=Paper=
{{Paper
|id=Vol-3691/paper39
|storemode=property
|title=Understanding Block-based Code with Preservice Mathematics Teachers
|pdfUrl=https://ceur-ws.org/Vol-3691/paper39.pdf
|volume=Vol-3691
|authors=Elvia R. Ruiz Ledezma,Fermín Acosta Magallanes,Alma R. Villagómez Zavala
|dblpUrl=https://dblp.org/rec/conf/cisetc/LedezmaMZ23
}}
==Understanding Block-based Code with Preservice Mathematics Teachers==
https://ceur-ws.org/Vol-3691/paper39.pdf
Understanding Block-based Code with Preservice
Mathematics Teachers
Elvia R. Ruiz Ledezma1, Fermín Acosta Magallanes2 and Alma R. Villagómez Zavala3
1 Instituto Politécnico Nacional, CECyT 11, Av. de los maestros 217, Casco de Santo Tomás, Mexico City, Mexico
2 Instituto Politécnico Nacional, UPIITA, Av. Instituto Politécnico Nacional 2580, Ticomán, Mexico City, Mexico
3 Escuela Normal Superior de México, Hacienda de Sotelo 201, El Rosario, Mexico City, Mexico
Abstract
The present study shows the difficulties and achievements presented by a group of students in the fifth
semester of the degree in Teaching and Learning of Mathematics in Secondary Education of the Escuela
Normal Superior de México, in Mexico City, on the final design project. of digital materials with
programming in Scratch, the analysis was carried out within the framework of computational thinking
for science in its cognitive processes and the proposed scientific activity.
Keywords
Computational thinking, Scratch, STEM1
1. Introduction
Education in science, technology, engineering, and mathematics (STEM) has become an
increasingly important educational perspective, gaining great attention around the world [1],
with the objective: to train new talents with 21st century skills, developing the computational,
critical, and creative thinking [2]. Therefore, coding has been proposed as an integral part of
STEM Education, allowing interdisciplinary connections in relation to computational thinking
(CT) to address problems in everyday life and face challenges. Thus block-based coding
languages, such as Scratch, have become popular due to the use of drag code commands,
simplifying the text syntax used in other programs [3]. However, in a first approach, subjects have
difficulty processing nested structures, that is, placing one control structure inside another, as
well as algorithm sequences and the interaction between blocks of code, because not all students
They are at the same level of handling a computer equipment.
Our work aims to show the difficulties and achievements presented by a group of students in
the 5th semester of the bachelor’s degree in teaching and Learning of Mathematics in Secondary
Education of the Escuela Normal Superior de Mexico, when covering the study program
"Mathematics in Science and Technology” (MST), having as its final project the design of digital
materials with programming in Scratch.
This paper is divided into five sections in addition to this space where we show: the theoretical
perspective, the interpretation of the study program, the methodological process, the most
relevant findings, conclusions, and references.
CITIE 2023: International Congress on Education and Technology in Sciences, December 04–06, 2023, Zacatecas,
Mexico
ruizelvia@hotmail.com (E.R. Ruiz); ferminacosta66@hotmail.com (F. Acosta); amyy_0214@hotmail.com (A. R.
Villagómez)
0000-0001-9528-4146 (E. R. Ruiz); 0000-0003-1471-5376 (F. Acosta); 0000-0003-0021-8977 (A. R. Villagómez)
© 2023 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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2. Theoretical framework
The cognitive processes employed in interactions with computational tools are an important
aspect of computational thinking as originally conceptualized by Papert and are crucial to CT-S.
That is, preparing students for the increasingly computational nature of science. It is essential to
develop students' abilities to think about the functionality and position of computational tools
within an activity [4].
Cuny, Snyder and Wing, defined [5], “Computational thinking is the thinking processes
involved in formulating problems and their solutions, so that the solutions are represented in a
form that can be carried out effectively by an information processing agent” (p. 1).
2.1. Computational thinking for science framework
Our research through the conceptual framework that describes CT-S takes an evidence-
centered approach, a model of cognition [6], to identify the types of cognitive processes that are
already being leveraged in classrooms that reflect CT-S. Such a framework will allow us to (a)
delineate subconstructs that specify the cognitive processes characteristic of CT-S and (b)
operationalize the subconstructs of CT-S to develop performance tasks that can elicit CT-S. That
is, beyond knowing what activities are likely to engage students in CT-S, a testable model of how
those practices engage students in CT-S is necessary. Additionally, identifying which of those
activities’ students are likely to participate in.
The framework is a table of four rows and three columns, which creates 12 cells (Table 1). The
rows represent four categories of science activity (data collection, data processing, modeling, and
problem solving) where computational tools are likely to be leveraged in science learning. The
columns represent three interactions with computational tools (Reflective use, Design, and
Evaluation of computational tools) that involve the cognitive processes characteristic of
computational thinking [4]. Each cell within the frame represents the CT-S as the intersection of
a row with a column. That is, every time a person participates in a science learning experience
that can be categorized by one or more of the cells of the framework, they are engaging in
computational thinking for science.
Table 1
The computational thinking for science framework
Cognitive Processes
Science Activity Reflective Use Design Evaluation
Data Collection How can symbology How can The pseudocode allows for
be used to design the diagram efficient block allocation.
diagram for effective instructions be Under what conditions does it
coding? translated with work or under what
block conditions does it fail?
structures?
Data Processing What software What would be The software is being used to
features can help needed from create a visualization of
identify the software to help structures. What are the
relationship between find patterns possibilities or limitations that
scripts? related to help communicate them?
specialized
commands?
Modeling How can you use the What rules need Which aspects of this digital
three sections of the to be included in model accurately reflect the
software to predict the organization selection, and which do not?
the actions in it? of sequences?
Problem-Solving How can screen How can you How should I test it and how
reading software be create an will I know I've tested it
used to ensure that algorithm to enough?
the procedure is evaluate the
communicated claims and
correctly? reasoning of the
respective
arguments?
3. Interpretation of the study program
The MST program aims to ensure that heuristic experiences foster creativity and ingenuity, with
an approach where digital technology is closely linked to science and favors the creation of
development projects. of materials and activities that contribute to the generation of
mathematical knowledge, the strengthening of mathematical skills and thus the development of
professional and disciplinary competencies.
As well as the development of creativity and technological innovation skills, both in the
management of electronic devices and their programming. The contents of the MST program are
organized into two blocks. In one block, it is expected to recover the historical understanding of
the emergence of mathematics as a response to a need for communication, systematization, and
modeling. In two block the link between science, mathematics and technology is emphasized,
from Scratch programming and the development of didactic, technological, and digital materials.
4. The methodological process
Eleven normal students from the fifth semester of the bachelor’s degree in teaching and Learning
of Mathematics in Secondary Education in Mexico City participated (Figure 1).
Our research is a descriptive explanatory work that describes structured situations that
provide a sense of understanding of the phenomenon referred to [7].
Three phases were considered, according to the CT-S framework, adapted to the use of
programming in Scratch.
• Reflective use of programming.
• Designing with a programming language.
• Evaluating programming with a computational tool.
4.1. Reflective use of programming
We started with the design of the algorithm, using a structured programming technique that
also served for programming, helping to document the programs. There are three ways to
represent algorithms: written, graphical and auxiliary. The MST study program proposes the
graphic form of diagrams. To design them, certain symbols or figures are used that represent an
action within the procedure. The symbols are joined with arrows called flow lines that indicate
the order in which the steps must be executed and the pseudocodes that are the descriptions or
instructions of the flow chart. For programs, variables are needed, which can be numeric or
characters.
Figure 1. Students working on their project
4.2. Designing with a programming language
Learning Scratch offers students in training great possibilities due to its applications, it allows
them to promote creativity and thinking skills, learning basic concepts of computing and
mathematics, as well as promoting interpersonal communication and a sense of collaboration.
This program is extremely intuitive, without requiring memorization of commands for its
mastery. It is available for various operating systems. The Scratch screen is divided into three
sections. On the right the commands that make up the routines of this language are added one by
one, in the center the commands that each of the ten categories of actions have been presented
and on the left the block of commands is executed through a click. Actions are linked by means of
labels or blocks. In this phase, the student began his design with the use of a flowchart and
pseudocode since it is crucial to plan and visualize the flow of actions in Scratch programming
and represent the logical sequences of commands to be executed in a concrete way. Basic
exercises were then carried out to help in understanding the use of the blocks, thus the difficulty
was increased according to their progress.
4.3. Evaluating programming with a computational tool
We included the generation of educational programs and considered that the project was
finished, that it had an optimized design, that it had been completely developed and that the
minimum functionality tests were covered with the analysis of system requirements, the
evaluation was based on rubrics (Table 2).
4.4. The application scenario
Every time a subject participates in a science learning experience that can be categorized by
one or more of the cells of the framework, he or she is engaging in computational thinking for
science. For each cell in Table 1, a question is provided that a subject would likely need to engage
in CT-S to answer successfully. As an example, the student who answers the question in the upper
left corner of the frame will need to engage in the reflective use of programming tools: diagram
and pseudocode, to work toward data collection. Initially you will use the elements of the diagram
and the specific variables in the approach to a problem. You can do this by participating in the
reflective use of the diagram while interacting with its elements, until you form a mental model
of the functionality of programming. As the student continues to interact with this tool, their
discoveries reinforce, revise, or complement their developing mental model. Once the student has
a working mental model, they can use it toward the use of commands contained in Scratch's
categories of actions, linked by blocks. Design can occur throughout an iterative creation process
in which the subject has to repeatedly update and modify his or her mental model of the
functionality of the computational tool in relation to a sequence of commands in each number of
cycles.
To participate in the assessment, students must know what the digital model should do in
different settings to determine if it is a complete and accurate model. To do this, they investigate
of their efficiency running the program. Once this evaluation was completed, students would be
able to determine how well it works. Therefore, each student will have built a mental model of
the possibilities and limitations of the functionality of the computational tool and how it could be
used in their activity, so students are involved in CT-S.
In phase one for the reflective use of a computational tool in programming with Scratch, the
evidence shown by the students in relation to the representation of the algorithms in graphic and
written format with flowcharts and pseudocode was reviewed (Figure 2), under the criteria that
were considered, namely, the problem statement and the project design by 30% and 70%
respectively.
For phase two, the students, using their own criteria, manage to solve the rules, using the
program's sentences. At this stage, the coding of the project logic implemented in Scratch is
prioritized because it reflects the application of the knowledge provided by the class work. In this
phase, documentation and integration formed another segment to evaluate and provide feedback,
65% of the group of students obtained excellent performance and 60% improved compared to
the previous phase, demonstrating that the feedback allowed them to improve their performance.
In phase three, the implementation of the system, where prior knowledge and the user
interface are involved, the results indicate that 11.2% of the students did not complete the
project, while 88.8% achieved a finished project with a good design, development and tested
(Figure 3). Thus, 80% of the group managed to integrate prior knowledge and adequately
complete the program in contrast to the 20% who had problems integrating the information.
Table 2
Rubric established to evaluate the development of the project based on the CT-C framework
Aspects/ Excellent Good Regular Insufficient
%assigned
Data Collection (20-16%) (15-11%) (10-6%) (5-0%)
20% Can use symbology Can use Can use Cannot use
in the design of the symbology in symbology in symbology in
diagram, the design of the the design of the diagram design.
translating the diagram, diagram without
instructions into translating the translating the
block structures instructions into instructions into
and modifying block structures. block structures.
them according to
the needs raised.
Data (20-16%) (15-11%) (10-6%) (5-0%)
Processing
20% Can identify the Can identify the Can identify the Cannot identify
relationship relationship relationship the relationship
between between between between
specialized scripts specialized specialized specialized
to find related scripts to find scripts without scripts.
patterns and related finding related
modify them patterns. patterns
according to your
needs.
Modeling (30-21%) (20-16%) (15-11%) (10-0%)
30% Can use all three Can use all three Can use all three Cannot use all
sections of the sections of the sections of the three sections of
software, software, software, the software,
predicting the predicting the predicting predicting the
actions in it with actions in it with actions in it actions in it.
the use of rules for the use of rules without
sequential for sequential considering the
organization and organization. use of rules for
modifying sequential
according to the organization
stated needs.
Problem- (30-21%) (20-16%) (15-11%) (10-0%)
Solving
30% Can use screen Can use screen Can use screen Cannot use
reading software reading reading screen reading
to ensure you software to software to software to
communicate the ensure you ensure you ensure you
procedure communicate communicate communicate
correctly, creating the procedure the procedure the procedure
an algorithm to correctly, correctly, correctly.
evaluate the creating an without creating
respective algorithm to an algorithm to
statements and evaluate the evaluate the
reasoning, respective respective
modifying statements and statements and
according to the reasoning. reasoning.
needs raised.
Figure 2. Example of a program in graphic form, prepared by a student
Figure 3. Example of a program carried out by one of the students
5. Discussion
The students began their reflective use, manipulating the commands of the Scratch program. By
pressing certain blocks and observing the results of their actions, they subsequently reflected on
their manipulations and began to form a mental model of the functionality of this language. As
the students continued to interact, their discoveries reinforced, revised, or complemented their
developing mental model. We were able to observe that reflective use is bidirectional in the
transfer of information. Once the student had a mental model, he was able to use language more
intentionally to process the algorithms previously contained in the flowchart, so that he could
analyze to learn how to translate them.
Reflective use can also occur when the student begins his activity with an incomplete or
inaccurate mental model of the functionality of a program, allowing him to re-investigate and
modify his mental model already with the use of the programming language, testing with the
computational tool, choosing the commands that lead you to the design of your program.
6. Conclusions
The CT-S model and its cognitive framework allowed us to review the bidirectional interactions
between the student and the programming design of the prepared materials.
In phase two, one of the problems that arose is that not everyone has a good understanding of
mathematical logic to be able to visualize the logical sequences of the algorithm.
The most complicated procedures to teach were loops, conditionals, and manipulation
between variables, because they are abstract procedures.
Using diagrams is crucial to plan and visualize the flow of actions in Scratch programming,
these represent the logical sequences of commands to be executed in a concrete way to
understand.
At first, it is common to make mistakes such as not connecting blocks correctly, forgetting the
loop blocks or necessary conditions, not fully understanding how Scratch variables and events
work.
It is important to start with basic exercises that help understand the use of the blocks and
increase the difficulty according to the progress of the group.
References
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