Mathematical Problem-Solving Abilities and Chess: An Experimental Study on Young Pupils

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.

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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

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

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

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.

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.

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.

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

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).