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.
Education in science, technology, engineering, and mathematics (STEM) has become an
increasingly important educational perspective, gaining great attention around the world [
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.
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 [
Cuny, Snyder and Wing, defined [
Our research through the conceptual framework that describes CT-S takes an
evidencecentered approach, a model of cognition [
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 [
Evaluation can The pseudocode allows for efficient block allocation.
Under what conditions does it work or under what conditions does it fail?
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?
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.
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 [
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.
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.
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.
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).
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.
(20-16%) (15-11%) (10-6%) Can use symbology Can use Can use in the design of the symbology in symbology in diagram, the design of the the design of the translating the diagram, diagram without instructions into translating the translating the (5-0%) Cannot use symbology in diagram design. block structures instructions into and modifying block structures. them according to the needs raised.
(20-16%) (15-11%) instructions into block structures.
(10-6%) (5-0%) 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.
(30-21%) (20-16%) (15-11%) (10-0%) 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.
(30-21%) (20-16%) (15-11%) (10-0%) 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.
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.
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.