Digital Fabrication in Education – Empowering Math Classes with an Active and Meaningful Approach
Introduction
When it comes to the learning process of Mathematics, studies show that different factors lead students to have poor performance in the subject. Ziegler & Loos (2017) indicate that the difficulty that students have in their learning is related to the lack of connection between the subjects covered at school with the real world. Niss and colleagues (2017) point out that the need for mathematics to be taught within a functional context has been the basis of educational reforms in some countries.
To collaborate with this discussion, this article seeks to relate Mathematics in the Makerspace resources with the metaphor of the term Mathland presented by Seymour Papert in his book Mindstorms: Children, computers, and powerful ideas (2020), in which the author compares the Math language learning process with the way a person learns French when growing up in France.
Thus, inspired by the term coined by Papert, this work presents the Makerland metaphor, when considering that the Makerspace and its resources are elements to enhance the learning of Mathematics concepts while the student develops their projects.
Based on this reflection, two complementary points in the prototyping of learning objects stand out. The first is the development of projects that aim at the explicit application of Mathematics concepts. These projects are related to the production of resources that aim the learning the discipline during the planning, execution and presentation stages. For example, the project carried out by the students was called Polygonal Jewels (Figure 1).
FIGURE 1 – Polygonal Jewelry Project
The objective of this project was to carry out a study on polygons in a concrete way. Students modeled their objects using paper, pencil, ruler, compass and protractor and later these sketches were transferred to the Illustrator® vector illustration software. The final objective was the elaboration of MDF Jewels with varied combinations of polygons, within the scope of Plane Geometry.
However, for the final execution, the students did not explore the Mathematics concepts that were used when transferring the project to the Laser Cutter software (Figure 2), nor the concepts used during the use of the equipment. This observation indicates the second point, which is the learning of Mathematics concepts in the use of Makerspace resources during the prototyping and production process.
In the Laser Cutter, for example, the relationship between the speed of the equipment while cutting a resource and the laser power to perform this cut, the definition of perimeter and area to be cut, the time to perform the cut, symmetry relationships, relationships between variables and Cartesian coordinates, are usually applied.
FIGURE 2 – Mathematics in the Control Panel of a Laser Cutter software
This paper discusses this second point, where the use and learning of Mathematics subjects in the Makerspace are directly linked to the concept of learning without being taught (Papert, 2020).
Theoretical foundation
Considering the great advance of new information and communication technologies, Seymour Papert’s theory of learning, Constructionism, stands out. The theory is based on Piaget’s Constructivism and highlights that the educational process happens more effectively when students are coauthors of their own knowledge and share it with their peers. (Blikstein, 2008).
In his book The Children’s Machine: Rethinking school in the age of the computer Papert states that:
“One of my central mathetic tenets is that the construction that takes place “in the head” often happens especially felicitously when it is supported by construction of a more public sort “in the world” […]. Part of what I mean by “in the world” is that the product can be shown, discussed, examined, probed, and admired. It is out there”. (Papert, 1993, p. 142)
Papert also argues that technology is not a means to improve traditional education, but a powerful resource to promote emancipatory learning, making it possible to meet different learning styles.
The constructionist learning theory was forged on the exploration and teaching of Mathematics concepts through technological resources and contributed to pointing out a new path for Mathematics Education.
Thus, as the Logo Language was created by Papert’s research group for a teaching process where students and educators are learners and everyone learns from their mistakes (Papert, 2020), the Makerspace’s prototyping resources also provide for the creation of Microworlds (Papert, 2020) for learning Mathematics. Considering that each personal project has its own narrative, which Seymour Papert saw in the use of the computer and Logo Language elements for learning carried out by students, today this concept can be extended to Makerspaces.
The Makerspaces are inspired by the Digital Fabrication and rapid prototyping environment called FabLab, which originated in 2002 at MIT through the collaboration between the Grassroots Invention Group and the Center for Bits and Atoms (CBA) to bring Digital Manufacturing to ordinary people (Blikstein & Krannich, 2013). These spaces leverage and boost the production of learning objects, enabling projects closer to reality to be prototyped.
Thus, Makerbased Learning teaches the student how to deal with challenges and face unexpected problems for which there is no preestablished explanation, acquiring the necessary skills to participate in the construction of new skills (Gavassa, 2020). However, it is important to consider the integration of Makerspaces in the school curricula accompanied by actions so that their use provides authentic and meaningful learning experiences (Fernandez et al., 2021).
When it comes to Mathematics Education, Brazil has undergone significant reforms. In 2018, the Brazilian Ministry of Education approved the Common National Curricula Base (CNCB – BNCC in Portuguese), a document that defines the essential knowledge that all basic education students have the right to learn.
In the field of Mathematics and its technologies, the BNCC conceptualizes the discipline as:
“Human science, the result of the needs and concerns of different cultures […] and a living science, which contributes to solving scientific and technological problems and to underpin discoveries and constructions, including impacts on the world of work”. (BRASIL, 2018, p. 267)
In Brazilian reality, the Mathematics discipline is organized into 5 Thematic Units (TU). They are:
 Numbers: developing skills related to numerical thinking and the meaning of operations.
 Algebraic Thinking: identifying the dependency relationship between two quantities and solving problems through equations and inequations.
 Geometric Thinking: interpreting and moving a figure on the Cartesian plane, and identifying isometric transformations and producing enlargement and reduction of figures.
 Quantities and Measures: building and expanding the notion of measure by studying different quantities, in addition to obtaining means for calculating areas of plane surfaces and the volume of some geometric solids.
 Probability and Statistics: building sample space for equiprobable events, in addition to planning and carrying out sample research.
In addition, the CNCB also includes Computational Thinking (CT) in the scope of Mathematics. The CT is an approach used to carry out thinking processes, in the formulation of problems and their solutions, and can be applied in areas of knowledge that go beyond Computer Science (Wing, 2011).
Methods
To carry out this work, an exploratory study was conducted with 21 students, users of Makerspace, from a school in a state capital in Brazil. The objective was to obtain further clarification on how they perceive the use of Mathematics concepts in the use of equipment during the preparation of their projects. Thus, a questionnaire was designed for this study by observing the routine of students when prototyping their projects in Makerspace.
The first questions in the questionnaire investigated how much students perceived the use of Mathematics concepts in the Makerspace, and at which stage of project development their use was noticed. In addition, it sought to identify which equipment is the most important to students.
The remaining questions were related to a preliminary study, which identified the main Mathematics issues that are explored during the use of resources in the Makerspace. These subjects were organized in Thematic Units (except for Probability and Statistics, which were removed from the scope of this work because their use was not observed in a significant way).
The Makerspace resources listed in this study were Laser Cutter, 3D Printer, Robotics & Automation and Low Tech Resources such as Drill, Scissors, Box Cutter and Glue.
Collected Data and Discussion
The responses collected in the applied questionnaire revealed important insights into the interaction of students in the Makerspace using Mathematics concepts.
Initially, the majority, 57.1%, indicated that, about how resources are used, the most important equipment for their projects is the Laser Cutter, followed by Low Tech Resources, 3D Printer and finally Robotics & Automation. This result aligns with what is observed in the Makerspace. Regarding the perception of the use of Mathematics in the process of carrying out projects, 57.1% stated that its use is very frequent and 19% reported that it was only frequent. The others stated that it is occasional or that they do not notice the use of Mathematics.
Regarding the stage that noted the greatest use of this area of knowledge, between Modeling and Production, 61.9% of respondents said that for them in both stages Mathematics is used, and 38.1% said that only during Modeling they see the use.
The following table (Table 1) shows which Math concepts students perceived being explored while using Makerspace resources. It is important to highlight that these concepts were addressed in Thematic Units according to the organization of the scope of the discipline in Brazil, but they can inspire and be adapted to the educational realities of other countries.
TABLE 1 – Math concepts that students perceive being explored in each resource

Laser Cutter  3D Printer  Robotics & Automation  Low Tech Resources 
Numbers 
6.8%  5.7%  6.7%  3.7% 
Algebraic Thinking 
23.8%  19.7%  15.6%  6.2% 
Geometric Thinking  16.0%  13.9%  15.6% 
19.8% 
Quantities and Measures  31.6%  37.7%  28.9% 
40.7% 
Computational Thinking  21.8%  23.0%  33.3% 
26.9% 
From the results presented in the table, it can be seen that students understand that Quantities and Measures are the most used TU in Modeling, Prototyping and Execution processes. This result points to the perception of the importance of this TU when dealing with material resources, which require calculations related to measurement units, figure areas and solid volumes. Computational Thinking and Algebraic Thinking are the next ones. The manipulation of variables and methodologies to break down problems were themes highlighted by the students. It was surprising that the TU Numbers had such a low indication since the use of elements and operations with rational numbers is the foundation for carrying out the projects.
Conclusions
First, the study sought to analyze the resources available in Makerspace, from equipment to software, to list the main Mathematics subjects that are used during its use. This is one of the contributions of this research.
Subsequently, the application and analysis of the questionnaire pointed to the relationship between the Mathland metaphor and the proposal of a Makerland where resources used in the Makerspace are Microworlds and issues related to Mathematics are naturally explored.
It was observed that the Makerspace creates an environment where Mathematics is a natural vocabulary for those who prototype projects, thus providing the use of the discipline’s resources as naturally as when learning to speak French living in France.
The students identified the use of Mathematics concepts during the Modeling, Prototyping and Production processes and their perceptions aligned with what was identified in the preliminary study. The next step of this study is to systematically organize these issues so that they can be explored in an objective way when the student carries out projects in the Makerspace, so that what is applied and learned from the discipline, during the prototyping process, can be evaluated. The result of this new research will be published in the future.
References
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