=Paper=
{{Paper
|id=Vol-2524/paper7
|storemode=property
|title=Scratch to foster pre-service teachers' creativity
|pdfUrl=https://ceur-ws.org/Vol-2524/paper7.pdf
|volume=Vol-2524
|authors=Alicia Sánchez,Miguel Navarro Noguera
|dblpUrl=https://dblp.org/rec/conf/psychobit/Sanchez19
}}
==Scratch to foster pre-service teachers' creativity==
https://ceur-ws.org/Vol-2524/paper7.pdf
Scratch to foster pre-service teachers’ creativity*
Alicia Sánchez 1[0000-0001-6569-6828]
1 University of Barcelona, Passeig de la Vall d’Hebron, 171, 08035 Barcelona, Spain
asanchezb@ub.edu
Abstract. Although creativity is a key component of mathematical activity, the
Mathematics lessons at school are rarely related to creative work. This situation
could be reversed if the teacher training programs included some specific training
in how to enhance students’ creativity, among other factors. The aim of this paper
is to present the redesign of an activity in order to promote pre-service teachers’
creativity. The first design of the activity was implemented in a group of second-
ary school pre-service teachers from a master’s degree in teaching in secondary
school (specialization in Mathematics). The implemented activity was used to
introduce the programming language Scratch, the teacher and the document that
the pre-service teachers had, guided the activity. In the redesign, based on the
seminars of the DoCENT project, some important characteristics are changed to
make it a more open activity and to improve the interactions between the partic-
ipants. These aspects are usually considered as helpful to enhance creativity.
Keywords: Mathematical creativity, Scratch, Secondary school pre-service
teachers.
1 Introduction
The mathematical activity is usually identified as creative [5, 8], despite lessons at
school rarely promote students’ creativity. Several authors [2, 4, 5, 7, 8] highlight the
importance of enhancing students’ creativity since they start school and doing it for all
the students, and not only for those that have good marks. Mathematical creativity at
school level is frequently associated with posing and solving problems, including pro-
cesses such as modelling, generalization, making connections and validation [2, 5, 7].
In accordance to this, the teacher training programs could include some training in how
to promote students’ creativity at school. The aim of this paper is to present the redesign
of an activity implemented with a group of secondary school pre-service teachers, in
order to promote their creativity. By the practice of this type of activity, they could also
think on how to promote their future students’ creativity.
* Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
2
2 Context
Activities presented here were designed for a group of secondary school pre-service
teachers, from a master’s degree in teaching in secondary school (specialization in
Mathematics). This activity is included in the course of Material and LKT resources in
Mathematics education. The course consists of 5 sessions of 4 hours each. Only one
session is completely dedicated to LKT resources. In this session, pre-service teachers
work with Geogebra [3] and Scratch [6]. Only the activities with Scratch are com-
mented in this paper. The master’s degree does not include a specific training in how
to enhance students’ creativity.
3 First design
The main objective of the first design of the practice with Scratch [6] was just to intro-
duce the programming language. In order to do so, two exercises were planned. The
pre-service teachers have a document with the description of the exercises.
3.1 First exercise
The first exercise consisted in guessing what a sequence of blocks will produce, before
executing it. The sequence made the mascot draw a square. All the steps followed by
the mascot were identified with a particular block, no loops were used. First, the pre-
service teachers should predict the result and copy the code to check their answers.
Then, they were suggested to change the code in order to get the mascot oriented in a
different way. After this, they were suggested to use the block Repeat to optimize the
code. The last question was the generalization of the sequence to make it useful to draw
any regular polygon. In this case, no instructions in advance are provided, just the pos-
sibility of using a variable to introduce any data after the mascot’s question.
Fig. 1. Example of some steps in the second exercise
3.2 Second exercise
Thinking on how the pre-service teachers could use Scratch, the objective is to program
an algorithm that secondary school students use frequently. In particular, they design a
3
program that calculates the roots of a quadratic equation given their coefficients (see
Fig. 1). Some tips are provided in the description of the exercise, for example how to
use the variables in Scratch. Also, the pre-service teachers are prompted to think on
which condition is necessary to assure that the equation has real solutions.
4 Implementation
In order to assess the implementation, I will use the didactic suitability criteria of the
Ontosemiotic Approach [1] as a guide. The didactic suitability is divided into six types:
epistemic, cognitive, emotional, interactional, mediational and ecological suitability.
For each suitability criterion, some observable components and characteristics enable
us to assess the implementation of a teaching and learning process in practice. Only
some of the components are commented here.
The activity was implemented in a group of 31 pre-service teachers. The session of
4 hours included the practice with Geogebra [3] and Scratch [6]. The pre-service teach-
ers received a document with all the exercises at the beginning of the session. It was
not necessary that they did all the exercises, they could choose those that they found
more interesting. If they had some experience with the programs, they could do the
exercises on their own; otherwise, the teacher selected some exercises to do all together,
guiding the resolution. They did not have to present any evidence of their work at the
end of the session. In addition, they worked individually, each one used their own com-
puter, although they could talk to other classmates or ask questions.
4.1 Epistemic suitability: Mathematical processes
There are some mathematical processes that could be remarked in this activity. In the
first exercise, the pre-service teachers have to identify some elements that combine the
use of non-specific and specific mathematical vocabulary. For example, the turns (to
draw the square) are expressed in degrees. Then, they automatize part of the code. Fi-
nally, they make a generalization of the whole process. In the second exercise, they
have to construct the algorithm of the quadratic formula and then transcribe it using the
Scratch language. In this case, the mathematical model is predetermined.
4.2 Mediational suitability: Time and material resources
The pre-service teachers were especially interested in Geogebra [3] because the teach-
ers in the master’s degree usually talk about it, although most of the pre-service teachers
had not used it much. In addition, some days after, some of them were participating in
an event of the Catalan Association of Geogebra, so they wanted to know the basics of
the program before attending the event. This made that most of the session was dedi-
cated to Geogebra and it only remained one hour for the Scratch practice. Some pre-
service teachers were working on their own, instead of following all the exercises that
the teacher presented. They could have started with the Scratch exercises before, but
they did not. Regarding the resources, the computer lab was not available, so the pre-
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service teachers had to bring their own computers. Since they had different versions of
Geogebra, they could not work with it as fluently as they wanted. Nevertheless, they
did not have this problem with Scratch because they used the online version [6].
4.3 Interactional suitability: Students’ interactions and the teacher
Most of the pre-service teachers participated actively in the class discussion. In this
session, when they had some problems with the programs, they asked the teacher or
other classmates, if the teacher could not answer in that moment. When there was a
problem that the teacher considered especially relevant, then the teacher presented it in
the blackboard to discuss all together. For example, in the first exercise, when they had
to do the generalisation of the program for any regular polygon, they doubted how to
calculate the turn of the mascot. The question was presented in the blackboard. Some
of them had already calculated it and gave their solutions. Afterwards, they noticed that
when they increased the number of sides of the polygon, the mascot failed in the draw-
ing. In this case, the reason of the error in the drawing was not in the code programmed,
the mascot cannot complete some movements if it arrives to the borders of the screen.
5 Redesign
This redesign has been developed based on the seminars of the DoCENT project in
which I participated. First, the activity would be in pairs or groups of three, since this
distribution facilitates the interaction between the pre-service teachers. They would be
asked to try to solve their questions in the little group, before asking the teacher. More-
over, the time dedicated to the activity should be increased. Indeed, the first exercise,
that would be the same, could be done in a session before to introduce the programming
language and dedicate two hours in another session to do the new activity. The second
exercise would be changed. The pre-service teacher could choose what they want to
program, it is not necessary that they use the quadratic formula. The new phases of the
exercise are described as follows.
5.1 Design of the application (at least 20 minutes)
In this phase, they have to choose which type of equation they want to solve and which
method they will use. Once they have decided what they want to do, they have to think
on which tools of Scratch [6] can be useful to do that. The teacher can intervene if there
is a technical problem. If there is a comprehension problem and the pre-service teachers
cannot solve it, the teacher will start a dialogue with them to clarify their objectives.
5.2 Programming the application (at least 30 minutes)
In this phase, some errors can be expected, but the pre-service teachers should try to
solve them on their own. If they cannot detect an error, the teacher can suggest them to
separate the blocks and execute them in order to find in which point the sequence does
5
not work properly. If there are several groups that have the same problem, the teacher
should prompt them to discuss the problem together.
5.3 Final discussion: How could we use it with future students? (at least
40 minutes)
In this final phase, there is a discussion with all the group about what they did, difficul-
ties and improvements. After this, they should think on how they would implement the
activity in a secondary school class: working on pairs/groups, time, teacher’s interven-
tion. Finally, they could also explain their expectations: objectives, possible difficulties.
6 Conclusions
With this redesign, the activity would be more open, not so guided as in the first design.
Some authors remark the openness as a characteristic of activities that can be useful to
promote creativity [2, 7]. In particular, in Mathematics, open problems usually generate
more diversity of the mathematical processes that are involved in the resolution, than
close-ended problems. In addition, more time should be dedicated. This is especially
important to improve the interactions between students. They need time to think on how
to solve the task and the possible errors that appear. Interactions are also an important
aspect [4]. Pre-service teachers would participate even more and the teacher would not
be the only reference of knowledge, they should listen to other classmates to solve their
problems and check for the validity of their answers. The assessment regarding crea-
tivity is also a key aspect that we should address in a further redesign of the activity.
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