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DOI: 10.1177/2158244015596050

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Article

Introduction

Many studies have analyzed the relationship between general

intelligence and chess abilities. In particular, some of them

have investigated the correlation between these two variables

suggesting that the chess players’ population (both adults and

children) is more intelligent than the general one (Doll &

Mayr, 1987; Frydman & Lynn, 1992; Horgan & Morgan,

1990). This evidence, however, does not necessarily lead to

the conclusion that chess improves intelligence because the

direction of the causality is uncertain (Gobet & Campitelli,

2002). In fact, there are several possible alternative explana-

tions for that: A high IQ could be the cause of a high chess

ability (and not vice versa); in other words, an intelligent indi-

vidual achieves a high chess ability just because chess requires

a high degree of intelligence, but it does not increase it; or,

alternatively, high-IQ people could be “selected by the game”

much more easily than others: Subjects playing chess can find

out that they are good at the game, so they are encouraged to

continue to play it. However, whoever turns out to be not so

good at chess can be discouraged to play it again. In this case,

chess “selects” motivated people with a high IQ who are able

to play well (Gobet & Campitelli, 2006).

Beyond the question of direction of causality, the more

general problem of the transfer of skills must be held in

consideration. If the former problem is addressable by using

a proper experimental design (experimental and control

groups; pre- and post-tests), the latter represents a theoretical

problem since the seminal work of Thorndike and Woodworth

(1901). Their theory of identical elements states that the

transfer of cognitive abilities, from a domain to another one,

occurs only when the domains share common elements. This

implies that the transfer of skills is quite rare and limited to

the extent that there is an overlap between the domains

(Anderson, 1990; Singley & Anderson, 1989; Travers, 1978).

Some studies have shown that this applies to the game of

chess too. In her classical study, Chi (1978) demonstrated

that chess players’ memory skill for chess positions did not

extend to digits recall. Schneider, Gruber, Gold, and Opwis

(1993) replicated the study and obtained the same outcomes.

More recently, Unterrainer, Kaller, Leonhart, and Rahm have

found that chess players’ planning abilities did not transfer to

the Tower of London, a test assessing executive function and

596050SGOXXX10.1177/2158244015596050SAGE OpenSala et al.

research-article2015

1University of Liverpool, UK

2University of Milan, Italy

Corresponding Author:

Giovanni Sala, Brownlow Street, Liverpool L69 3GL, UK.

Email: giovanni.sala@liverpool.ac.uk

Mathematical Problem-Solving Abilities

and Chess: An Experimental Study on

Young Pupils

Giovanni Sala1,2, Alessandra Gorini2, and Gabriella Pravettoni2

Abstract

Chess is thought to be a game demanding high cognitive abilities to be played well. Although many studies proved the link

between mastery in chess and high degree of intelligence, just few studies proved that chess practice can enhance cognitive

abilities. Starting from these considerations, the main purpose of the present research was to investigate the potential

benefits of in-presence chess lessons and on-line training on mathematical problem-solving ability in young pupils (8 to 11

years old). Five hundred sixty students were divided into two groups, experimental (which had chess course and on-line

training) and control (which had normal school activities), and tested on their mathematical and chess abilities. Results show

a strong correlation between chess and math scores, and a higher improvement in math in the experimental group compared

with the control group. These results foster the hypothesis that even a short-time practice of chess in children can be a useful

tool to enhance their mathematical abilities.

Keywords

education, social sciences, achievement, science, math, and technology, curriculum, educational research, education theory

and practice, educational psychology, applied psychology, psychology, cognitivism, approaches, experimental psychology

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2 SAGE Open

planning skills (Unterrainer et al., 2011); in Waters, Gobet,

and Leyden (2002), chess players’ perceptual skills did not

transfer to visual memory of shapes; and finally, chess abili-

ties did not correlate with performance in a beauty contest

experiment (Bühren & Frank, 2010). All these studies have

suggested that transfer is, at best, improbable, and that chess

players’ special abilities are context-dependent.

Given that the more specific a skill is, the less that skill is

transferable to another domain; nevertheless, it is reasonable

to suppose that a game requiring attention, logical thinking,

planning, and calculation abilities would be able to improve

at least some of the aforementioned abilities, which are

linked to the problem-solving competence and, overall, to

general intelligence, at the beginning of their development.

Put simply, if chess players’ abilities do not transfer to other

domains, it is not impossible that chess helps children devel-

oping the above abilities, especially when these latter are yet

to be fully developed, and still general enough to allow the

transfer.

This hypothesis is supported by those studies investigat-

ing the effect of the chess courses on children’s mathematical

abilities (Barrett & Fish, 2011; Hong & Bart, 2007; Kazemi,

Yektayar, & Abad, 2012; Scholz et al., 2008; Trinchero,

2012a). Such studies have found that children attending

chess lessons show significant improvements in mathemati-

cal abilities. This is even true for low-IQ subjects: Scholz

et al. (2008) found that children with an IQ ranging from 70

and 85, attending 1 hr per week of chess lesson instead of 1

hr of mathematics, performed significantly better in addition

and counting than children who did not receive chess les-

sons; Hong and Bart (2007) found a correlation between

chess ability and non-verbal intelligence in students at risk of

academic failure, suggesting that chess ability can be a pre-

dictor of improvement in cognitive abilities; Barrett and Fish

(2011) tested 31 students, receiving special education ser-

vices, divided in 2 groups: One had chess lesson once a week

instead of a lesson of mathematics, whereas the other one

had two lessons per week of mathematics, but no chess les-

son. This study showed that the chess group improvements in

“number, operations and quantitative reasoning” and in

“probability and statistics” were significantly higher than

those obtained by the other group who did not attend any

chess activity. Similar results have also been found in pupils

with normal IQ and without specific disabilities (Kazemi

et al., 2012; Liptrap, 1998; Trinchero, 2012a, 2012b). In all

these studies, positive effects of chess appeared after at least

25/30-hr courses. Studies of Trinchero (2012b) and Kazemi

et al. (2012), which investigated the effects of a chess course

on children’s (third graders in Trinchero, 2012b, fifth, eighth,

ninth graders in Kazemi et al.) mathematical problem-solving

ability, deserve a particular attention. Both of these studies

have found a significant improvement in problem-solving

scores in chess-trained children compared with children who

have not performed any chess-related activity. These results

suggest that chess could increase not only basic mathematical

abilities (as calculation or addition) but also competences,

such as mathematical problem-solving abilities. Starting

from these data, the aim of the present study was to verify

whether a blended strategy (Trinchero, 2013) consisting in a

10- to 15-hr chess course supported by a computer-assisted

training (CAT) is able to improve mathematical problem-

solving ability in children in a shorter time compared with

other previous studies. Assuming that at least some chess

abilities can be transferred from chess to the mathematical

problem-solving domain, our hypothesis is that the chess-

trained children group will show a significantly higher

improvement in mathematical problem-solving skills com-

pared with children who did not receive any chess training,

and among the subjects who received chess training, those

who used the CAT more will show a higher improvement.

Material and Method

Participants

The study was conducted on a total of 31 classes (third,

fourth, and fifth grades) from 8 different schools of Northern

Italy. The classes were randomly assigned to two groups,

including 17 classes in the experimental group and 14 in the

control group.

The experimental group included 5 fifth-grade classes, 10

fourth-grade classes, and 2 third-grade classes for a total of

309 students (169 males and 140 females). One hundred

ninety-three children included in this group declared to be

able to play chess before the beginning of the study. The con-

trol group included 6 fifth-grade classes, 3 fourth-grade

classes, and 5 third-grade classes for a total of 251 partici-

pants (116 males and 135 females). Seventy-two children in

this group declared to be able to play chess before the study.

Study Design

Students in the experimental group received a mandatory

chess course based on the SAM (Scacchi e Apprendimento

della Matematica; Chess and Maths Learning) protocol

(design by the Italian Chess Federation instructors Alessandro

Dominici, Giuliano d’Eredità, Marcello Perrone, Alexander

Wild; for further information, see www.europechesspromo-

tion.org). In addition, each pupil in the experimental group

was provided with a free software, named CAT (see

Trinchero, 2012a, for further details), for learning the game

of chess every time he or she wanted. The use of CAT was

not mandatory, yet highly recommended. The pupils of the

experimental group were given the opportunity to play CAT

at home. Two variables were recorded by CAT: time of utili-

zation and level achieved.

On the contrary, students in the control group performed

only the normal school activities without any chess-related

activity. The chess courses lasted between 10 and 15 hr (1 or

2 hr per week, according to the schedule and the availability

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Sala et al. 3

of the schools involved), and were conducted by three Italian

Chess Federation teachers. The teaching program and the

methodology were exactly the same for each course. Courses

were aimed at teaching the basic rules and tactics of the game

(material value, checkmate patterns, basic endgames).

All students (both in the experimental and in the control

groups) were tested before and after the intervention using

the seven Organisation for Economic Co-Operation

and Development–Programme for International Student

Assessment (OECD-PISA) items (Organisation for

Economic Co-Operation and Development, 2009), a vali-

dated instrument to assess mathematical problem-solving

abilities with several degrees of difficulty (see Table 1), and

a 12-items questionnaire to assess chess abilities (Trinchero,

2013; see Table 2). Time between the pre- and post-test eval-

uation was 3 months.

The design of the study is summarized in Table 3.

The main limitation is the lack of a placebo group, that is,

a group whose participants undergo alternative intervention.

The two-groups design does not allow to understand whether

the potential improvement in math performance was due to

chess-specific or chess-unspecific factors. It is possible that

other non-specific ludic activities, demanding attention and

slow thinking, can increase mathematical problem-solving

abilities as well. The second limitation is that the number of

pupils declaring to be able to play chess is significantly

greater in the experimental group than the control one. It is

advisable, for future studies, to select participants from not-

chess-players samples, or to match the numbers of players

between groups to better control this variable. The third limita-

tion is that chess lessons were administered by three different

instructors. This was necessary for organizational needs, but

we tried to control it asking the three instructors to follow the

same didactic protocol throughout all the chess courses.

Finally, the classes were randomly assigned to the two

groups, but the single student were not (that is, every student

remained in his/her regular school class). Nevertheless, it

must be noticed that organizing a well-designed experimen-

tal research in educative contexts is difficult, and randomiz-

ing students without their classes is often a non-acceptable

practice in schools due to organizational reasons.

Results

Data were analyzed using a series of t tests, mixed linear

models, and correlation analyses.

The two groups were equal in terms of mean age: M(e) = 8.99

years (SD = 0.90 years), M(c) = 9.05 (SD = 1.12 years),

t(558) = −0.76, p = .45, and pre-intervention mathematical

Table 1. The Seven Mathematical Problem-Solving Items of the Seven OECD-PISA Items.

Math abilities involved

Estimated difficulty

(from OECD-PISA) Score Analogy with chess ability

Calculate the number of points on the opposite face

of showed dice

478 (Level 2) 0/1 Calculate material advantage

Extrapolate a rule from given patterns and complete

the sequence

484 (Level 3) 0/1 Extrapolate checkmate rule from chess situation

Calculate the number of possible combination for

pizza ingredients

559 (Level 4) 0/1 Explore the possible combination of moves to

checkmate

Calculate the minimum price of the self-assembled

skate-board

496 (Level 3) 0/1 Calculate material advantage

Recognize the shape of the track on the basis of the

speed graph of a racing car

655 (Level 5) 0/1 Infer fact from a rule (e.g., possible moves to

checkmate)

Establish the profundity of a lake integrating the

information derived from the text and from the

graphics

478 (Level 2) 0/1 Find relevant information on a chessboard

Estimate the perimeter of fence shapes, finding

analogies in geometric figures

687 (Level 6) 0/1 Find analogies in chessboard situations

Note. OECD-PISA = Organisation for Economic Co-Operation and Development–Programme for International Student Assessment.

Table 2. The Twelve Chess Items Used to Evaluate Chess

Knowledge.

Chess ability Score

Explain checkmate situation 0/1

Identify checkmate situation −3/+2

Establish if a move is allowed for a piece −2/+2

Identify castling situation 0/1

Calculate material advantage 0/1

Identify common elements in three chess

situations

−3/+3

Identify pawn promotion 0/1

Identify the possibility of insufficient material 0/1

Identify checkmate situation 0/1

Identify checkmate-in-one-turn situation 0/1

Reconstruct sequence of chessboard events 0/1

Identify common elements in three chess

situations

−3/+3

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4 SAGE Open

problem-solving scores, M(e) = 1.65, SD = 1.15;

M(c) = 1.71, SD = 1.12, t(558) = −0.60, p = .55. Post-

intervention mathematical problem-solving scores were

M(e) = 2.08, SD = 1.34; M(c) = 1.76, SD = 1.24.

Because the participants were from eight different

schools, a mixed linear model was performed, to rule out the

potential role of school of provenance (as participant vari-

able) in determining math post-test results (dependent vari-

able). The model showed a significant effect of group, fixed

factor, F(1, 45.670) = 7.179, p = .01; and a significant effect

of math pre-test scores, fixed covariate, F(1, 550.297) =

109.080, p < .001; but no significant effect of age, fixed

covariate, F(1, 184.246) = 2.809, p = .10; and no significant

effect of school of provenance, var(u0j) = 0.035, p = .32,

either. Figure 1 summarizes math pre- and post-intervention

scores in the two groups.

Regarding the chess performance, pre-intervention

chess scores were significantly higher in the experimen-

tal group than in the control group, M(e) = 3.34,

SD = 4.08; M(c) = 1.34, SD = 2.99; t(558) = 6.49, d =

0.56, p < .001. A mixed linear model was performed, to

rule out the potential role of school of provenance (as

participant variable) in determining chess post-test results

(dependent variable). The model showed a significant

effect of group (fixed factor), F(1, 125.917) = 309.433,

p < .001, and a significant effect of chess pre-test scores

(fixed covariate), F(1, 507.482) = 251.567, p < .001; but

no significant effect of age (fixed covariate), F(1,

342.990) = 0.306, p = .58, and no significant effect of

school of provenance, var(u0j) = 0.523, p = .17, either.

Figure 2 summarizes chess pre- and post-intervention

scores in the two groups.

Post-intervention chess scores and math performance in

the experimental group were significantly correlated (r = .29;

p < .001; N = 309).

Experimental group participants’ use of CAT was quite

heterogeneous: M = 3.24 hr (SD = 4.29), M = 6.00 levels

achieved (SD = 4.94). Post-intervention math scores and the

CAT level achieved by students in the experimental group

were significantly correlated too (rs = .22; p < .001; N = 309);

however, post-intervention math scores and CAT time of use

were not correlated (p = .29).

Table 3. Description of the Experimental Design.

Groups nActivities

Experimental 309 Pre-test Blended chess training (10/15 hr of chess course and non-mandatory

CAT activities; 3 months)

Post-test

T(0) T(1)

Control 251 Pre-test Regular school activities (not chess-related activities; 3 months) Post-test

T(0) T(1)

Note. CAT = computer-assisted training.

Figure 1. Math scores in the two groups of pupils measured before and after the intervention.

Note. The experimental group performance in the post-test was significantly higher than in the pre-test, whereas the control group did not show any

improvement.

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Sala et al. 5

Discussion

The hypothesis of the study, according to which the mathe-

matical problem-solving scores gain in the experimental

group would be significantly higher than the one in the con-

trol group, is confirmed. Moreover, we found that both the

chess scores and the CAT level achieved by the students in

the experimental group were significantly correlated with the

mathematical problem-solving scores. Because part of proto-

col was not mandatory, that is, CAT activities at home, it is

possible that those who played CAT more (in terms of time)

were more motivated by chess, and hence the better mathe-

matical scores. However, only the level achieved by the

pupils proved to be correlated to math post-test scores,

whereas time of utilization did not. If we assume that the

time spent playing CAT was, to a certain extent, a measure of

the participants’ motivation toward chess, then this seems to

suggest that motivation was not a crucial factor of math

results. On the contrary, chess ability, assessed by chess

score and CAT level achieved, proved to be more reliable at

predicting math scores. In summary, these results show that

a blended strategy of intervention (in-presence chess lessons

followed by home training) can be effective both to teach

chess and to enhance mathematical abilities. These outcomes

are impressive considering that, compared with the previous

studies based on 25/30 hr of chess lessons, our intervention

consisted only in 10/15 hr of in-presence chess teaching

activities.

Given these results, how can the education and practice of

chess affect the logical–mathematical abilities of the young

pupils? To answer this question, we can hypothesize that the

intrinsic feature of the game can be the cause of the phenom-

enon to be explained. Chess is based on some mathematical

elements as the values and the geometrical movements of the

pieces. According to Scholz et al. (2008), the practice of the

game can convey some notions of the mathematical domain

as the concept of numerosity. Throughout a chess game, a

chess player is requested to pay attention to the material

advantage (or disadvantage) because, together with the two

Kings safety, it is the most important aspect of the game.

Material advantages are calculated by summarizing all the

white and black pieces’ values (every piece has a specific

value, depending on how it moves); the comparison between

these two sums gives the players the basic criterion for the

evaluation of the chess position:

This conception fits well in the context of positive conditions for

transfer [“Low road transfer happens when stimulus conditions

in the transfer context are sufficiently similar to those in a prior

context of learning to trigger well-developed semi-automatic

responses.” (Scholz et al., 2008, p. 139)] described by Perkins

and Salomon (Perkins & Salomon, 1994), since the strength of

the chess pieces can be used as a metaphor for numbers. (Scholz

et al., 2008, p. 146; emphasis added)

In other words, chess could have the power to “material-

ize” some mathematical abstract concepts so that children

can learn and manage them much more easily. In Kazemi

et al. (2012), a similar explanation is given:

When students experience the subtlety and sophistication of

chess play, upon encountering complex and subtle matters, they

often associate or link these two elements and discover the logic

and subtlety of mathematics. In reality, this complexity may take

tangible or real forms for students (p. 378).

This is also consistent with the concept of embodiment of

mathematical elements described in Lakoff and Núñez

(2000).

Figure 2. Results of the two groups in chess ability.

Note. Only the experimental group improvement was statistically significant.

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6 SAGE Open

Furthermore, chess, by its nature, is a game that forces

players to use skills that go beyond the simple calculation of

variations, or mere mnemonic exercises: Playing chess is an

exercise of competence. A chess player must monitor his

own strategies and, therefore, his own thoughts, focus on

detail, and use abstraction and generalization, even at ama-

teur level. The positions appearing on the chessboard during

the game are problems to be solved by choosing a move or a

combination of moves. In addition, the absence of the alea-

tory element forcefully leads players to attribute the cause of

their success (or failure) to the quantity and quality of their

effort and their own strategic choices, promoting the empow-

erment process. In other words, a chess player becomes

aware of his own self-effectiveness. According to Trinchero,

children’s attentive skills could be enhanced by the practice

of the game of chess, and this fact could explain the improve-

ments in mathematical problem-solving abilities related to

game practice: “this difference may be due to the increased

capacity of the pupils of reading and interpret correctly the

mathematic problems, apply their mathematic knowledge

and reflect on their own actions and strategies, as effect of

chess training” (Trinchero, 2013).

We can summarize the above concepts by saying that

chess increases mathematical problem-solving skills because

(a) math and chess are isomorphic domains; by playing

chess, math concepts are made less abstract and thus more

manageable; (b) a chess player must use high skills as plan-

ning, abstract thought, calculation of variants, monitoring of

strategies, and thoughts that are necessary in mathematical

skills; (c) a chess player perceives the victories and defeats

as a result of his choices on the board, the correctness of

which is proportional to the practice and the efforts of the

player himself; this is supposed to increase the empower-

ment of the player and, consequently, the confidence in his

own abilities; (d) the chess player becomes aware of the

necessity of enduring attention, addressed to both the simple

elements of the game and to the dialectical relationship

between elements; attention that is already potentially pres-

ent in the participant, but that the actual environment and

habits tend to reduce; (e) chess is an amusing and rewarding

activity that encourages children to play more. In other

words, chess gets a “virtuous circle” started, and this circle

can be very useful also to develop good mathematical

abilities.

This explanation is realistic because it can be compatible

with two opposite paradigms about the conditions under

which cognitive transfer happens and, in a vaster perspec-

tive, about the features of human intelligence. Logical skills

(and intelligence) can be considered context-dependent or

context-independent. In the first case, the problem-solving

ability is strictly linked to the domain of application; thus, a

participant can show problem-solving skills as good in a

field of knowledge and as bad in another one. In the second

case, logical skills are universal and disconnected from the

context of application. According to the latter perspective,

the human intelligence is the sum of several basic abilities

through which higher competences, such as problem-

solving, arise. The issue is still debated.

As we previously said, the assumption subtending our

hypothesis is that some abilities can be transferred from

chess to the mathematical domain. Transfer can occur when

there is a certain degree of overlap between the two domains,

and the extent of the transfer itself is limited to that degree

(Thorndike & Woodworth, 1901). Thus, the more specific

knowledge becomes, the more difficult transfer of skills can

arise (Ericsson & Charness, 1994), and the ability in a cer-

tain task depends on the context of application. In these

terms, it is unlikely that chess can be useful to teach

mathematics.

Nevertheless, several authors think that the transfer is

possible because of the general nature of the cognitive pro-

cesses: a fluid intelligence (Jaeggi, Buschkuehl, Jonides, &

Perrig, 2008; Sternberg, 2008) that can be trained. If chess

training can boost some basic abilities easily generalizable to

mathematics domain (because of the similarity between the

two domains), then it is possible that chess improves a higher

competence such as mathematical problem solving. In other

words, the problem of the transfer is played on a trade-off

between generality skill and a sufficient isomorphism

(Atherton, 2007) between the nature of the domain in which

the pupil exercises the skill and the new domain into which

the skill can be transferred; a trade-off between universality

and specificity (Sala, 2013). Thus, the two perspectives

should not be considered irreconcilable. The question is, in

what ratio is a certain competence based itself on general

cognitive abilities and in what ratio on a domain of applica-

tion? Regarding chess, the data, currently, do not allow to

infer the answer.

It is possible to suppose that chess is a sort of medium

through which some cognitive abilities are boosted. A theo-

retical framework for this hypothesis could be the concep-

tion of intelligence described by Feuerstein, Feuerstein,

Falik, and Rand (2006). According to this perspective, intel-

ligence is a repertoire of universal cognitive functions, able

to operate on every content. Some of these functions such as

the “precision and accuracy in the data collection,” the “abil-

ity to understand the existence of a problem,” the “ability to

distinguish relevant from non-relevant data,” the “need of

logical proves,” and the “planning behavior” are necessarily

needed during a chess game. For example, a chess player

searching for a checkmate combination has to realize that the

position on the chessboard offers that opportunity, has to col-

lect the data very carefully (a single piece or square not con-

sidered and the combination could fail), has to select the

relevant data (not necessarily all the pieces are involved), has

to plan the combination considering the foe’s defense

chances, and needs to prove the cogency of his inference. All

these functions contribute to solving the chess problem and,

in a more general sense, are undoubtedly involved in every

field of problem-solving application.

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Sala et al. 7

If the assumption of a repertoire of universal cognitive

functions, context-independent and thus applicable to sev-

eral domains, is accepted, then it is necessary to ask for the

reason why chess is one of the ideal mediums. The afore-

mentioned features of the game (aleatory component null,

need of heuristic thought, similarities with mathematics

domain) are essential, but it must be considered that chess is

a content itself. According to Feuerstein et al. (2006), a cog-

nitive function has to be trained with a specific content,

selected for its intrinsic features. The content must not be so

unfamiliar to invest a great effort that would take precious

cognitive resources and would not allow the pupil to concen-

trate on the function to strengthen. However, the content

must not be too familiar either, because it would not be able

to induce a state of attention in the pupil; so he would not

mobilize his cognitive resources because of the lack of intrin-

sic motivation. Chess could be an ideal medium because it is

familiar enough: It is a board game, quite known, and based

on quantity, calculation, and planning, which are concepts

already experienced by children in school; however, chess is

a game compelling and new for most of the children involved

in a chess course, so it is simple to induce passion for it.

Furthermore, it is important to underline not only the

intrinsic features of the game of chess but also the method

through which chess is taught. If it is assumed that a chess

course is a tool to boost problem solving or similar abilities,

then a chess teacher is supposed to propose activities selected

on purpose. In this sense, it is important to note that, although

in the present study, the number of pupils declaring to be able

to play chess in the pre-test is higher in the experimental

group (193) than in the control group (72), and, consequently,

chess scores are higher in the experimental group pre-test,

the mathematical problem-solving scores of the experimen-

tal group are not significantly different. This fact can be

explained by saying that the mere knowledge of chess basic

rules (as the movement of the pieces) is by far insufficient to

train cognitive skill. It is hard to see why knowing that the

Rook can move vertically and horizontally, for example,

should improve children problem-solving skills, or any other

intellectual skill. On the contrary, knowing how to find the

shortest path from one square to another one for the Rook, or

knowing whether it is worth to give up a Rock for a Queen,

is a more demanding task for the intellectual skills of the

pupil. A pupil playing a chess game moving the pieces cor-

rectly (that is, according to the rules), but without any plan or

calculation, does not use any problem-solving ability.

On the contrary, it is reasonable to assume that a pupil

playing a chess game moving the pieces according to a strat-

egy (albeit ingenuous or shallow for an expert chess player)

and paying attention to the dynamic relationships between

the pieces is training his or her problem-solving ability.

Further studies are needed also to deepen our knowledge

about the effect of chess training on cognitive abilities. We

can consider three main lines of research: (a) the study of the

cognitive processes subtending the outer phenomenon, that

is, the amelioration in mathematical problem-solving com-

petence; (b) the long-term effects of chess training on math-

ematical abilities; and (c) the comparison between chess and

other mathematical games.

The first line refers to the already discussed issues: If it is

possible to state that a chess course, with a proper didactic

program and methodology, improves children mathematical

problem-solving abilities, it is not yet possible to say exactly

why this happens. Which are the cognitive skills strength-

ened by chess? Just a few experimental studies directly

assessed the increments of some cognitive abilities after a

chess intervention. In the study of Scholz et al. (2008), the

experimental group did not improve in the concentration

abilities, suggesting that the amelioration of the experimental

group calculation scores was not due to the increase of the

concentration of the participants. However, it must be con-

sidered that the participants of that study were children with

IQ (70-85) lower than the average of the population, so that

sample could not be representative for the general popula-

tion. In the study of Kazemi et al. (2012), the participants

were tested, after a 6-month chess course, to assess their

meta-cognitive abilities, along with their problem-solving

skills: The researchers found a significant advantage for the

experimental group (who received the chess course) both in

the meta-cognition scores and in problem-solving scores.

This fact leads to think that the meta-cognitive abilities

boosted by chess practice can be successfully transferred into

mathematics domain.

The second line of research, suggested by Gobet and

Campitelli (2006), is necessary to assess the endurance of

chess training benefits during the 2 or 3 years. To date, fol-

low-up data related to chess and its educational benefits do

not exist. If these benefits disappeared, for example, 1 year

after the intervention, then chess would not be an educational

useful tool. If the transfer is possible only when there is an

overlap between the two domains, then an activity getting

more and more specific, at a certain point, becomes ineffec-

tive, because it insists on capacities not shared by the two

domains, and thus not transferable. So, it is likely that the

benefits of the chess training diminish with the second or the

third year of training (following a sort of logarithmic curve)

because of the increasing specificity of the topics. In other

words, it would be important to know when the costs of a

chess course overcome the benefits.

The third line of research could be useful to understand

whether other mathematical games can be used as educa-

tional tools, and to understand which mathematical skills are

enhanced by chess and by other games. Ferreira, Palhares,

and Silva (2012) tested the correlation between the skills of

children in some games (such as Dots and Boxes, Wari and

Traffic Lights) and several mathematical factors (such as

numeric and geometric progression, counting, rotation) find-

ing that every game has specific correlation with one precise

factor. The study, although interesting, is correlational, so it

is impossible to infer that those games can boost some

by guest on March 10, 2016Downloaded from

8 SAGE Open

mathematical abilities. Gobet (personal communication)

suggests that some aspects of the school curriculum might be

better illustrated by other games, such as Awele, Go, and

Bridge. Not enough has been done to infer anything certain.

In conclusion, although many aspects of the potential

benefits of chess practice in children are still unknown, we

can state that the game of chess is a powerful tool to build

children’s problem-solving competence in the mathematical

domain, even with brief courses, such the one we propose to

our pupils.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect

to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research and/or

authorship of this article.

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Author Biographies

Giovanni Sala, PhD student at the Institute of Psychology, Health

and Society (University of Liverpool). His main research interests

are Memory, Learning and Transfer of skills in primary school

children.

Alessandra Gorini, PhD, researcher at the European Institute of

Oncology in Milan. Her main research interests are Medical deci-

sion making and Patient empowerment.

Gabriella Pravettoni, PhD, full professor of Cognitive Psychology

at the University of Milan. She is also director of the Interdisciplinary

Research Center on Decision Making Processes (IRIDe).

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