysis, 24 studies passed the selection criteria,

with 40 effect sizes. The overall effect size of chess instruc-

tion was moderate, with g = 0.34. It was also found that stud-

ies with at least 25 hours of chess instruction were more likely

to have a positive effect on mathematics, reading, and cogni-

tive abilities (g = 0.43) than studies with less than 25 hours

treatment (g = 0.30). Only one study (Fried & Ginsburg, n.d.),

which was interested in perceptual and visuo-spatial skills,

included a placebo control group. This study showed no dif-

ference between the chess group and the placebo group,

which consisted of attending counselling sessions. Unfortu-

nately, Fried and Ginsburg’s (n.d.) study did not investigate

the effect of chess instruction on children’s mathematical

ability. Therefore, this study cannot corroborate or disprove

any claims about the effectiveness of chess in enhancing

mathematical abilities.

The lack of a placebo control group – i.e., a group attending

other activities non-related to chess – has thus been identified

as the most serious flaw of the previous studies in the field.

These studies often compared the practice of the game of

chess to regular school activities. However, chess practice

may exert a moderate positive influence on children’s aca-

demic just because it is a novel activity in their curriculum

that is fun, and this may induce a state of increased attention

and motivation.

From an educational (and practical) perspective, this might

be irrelevant. Policy makers and educators might be inter-

ested in the effectiveness of chess instruction, regardless of

any chess-specific or non-chess-specific element causing the

improvement in pupils’ academic skills. Assuming this

“whatever works” perspective, the only element of interest

would be the size of the effect – i.e., how much children at-

tending chess courses improve their academic skills, such as

mathematical literacy.

Nonetheless, evaluating whether the benefits of chess prac-

tice on children’s academic skills are due to elements specific

or non-specific to the game of chess is an important theoreti-

cal question. In fact, assuming that skills acquired in chess

lead to benefits in domains such as mathematics clearly im-

plies the presence of far transfer. Far transfer occurs when a

set of skills acquired in one domain (e.g., chess) generalizes

to other domains (e.g., mathematics) that are only loosely re-

lated to the source domain.

The Problem of Transfer in Chess

Since transfer is a function of the extent to which two do-

mains share common features (Thorndike & Woodworth,

1901), far transfer rarely occurs, as shown by substantial re-

search in education and psychology (Donovan, Bransford, &

Pellegrino, 1999; Gobet, 2015a,b). Moreover, in line with

Thorndike and Woodworth’s (1901) hypothesis, several stud-

ies have shown that chess players’ skills tend to be context-

bound, suggesting that it is difficult to achieve far transfer

from chess to mathematics. In her classic study, Chi (1978)

demonstrated that chess players’ (both adults and children)

memory for chess positions did not extend to the recall of

digits. Chess players outperformed non-chess players in re-

membering chess positions, but no difference occurred with

lists of digits. The same result was obtained in a study carried

out by Schneider, Gruber, Gold, and Opwis (1993). Waters,

Gobet, and Leyden (2002) found that chess players’ percep-

tual skills did not generalize to visual memory of shapes.

More recently, Bühren and Frank (2010) found that chess

grandmasters did not outperform chess amateurs in the eco-

nomic game known as beauty contest. Finally, Unterrainer,

Kaller, Leonhart, and Rahm (2011) found that chess players’

planning abilities did not transfer to the Tower of London, a

test assessing executive function and planning skills.

The Present Study

The research on the transferability of chess players’ skills to

other domains offers a complementary perspective to the re-

search on the benefits of chess instruction on children’s aca-

demic (e.g., mathematics) achievement. Whilst the latter has

provided encouraging results, the former has offered results

that seem to preclude any generalizability of chess-specific

skills.

A possible explanation may be that chess instruction shares

with the domain of mathematics some general features, such

as quantitative relationships (e.g., the value of the chess

pieces) and problem-solving situations (e.g., tactics), which

can in turn generalize to mathematics. However, this transfer

can occur only when these skills are at the beginning of their

development, and hence still generalizable. Put simply, chil-

dren studying the four operations may take advantage of an

activity (i.e., chess) dealing with the calculation, for example,

of the pieces’ values. By contrast, it is hard to believe that

knowing advanced chess techniques, such as Lucena’s

method in Rook endgames, might be beneficial for college

students’ skills in calculus or combinatorics. In the former

case, there may be an overlap between the domain of chess

and mathematics, in the latter there is none. This may explain

why the studies dealing with the effect of chess instructions

on children’s mathematical ability have provided positive re-

sults, whilst studies regarding the generalizability of chess

masters’ skills have showed no effect.

An alternative explanation has been suggested by Kazemi

et al. (2012), according to which chess instruction improves

children’s metacognition – i.e., the ability to monitor one’s

own cognitive processing (Brown, 1987; Flavell, 1979) –

which, in turn, enhance their mathematical ability. Kazemi et

al. (2012) found that youngsters who attended a chess course

outperformed the control group not only in mathematical

ability, but also in metacognitive skills. Once again, unfortu-

nately, this study did not control for possible placebo effects.

In any case, since metacognitive skills have been claimed

to be one of the most important predictors of mathematical

ability (Desoete & Roeyers, 2003; Veenman, Van Hout-

Wolters, & Afflerbach, 2006), and since playing chess is an

activity for which the self-monitoring of one’s thinking pro-

cesses is essential (De Groot, 1965), Kazemi et al.’s (2012)

hypothesis is plausible. Obviously, the null hypothesis – i.e.,

chess instruction has no effect on children’s mathematical

and/or cognitive abilities, and the observed benefits are mar-

ginal and only due to placebo effects – may be valid too.

Since there is a need, in this field of research, to clarify

whether the observed positive influence of chess practice is

due to placebo effects or to chess training itself, we ran a

three-group design study. Beyond the usual experimental and

control groups – attending a chess course and regular school

activities, respectively – an active control group was added to

control for potential placebo effects. Moreover, the partici-

pants of this study were given – along with a test of mathe-

matical ability – a questionnaire assessing metacognitive

skills, in order to evaluate whether metacognition is the link

connecting chess instruction to the improvements in mathe-

matical ability, as proposed by several authors in the field.

This work thus investigates (a) whether chess instruction

enhances children’s mathematical ability, (b) whether this ef-

fect is mediated by metacognition, and (c) whether the effect

of chess instruction on the above two variables is genuine or

due to placebo effects.

Method

Participants

Fifty-two fourth graders in three classes of a primary school

in Italy took part in this experiment. The mean age of the par-

ticipants was 9.32 years (SD = 0.32). Parental consent was

asked and obtained for all the participants.

Material

A six-item test was designed to test participants’ mathemati-

cal ability (range score 0 – 6). The items used were all from

the Italian version of the IEA-TIMSS international survey

among fourth graders (Mullis & Martin, 2013), a test with

good psychometric properties. These items were chosen be-

cause they measure not only procedural mathematical

knowledge (e.g., 3 + 7 = ?), but also problem-solving ability.

In fact, all the items required solving a mathematical problem

1

Randomizing participants instead of classes is unpractical in

schools, especially when interventions replace part of the curricular

hours. The participants were assigned to the three classes according

to accidental sampling – i.e., the teachers did not adopt any particu-

lar didactic criterion (e.g., the students struggling with math in a par-

ticular class).

starting from a given set of data. An example of such items is

provided in Figure 1.

Figure 1. An example of the items used in the test of mathe-

matical ability.

To assess participants’ metacognitive skills, we used the

Italian version of Panaoura and Philippou’s (2003) question-

naire (15-item version; range score 15 – 75). Participants

were given 45 minutes for completing the battery of tests.

Design

The three classes were randomly

1

assigned to three groups:

• One class attended 15 hours of chess lessons during

school hours, along with regular school activities

(experimental group).

• One class attended regular school activities only

(control group).

• One class attended 15 hours of Go

2

lessons during

school hours, along with regular school activities

(placebo group).

Importantly, the two interventions – i.e., chess and Go

courses – replaced part of the hours originally dedicated to

2

Go (or Baduk) is an Asian strategic board game for two players.

The objective of the game is to surround a larger portion of the board

(called Goban) than the opponent. To pursue this aim, the two play-

ers place stones (the game pieces) on the board.

mathematics and sciences. This way, we could confront the

effectiveness of chess (and Go) instruction with the tradi-

tional way of teaching mathematics or mathematics-related

subjects – such as sciences.

The chess and Go lessons followed a pre-arranged teaching

protocol, which consisted of the basic rules of the games, tac-

tical exercises, and playing complete games. All these activ-

ities focused mainly on problem-solving situations, such as

finding the correct move and evaluating the ad-

vantages/weaknesses in a particular position. It must be no-

ticed that the two courses (chess or Go) did not deal with or

introduce any mathematics-related topics, unless these were

part of the respective games (e.g., in chess, a Bishop is worth

three Pawns). That is, the two courses had only chess- and

Go-related contents. In order to rule out possible extraneous

effects related to instructor personality (e.g., Pygmalion ef-

fect), the chess and Go interventions were carried out by the

same instructor, who is an experienced teacher and both a

chess and Go trainer. The tests of mathematical ability and

metacognition were administered twice, once before the be-

ginning of the course and once after the end. The experi-

mental design is summarized in Figure 2.

Figure 2. The experimental design.

Finally, the chess/Go trainer, the teachers, the parents, and

the children involved reported no unpleasant issues. On the

contrary, the people who took part in this project expressed a

positive feedback.

Results

Mathematical Ability

No significant differences between the three groups were

found in the pretest scores (F(2, 51) = 1.030, p = .365). A

univariate analysis of covariance (ANCOVA) was used to

evaluate the role of group (independent variable) and mathe-

matics pretest scores (covariate) in affecting mathematics

post-intervention scores (dependent variable).

The results showed a significant effect of the covariate

(F(1, 48) = 21.834, p < .001), and a significant effect of group

(F(2, 48) = 3.371, p = .043). The pairwise comparisons

showed that the control group outperformed the Go group (p

= .017), the chess group marginally outperformed the Go

group (p = .088), whereas no significant difference was found

between the control and the chess group (p = .487). The re-

sults are summarized in Table 1.

Table 1. Mathematical ability scores in the three groups.

Note. Standard deviations are shown in brackets.

Metacognitive Skills

No significant differences between the three groups were

found in the pretest scores (F(2, 51) = 0.487, p = .617). A

univariate analysis of covariance (ANCOVA) was used to

evaluate the role of group (independent variable) and meta-

cognition pre test scores (covariate) in affecting metacogni-

tion post-intervention scores (dependent variable).

The results showed a significant effect of the covariate

(F(1, 48) = 47.809, p < .001), and no significant effect of

group (F(2, 48) = 0.367, p = .694). The pairwise comparisons

showed no differences between the three groups. The scores

are summarized in Table 2.

Table 2. Metacognitive-skill scores in the three groups.

Note. Standard deviations are shown in brackets.

Discussion

According to the results presented in this paper, chess seems

to be more effective in enhancing children’s mathematical

skills than Go, but not than regular school activities. This out-

come – which is consistent with the aforementioned reviews

(Gobet & Campitelli, 2006; Sala & Gobet, 2016) – might be

discouraging for researchers and teachers who have upheld

the implementation of chess instruction in school curricula.

However, the fact that the placebo group (Go instruction) un-

derperformed in this experiment – whilst the chess group

equalled the performance of the control groups – suggests

that some chess-related skills generalized to the domain of

mathematics (Scholz et al., 2008), and therefore that the ben-

efits of chess instruction, albeit limited, are not only the mere

by-product of placebo effects.

With regard to metacognitive skills, children do not seem

to benefit from any advantage from chess instruction. In fact,

the participants of the three groups performed equally, both

Group Pretest Posttest Adjusted mean

Chess 2.13 (1.26) 2.50 (1.41) 2.30

Go 1.81 (1.08) 1.62 (1.20) 1.63

Control 1.53 (1.13) 2.40 (1.55) 2.60

Group Pretest Posttest Adjusted mean

Chess 55.2 (11.0) 57.0 (10.5) 56.3

Go 52.7 (9.2) 54.8 (8.6) 55.8

Control 55.3 (6.5) 58.3 (6.0) 57.6

in the pretest and in the posttest, suggesting that metacogni-

tion does not represent the cognitive link between chess in-

struction and mathematical ability.

Strengths and Limitations of the Study

In spite of the long history of research on the benefits of chess

instruction on mathematical ability, which started more than

thirty years ago with Christiaen and Verhofstadt-Denève

(1981), the current study is the first to use a placebo group.

In addition to its design, it has several strengths. First, the

same instructor taught the experimental and placebo groups.

Second, the interventions were implemented during school

hours, and replaced part of the lessons dedicated to the teach-

ing of mathematics or mathematics-related subjects (i.e., sci-

ences), in order to compare directly chess and Go instruction

to ordinary school teaching. Finally, the design included both

a cognitive (i.e., metacognition) and an academic (i.e., math-

ematics) variable, in order to search for a possible causal link

between chess instruction and enhancement of children’s

mathematical ability.

The study also suffers from a few weaknesses. The sample

size was relatively small, which affected statistical power.

Randomization was done at the class level rather than the in-

dividual level. (However, as remarked in footnote 1, random-

ization at the individual level is nearly impossible in the con-

text of real schools.) Finally, only one measure of mathemat-

ical ability and metacognitive skills, respectively, was used.

Recommendations for Future Research

The present study supports the hypothesis according to which

chess skill transfers to mathematical ability. Importantly, be-

cause the effect was not observed in the Go condition, this

generalization of chess skill does not depend on placebo ef-

fects. However, this far transfer seems – when it occurs – to

be limited in size, which is in line with substantial previous

research in the field (e.g., Donovan et al., 1999). Further-

more, the results of this study do not corroborate Kazemi’s et

al. (2012) idea that chess instruction fosters children’s math-

ematical ability by enhancing their metacognitive skills.

Given the near-absence of studies controlling for placebo

effects in this line of research, it is essential to replicate and

extend this work. First, since the duration of treatment seems

to be positively related to the effect of chess instruction on

cognitive and academic outcomes (Sala & Gobet, 2016), fu-

ture studies should directly manipulate this variable, in order

to understand the optimal duration of chess courses. Second,

given that the positive effect of chess instruction does not ap-

pear superior to the regular curricular activities, it would be

interesting to compare the effect of chess interventions held

during school hours with the effect of chess interventions

held during extra-curricular hours. Third, there has been little

research that has explicitly tried to teach mathematics using

chess. Possible examples include illustrating the Cartesian

graph with the chess board and introducing the concept of

block distance – as opposed to Euclidean distance – with the

movement of the King. As it is known that awareness makes

transfer more likely (Gick & Holyoak, 1980; Salomon & Per-

kins, 1989), it is plausible that making explicit the links be-

tween chess and mathematics could facilitate transfer. Fi-

nally, other activities could be used with the placebo groups,

such as other board games (e.g., checkers) and music.

The chess-in-school field of research has been nearly ex-

clusively interested in establishing the presence of benefits of

chess instruction for curricular topics (mostly mathematics

and reading) and general cognitive abilities (e.g. intelligence

and creativity). However, very little research has been carried

out on the mechanisms (presumably) leading to such benefits.

A crucial aim for this field of research, then, is to develop a

detailed causal model explaining the cognitive processes that

mediate learning and transfer. With such a model, more pre-

cise hypotheses could be tested than it is currently the case.

Acknowledgments

The authors gratefully thank the principal, the teachers, the

parents, and the children involved in this study.

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