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Developing Mathematical Thinking with Scratch
An Experiment with 6th Grade Students
Luis Alberto Calao1, J. Moreno-Le´on2, Heidy Ester Correa1, and Gregorio
Robles3
1Instituci´on Educativa Candelaria Hacienda de Lorica, Colombia
inge484@yahoo.es
2Programamos.es, Sevilla, Spain
jesus.moreno@programamos.es
3Universidad Rey Juan Carlos, Madrid, Spain
grex@gsyc.urjc.es
Abstract. One of the latest trends in the educational landscape is the
introduction of computer programming in the K-12 classroom to de-
velop computational thinking in students. As computational thinking is
not a skill exclusively related to computer science, it is assumed – but
not yet scientifically proven – that the problem solving process may be
generalized and transferred to a wide variety of problems. This paper
presents a research designed to test whether the use of coding in Maths
classes could have a positive impact on learning outcomes of students in
their mathematical skills. Therefore, the questions we want to investigate
in this paper are if the use of programming in Maths classes improves
(a) modeling process and reality phenomena, (b) reasoning, (c) problem
formulation and problem solving, and (d) comparison and execution of
procedures and algorithms. We have therefore designed a quantitative,
quasi-experimental experiment with 42 participating 6th grade (11 and
12 years old) students. Results show that there is a statistically signif-
icant increase in the understanding of mathematical processes in the
experimental group, which received training in Scratch.
Keywords: computational thinking, maths, learning, coding, Scratch
Disclaimer
This document is a draft. The published paper can be accessed at
http://link.springer.com/chapter/10.1007/978-3-319-24258-3 2
Reference:
Calao, L. A., Moreno-Le´on, J., Correa, H. E., & Robles, G. (2015). Develop-
ing Mathematical Thinking with Scratch. Design for Teaching and Learning in
a Networked World (pp. 17-27). Springer International Publishing.
1 Introduction
One of the latest trends in the educational landscape is the introduction of
computer programming in the K-12 classroom to develop computational think-
ing (CT) in students, a skill defined by Jeannette Wing as one that “involves
solving problems, designing systems, and understanding human behaviour, by
drawing on the concepts fundamental to computer science” [22]. Although CT is
not a skill exclusively related to computer science [4,20], research shows that pro-
gramming is a very good mechanism for the development of this competence [12].
Thus, governments around the world are making computer programming part of
their national curriculum. For instance, nine countries in Europe have already
included coding into their schools: Bulgaria, Cyprus, Denmark, Estonia, Greece,
Ireland, Poland, Portugal and the UK (England) [19].
One of the pillars of CT is, according to the operational definition developed
by the Computer Science Teachers Association and the International Society for
Technology in Education [3], “generalizing and transferring this problem solving
process to a wide variety of problems”. Hence, the general research question
of this paper is how far CT affects other school subjects. In particular, this
study was designed to test whether the use of coding in math classes could
have a positive impact on learning outcomes of students in relation to their
mathematical skills. Therefore, the specific questions we want to give an answer
to in this research paper are following:
1. Modeling: Does the use of programming in math classes improve the model-
ing of processes and reality phenomena?
2. Reasoning: Does the use of programming in math classes improve reasoning?
3. Problem solving: Does the use of programming in math classes improve prob-
lem formulation and problem solving?
4. Exercising: Does the use of programming in math classes improve the com-
parison and execution of procedures and algorithms?
The structure of this paper is as follows: A brief overview of the mathemat-
ical skills of Colombian students is presented, and some research studies that
have investigated relationships between coding with Scratch, the programming
learning environment used in this experiment, in schools and learning are out-
lined in section 2. Then, in section 3 our work methodology is briefly described.
Section 4 presents the results we have obtained from applying our methodology
on a small group of Colombian students in the mathematics class. Finally, sec-
tion 5 contains the conclusions of our research, and some ideas and suggestions
for future work are discussed.
2 Background
2.1 Colombian Students and Maths
The results in international tests show that there is still much room for improve-
ment regarding the mathematical skills of Colombian students. In PISA 2012 [13]
(Programme for International Student Assessment), which assessed the compe-
tencies of 15 year old students in reading, mathematics and science (with a focus
on mathematics) in 65 countries and economies, Colombian students scored 376
points in mathematics on average, compared to an average of 494 points in
OECD (Organisation for Economic Co-operation and Development) countries.
Therefore, Colombia ranked 61st in mathematical competencies.
According to OECD report Does math make you anxious? [14], mathematics
can “provoke worry, stress and even feelings of powerlessness in some students,
and this anxiety towards mathematics is shown to be strongly related to math-
ematics performance.” In order to measure that anxiety, PISA 2012 included
questions regarding how students feel when they anticipate having to perform
mathematical tasks, when they anticipate their performance in mathematics
class, and while they are attempting to solve mathematics problems. The re-
sponses revealed that countries where students report higher levels of anxiety
were also those where students perform poorer in mathematics. Thus, Colom-
bia was one of the countries with higher levels of anxiety towards maths by
students [13].
2.2 Code to Learn with Scratch
The educational use of programming is not new. Back in the 1960s Seymour Pa-
pert developed the Logo programming language aiming to allow children to use
computers to create games, composing music or painting recursive drawings [15].
However, after a few years of success, programming disappeared from the K12
educational landscape because of the problems that students and teachers faced
trying to learn the language syntax, among other reasons [16].
Nevertheless, in the last years new visual programming languages, such as
Alice, Kodu and especially Scratch [18], have reawakened the interest of the
educational community in coding, not as an end in itself, but as a tool to develop
other skills and to improve learning outcomes and motivation in students, as
Mitchel Resnick, creator of Scratch, argues in Learn to code, code to learn [17].
Regarding the usefulness of programming with Scratch as a tool to improve
student learning, there is research literature that has a very promising outlook,
as coding has been successfully utilized in subjects like mathematics, science,
arts, writing or English as a second language, among others. Focusing on math-
ematics, Lewis and Shah [11] detect correlation between programming quizzes
and math tests grades, Ke [8] explains that students showed significantly more
positive attitude towards this discipline after the study, while Zavala, Gallardo
and Garc´ıa-Ruiz [23] observe improvements in the identification and comparison
of numbers, although no gain in relation to the spatial location was detected.
However, most of the studies reviewed did not follow basic recommendations to
develop research in education [2], and therefore, there is a need to carry out
empirical studies using control groups and providing quantitative data to prove
the potential of computer programming with Scratch as an educational tool to
improve academic outcomes.
Furthermore, there are research studies that analyze the development of prob-
lem solving skills while learning to program with Scratch. Most of the articles
reviewed confirm that students developed their problem solving skills after the
investigation [1,21,9,5,10], while no significant differences were detected in one
of the studies [6].
3 Methodology
3.1 Design
This research is a quantitative, quasi-experimental study, which includes a pre-
post test design with both experimental and control groups. In this type of
research, according to Hernandez, Fernandez and Baptista [7], an independent
variable is deliberately manipulated in order to observe its effect and relation to
one or more dependent variables through measurements of the subjects before
and after treatment application.
3.2 Population
The population that was part of this experiment is composed 42 students of 6th
grade of the Candelaria Hacienda school located in the municipality of Lorica,
Department of C´ordoba of Colombia. This institution is an official primary and
secondary school. The sample is intentional and not probabilistic, and it is com-
prised of 24 students from 6th-1 group, taken as experimental group, and 18
students from 6th-2 group, as control group.
3.3 Data Collection
As an instrument for collecting data, a rubric was elaborated to evaluate students
performance and skills in the mathematical processes involved in this investiga-
tion: modeling, formulation and problem solving, reasoning and exercising. This
rubric was prepared taking into account the conceptual approaches set by the
Ministry of National Education of Colombia in relation to the guidelines and
basic competence standards in mathematics.
The rubric consists of a set of criteria that evaluates the development of the
student in each of the four skills studied in this research. Depending on this
criteria, the students gets an evaluation that may be excellent,good,satisfactory
and deficient.
For instance, students with an excellent performance level in each skill should
be able to:
–Modeling: The student properly solves all the problems related to the mod-
eling process, in which the detection of variables and relationships among
them that establish a mathematical model is required, as well as detecting
patterns that are repeated in daily, scientific and mathematical situations,
and reconstruct them mentally.
–Reasoning: The student properly uses the reasoning process to resolve all
situation problems it faces, sensing regularities and relationships, making
predictions and guesses, or justifying arguments and reasoning.
–Problem solving: The student easily solves problems in situations which re-
quire deployment strategies to interpret the statements given, to find results
and to verify these results.
–Exercising: The student runs easily algorithmic procedures, realizing the
concepts on which they rest and recognizing when you can apply a given
technical or mathematical operation.
For the application of the rubric two standard test questionnaires were elab-
orated, one for the pre-test and one for the post-test, which were simultane-
ously applied to both the control group and the experimental group. Each ques-
tionnaire consisted of 16 questions equally distributed among the four skills to
evaluate. A copy, both in Spanish and in English, of the rubric and the two
questionnaires can be obtained from the replication package of this paper4.
3.4 Areas of Intervention
The initial stage of the experimental intervention, the experimental group begins
with several informal activities on sequences of processes, and then an introduc-
tion to the concepts of algorithm and programming is given. In a second stage,
students begin to learn to use the Scratch graphical programming environment,
conducting educational activities. These activities are initially aimed at basic in-
teractions with the program and then focused on the use of animated dialogues.
In a third stage the use of loops, conditionals and variables is trained. Finally,
in a fourth stage, the students test their creativity by programming their own
games and simulations making use of images, sounds and movements.
The intervention on the experimental group took place along 3 months. Mean-
while the control group continued the classes using the same kind of methodology
and activities they had been using up until that moment.
3.5 Data Analysis
For the data collection, as mentioned earlier, both a pre-test, developed before
the intervention, and a post-test, performed after the intervention, were applied
to both the control and experimental groups. In each of these tests, a rubric
prepared from the conceptual definition of each of the mathematical processes
that students are expected to develop in sixth grade of primary education in
Colombia are used.
In addition of the the overall average of the processes evaluated, the results of
the tests offer information regarding the four mathematical processes assessed in
this research. A t-test analysis for independent samples is performed comparing
the results of the means obtained by the experimental group and the control
group in the pre-test and post-test. Similarly, a t-test for related samples is
applied to compare the control and experimental groups separately.
4http://gsyc.urjc.es/~grex/repro/2015-ectel
4 Findings
Figure 1 shows the mean and standard deviation of the tests by the control and
experimental groups before the intervention. As shown in the figure, the results
of the pre-tests are very similar in both groups, which is congruent with the fact
that the groups are formed by students of similar characteristics.
Fig. 1. Pre-test. Mean and deviation for control (left) and experimental (right) groups.
Figure 2 shows the mean and standard deviation of the tests by the control
and experimental groups after the intervention. As shown in the figures, there is
a remarkable difference in the results of the post-tests, as the mean of the results
of the experimental group is 41.56 points above the one of the control group.
Fig. 2. Post-test. Mean and deviation for control (left) and experimental (right) groups.
Figure 3 offers a comparison of the results obtained for each of the four skills
under study for the control and experimental groups.
If the results of each mathematical process before the intervention are com-
pared, we can see that both the mean and the standard deviation are uniform,
presenting small differences in the modeling, reasoning and exercising, and only
showing a difference of more than 10 points in terms of problem solving where
Fig. 3. Comparison. Means obtained for the control (upper) and experimental (lower)
groups by mathematical process. Modelac stands for modeling,Razonam for reasoning,
Resoluc for problem solving,Ejercit for exercising and Promedio for average.
the experimental group shows a significant better performance than the control
group.
If the results of each mathematical process after the intervention are com-
pared, we can see that there is a significant difference in all the processes in
favour to the experimental group. Especially noteworthy are the results of the
exercising process, with a difference of over 68 points.
While no significant differences are observed in the results of the control
group, a uniform gain is shown in the results of the experimental group, where
the grades are significantly better in the post-test for all processes, and there is
an average increase more than 33.5 points.
It is remarkable that the control group has obtained a lower mean value in the
post-test than in the pre-test. While the difference is not significant, it however
means that students have not progressed in these skills in the three months of
the study. As this students have been attending their regular math classes as
usual, this result may hint that (at least some parts of) the math curriculum in
schools does not help in developing those skills.
The questions that have been included in the pre and post-test question-
naires are closely connected to the use of mathematics in real-life scenarios, and
can be considered as applying mathematics to usual situations. From our re-
sults, it seems that math learning at schools is more focused on the internals
of mathematics, rather than on acquiring skills to use math-based knowledge.
For this type of skill development, our experiment has shown that the use of
programming is of great value with a significant increase of the results obtained
by learners.
If we look more in detail at the four skills under study, we see that modeling
and reasoning are those skills that are more developed with the traditional way
of learning math. However with problem solving and especially with exercising
there is much room for improvement. From our experiment we have observed that
the exercising skill in students is particularly increased with the introduction of
programming. The mean value for this skill for the experimental group is even
the highest among all skills. This finding shows that introducing programming
offers students more insight in the comparison and execution of algorithms and
procedures than in traditional classes, which sounds meaningful as the nature of
programming is very related to those activities. In the case of problem solving,
although the gain in the experimental group is significantly higher then the one
for the control group, our results show that the growth is moderate. Further
research should be devoted to find out how to further improve this skill, and if
programming can be helpful in achieving this goal.
A t-test was performed to measure the average level of mathematical pro-
cesses in the control and experimental groups in order to assess whether the
results are similar or if they have significant differences. The null hypothesis
states that there are no significant differences in the sample means.
First, data in Table 1 show that there are no significant differences in the
results means of the control group and the experimental group in the pre-test,
as the p-value (0.195) is greater than 0.05. However, there are statistically sig-
nificant differences in the results of both groups in the post-test, as the p-value
(>0.001) is less than 0.05.
Second, we have applied the t-test to the related samples to study the dif-
ferences between the pre-test and post-test. Table 2 shows that no statistically
significant changes are observed in the control group between the pre-test and
post-test test, as the p-value (0.489) is grater than 0.05. However in the exper-
imental group there were significant differences between the pre-test post-test,
as the p-value (>0.001) is less than 0.05.
5 Conclusions and Further Research
The goal of this research was to analyze the effect of the development of com-
putational thinking through the use of the Scratch visual programming environ-
ment in the development of mathematical skills in sixth graders of elementary
Table 1. T-test of independent samples in the pre-test and post-test
Levene test T-test for equal mean
F Sig. t Sig. (bilat) Diff. means Typ. error 95% conf. interval
Inferior Superior
Pre-test Equal var.
assumed
0.052 0.821 -1.319 0.195 -6.406 4.857 -16.223 3.410
Equal var.
not as.
-1.308 0.199 -6.406 4.898 -16.343 3.531
Post-test Equal var.
assumed
3.155 .084 -9.246 >0.001 -41.563 4.495 -50.663 -32.462
Equal var.
not as.
-8.893 >0.001 -41.563 4.674 -51.125 -32.000
Table 2. Test of related samples. Control and experimental groups.
Related differences
t gl Sig (bilateral)
Mean SD Typical error 95% confidence interval
Inferior Superior
Control group 1.875 11.250 2.652 -3.719 7.469 0.707 17 0.489
Exp. group -33.750 14.315 3.0519 -40.097 -27.403 -11.05 21 >0.001
education, for which a comparison was made between two groups of similar char-
acteristics of the same grade, designating one as control group and the other as
experimental group. The latter was the one who received intervention, which
consisted in Scratch programming training for three months. Statistical tests
were applied to both control and experimental groups before and after the in-
tervention.
The results show that there is a statistically significant gain in the under-
standing of mathematical knowledge in the experimental group, which received
training in Scratch. This therefore leads to the conclusion that the development
of computational thinking using the Scratch visual programming environment
allows students of primary education to improve their performance in terms of
mathematical processes of modeling, reasoning, problem solving and exercising,
while, in parallel it also facilitates the generation of a motivating learning envi-
ronments.
Among the studied skills, we have found that the exercising skill (i.e., the
comparison and execution of procedures and algorithms) is the one that is less
developed in traditional math classes, but is the one that is especially strength-
ened by programming. Our findings show that modeling and reasoning skills
benefit as well significantly from programming. Finally, the problem solving skill
also increases, but is the one that has more room for improvement. Future re-
search should focus on how programming may enhance the problem solving skill;
some possible solutions could be to address this skill by designing specific pro-
gramming tasks or by introducing specific methodologies to learn programming.
As a future line of research, we note that during the intervention process
we observed that some learners faced some issues in reading and writing when
working with lively dialogues. However, students were highly motivated to im-
prove their skills and overcome the difficulties in order to create good Scratch
projects. This suggests a possible investigation into how the use of the Scratch
visual programming environment can have a positive impact on the development
of reading and writing skills.
At this moment the authors are performing a study with more than 40 teach-
ers from three different countries, Spain, Argentina and Ecuador, involving more
than 500 students. In this investigation educators from different grades are using
computer programming with Scratch to teach several kind of subjects, such as
mathematics, literature, English as a second language or social studies, among
others. Thus, the results of the research may allow us to measure to what extent
the development of computational thinking can have a beneficial impact on the
academic outcomes of learners in different disciplines.
Acknowledgments
The work of Jes´us Moreno-Le´on and Gregorio Robles has been funded in part
under project “eMadrid - Investigaci´on y Desarrollo de tecnolog´ıas para el e-
learning en la Comunidad de Madrid” (S2013/ICE-2715) funded by the Region
of Madrid. The work of Gregorio Robles has been funded in part by the Spanish
Government under project SobreSale (TIN2011- 28110).
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