In the spring of 2021, CREAMat, the Center for Educational Innovation established by the Generalitat of Catalunya, had already organized three online conferences.

We immediately contacted the people leading the initiative, who responded positively to the proposal to work together.

The next step was the invitation to present the project and the first prototypes of the pop-up exhibition (product 2 of the project) at the ALM29 international conference, which was held in Barcelona in July 2022.

Meanwhile, the local collaboration with Sao, a non-profit entity that deals with EpPA in problematic neighbourhoods of Barcelona, the University of Barcelona, some neighbourhood education centres and prisons, and, as mentioned, the CREAMat was already working.

The monthly online meetings allowed us to verify a great coincidence of sensitivity with respect to the topics that the EpPA raises: significance of the educational action in the personal and social sphere, deficit of the curriculum and specific training of teachers, variety of needs and objectives of users, from social integration to the achievement of skills up to the need for a usable qualification. At the same time as the driving force consolidated, new people joined in, bringing very varied and significant experiences, proposals and good practices.

This new structure, which without making it explicit, increasingly took on the characteristics of a Community of Practice, proposed a new cycle of conferences, springtime 2023, in one of which the materials of the Numeric All project were presented to a wider audience made up of teachers and students, in a partly face-to-face and partly online meeting that took place in the Mathematics Museum of Catalonia (MMACA).

We recently took a significant step towards verifying the validity of the materials of the Numeric[All] project during their presentation at the meeting held in Barcelona of the European Numeracy project, also dedicated to the mathematical education of adults.

In the coming months, other equally stimulating events await us, such as the piloting of the latest Numeric[All] products in various adult centres and with multiple teachers in the scientific area, although we would like to have a fruitful exchange with teachers in the humanistic area, convinced that mathematical language, when based on concrete activities close to people’s reality, can be used to acquire communication skills of all kinds.

It will be a further contribution to defining the structure, product and time horizon of the Community of Practice. The idea that we are finishing developing is to design specific training for AE mathematics teachers, both at literacy and higher levels.

We would like to be able to combine the more instrumental needs, often summarized in an increase in calculation ability, with more structural aspects of mathematical thinking: problem solving, recognition of structures, prediction and verification of results, but also with the emotions that mathematics can generate.

We like to think that the results obtained so far, both at the level of international projects and in giving local continuity to the initiatives, demonstrate the validity of the Numeric[All] project and its products.

To begin with, 3D printing can turn abstract concepts into tangible objects. This tactile approach can be particularly beneficial for subjects like mathematics and science, where abstract concepts often prove challenging. By turning these ideas into something students can touch and interact with, the learning process becomes more engaging and memorable. When students are introduced to mathematical modeling through 3D printing, they can better grasp intangible concepts.^[1] Moreover, the aspiration to materialize an idea into a physical form, encourages students to engage in precise virtual mathematical modeling, cultivate a concise and accurate mathematical vocabulary, and construct sequences of logical, verifiable instructions, ultimately leading to the acquisition of essential mathematical skills.^[2]

Furthermore, the hands-on approach not only aids in understanding but also enhances the teaching capabilities of educators. When teachers undergo professional development in this area, their proficiency in conveying mathematical modeling concepts is further enriched.¹ Mathematics, often seen as a subject filled with abstract concepts, can be made more accessible and engaging through 3D printing. For instance, visualizing complex geometrical shapes or calculus functions becomes more straightforward when students can touch and interact with 3D printed models. This tactile approach fosters both mathematical and design thinking, allowing students to see the practical applications of what they learn.^[3] In addition, 3D printing is not just a tool but a powerful learning catalyst. It encourages active learning, where students are not just passive recipients of information but active participants in the learning process. By integrating science, technology, engineering, and mathematics, 3D printing projects can be designed to challenge students’ problem-solving and design-thinking skills. This hands-on approach ensures that learning is not just confined to textbooks but spills over into real-world applications.^[4]

Furthermore, customized learning materials, especially for special needs education, can often be expensive. 3D printing offers a cost-effective solution. Once a design is created, it can be printed multiple times at a fraction of the cost of traditional manufacturing. Schools can thus produce as many units as needed without significant additional costs. When compared to traditional manufacturing methods, 3D printing stands out due to its additive nature. Traditional methods often involve subtracting material, leading to waste. In contrast, 3D printing adds material layer by layer, minimizing waste. This not only makes it environmentally friendly but also economically efficient. Schools and institutions can thus produce materials without the overhead costs associated with traditional manufacturing.^[5]

https://www.tctmagazine.com/downloads/14709/download/MakerBot%20SKETCH%20Classroom%20Hero.png?cb=fe46e82a241459e6e11c91504cc08246

Moreover, incorporating 3D printing into the curriculum allows students to collaborate on projects, fostering teamwork. 3D printing has emerged as a pivotal tool in STEM education, promoting active participation, design-centric thinking, and problem-solving skills. By integrating 3D printing into STEM projects, students are encouraged to collaborate, brainstorm, and iterate on their designs. This hands-on approach not only solidifies their understanding of complex concepts but also nurtures a spirit of teamwork and cooperation.^[6]

Canva

Lastly, one of the projects exemplifying the power of 3D printing in education is the ‘Numeric[All]’ project. Aimed at illiterate adult learners, the project uses 3D printed, non-formal mathematical tools to bolster basic educational and, absolutely crucial for the user, professional skills. By using such innovative tools, adult learners can engage with content in a more meaningful manner.

[1]  Asempapa, Reuben & Love, Tyler. (2021). Teaching Math Modeling through 3D-Printing: Examining the Influence of an Integrative Professional Development. School Science and Mathematics. 121. 85-95. 10.1111/ssm.12448.

[2] Levin, Laura & Verner, Igor. (2020). Fostering students’ analytical thinking and applied mathematical skills through 3D design and printing. 10.1109/EDUCON45650.2020.9125358.

[3] Ng, Tsz Kit & Tsui, Ming & Yuen, Manwai. (2022). Exploring the use of 3D printing in mathematics education: A scoping review. Asian Journal for Mathematics Education. 1. 338-358. 10.1177/27527263221129357.

[4] Wisdom, Sonya & Novak, Elena. (2019). Using 3D Printing to Enhance STEM Teaching and Learning: Recommendations for Designing 3D Printing Projects. 10.1163/9789004415133_010.

[5] Haghsefat, Kianoush & Tingting, Liu. (2020). 3D Printing and Traditional Manufacturing Technology Analysis and Comparison.

[6] Wisdom, Sonya & Novak, Elena. (2019). Using 3D Printing to Enhance STEM Teaching and Learning: Recommendations for Designing 3D Printing Projects. 10.1163/9789004415133_010.

The title of the course was “Recreational Mathematics for Teachers”. Among the many subjects addressed (Alcuin’s and Fibonacci’s Problems, Mathematical Puzzles, Pigeon-hole Principle, Sangaku, etc), some outputs of Numericall were presented and discussed.

The 30 teachers present appreciated the pedagogical worth of the modules. Their favorites were Dominoes, Hamilton, Sky Scrapers, and In the Balance. The discussions were very participated and the activities associated with these topics were enjoyed by all.

The lecturer, Professor Jorge Nuno Silva, used the opportunity to implement and play-test some of the lesson plans we are developing in the final stage of our project, PR4. These will constitute The Numeric[All] E-Book, which aims to provide various exploration ideas that pair with our exhibits.

It became clear that most of these teachers will use the Numeric[all] materials in their pedagogical activities in the near future.

The main objectives of the meeting were to review the blueprints, boards and instructions of the DIY creation kit associated to each of the 16 modules of the exhibition.

During 4 sessions of approximately 4 hours, divided into 2 groups, we analysed the proposals one by one, discussing possible improvements, while also reflecting and starting to design the activities that can be carried out in the classroom, and that will end up being part of the didactic guide of the project (C1 activities). In fact, the boards should always be a starting point to motivate and trigger a discussion. This subsequent deepening makes the scope and possibilities of the proposal visible and can also lead to a subsequent modification. A material or resource can be motivating or not depending on how it is used and how it is presented.

The heterogeneity of the groups formed by the project members and their different perspectives meant that the conversations that were generated greatly enriched the results. Any creative process of this kind is iterative and needs several revisions to refine the modules until a version is sufficiently convincing for everyone.

The more people try it out, the more input we get and the more we see which modules need to be modified, which are attractive and which are not, the appropriateness of their degree of difficulty and the interpretations to which the information they contain gives rise. The modules of a museum are a didactic resource that is considered valid in the long term, almost always after several modifications.

Concretely, at the organisational level, the participants were provided with a template where a representative of each group wrote down the comments that arose.

At the same time, another member was in charge of making the agreed modifications to the files.

As for the boards, the text was revised, trying to use clear, short and self-explanatory sentences, following the guidelines to make them inclusive and to ensure that the measurements of the images matched the measurements of the material associated with the module. The designs of iconographies to be added to the boards were specified, representing the main idea of the challenge they pose in order to facilitate the interpretation of the board for illiterate adults.

It was decided to separate some of the boards into 2 to avoid boards loaded with too much information.

In the revision of the DIYs, care was taken to ensure both the clarity and precision of the instructions and the suitability of the materials and options proposed. We all got down to work, cutting, folding and gluing pieces.

A whole afternoon was dedicated to 3D printing. The proposals of the different groups that had made 3D designs of the modules were analysed, looking at the advantages and disadvantages of each of the proposals to decide which would be the final one.

It was also decided which of the modules would have 3D printed versions and which would not.

Although a lot of progress was made, as the materials are piloted it is possible that more aspects will be detected that need to be modified, as the end users are the ones who have the final say, because this material is aimed at them, and our visions may have a certain bias.

Once the changes resulting from this meeting have been made, the first piloting with these new versions will take place at the MMACA on 14 June this year.

“Math anxiety” is defined as the negative affective reaction occurring in situations that involve numerical and mathematical activities, which can be more or less severe. Its causes are not univocal, but studies show that it might be linked to generalised anxiety, as well as test anxiety (i.e. fear associated with taking a test).^[1]  According to OECD data from 2012, 30% of students were affected by math anxiety, and the number was on the rise in many countries.^[2] Needless to say, math anxiety does not always disappear when children become adults…

Although it is not clear where exactly it comes from, we can nevertheless assume that it is fuelled by the social pressure surrounding mathematics and, in the case of women, by gender stereotypes. It appears, indeed, that math anxiety might be more prevalent in women than in men.^[3]  While some studies have shown that the difference in maths performance between women and men cannot be explained by gender differences^[4], other studies have found that women’s maths performances are disturbed by the stereotype that women do not have a “math brain”^[5]. This, of course, contributes to why women are less represented in STEM careers. This lack of women in STEM ultimately leads to a poorer scientific paradigm, and deprives it of a greater inclusivity and attention to social needs.

Picture from Pikwizard

People who suffer from math anxiety are also at risk of lacking basic numeracy skills, as being numerate requires having some knowledge of mathematics in order to organise our lives as individuals and citizens. If we are not confident in our mathematical abilities, we will not be properly able to make effective decisions in many situations in life. Anxiety might as well prevent low-skilled adults from trying to get further education, as they might not have the best memories from their school experience.

But then, how do we get rid of math anxiety? And how do we eventually get rid of the myth of the “math brain”? First, maths needs to be made meaningful and intuitive again. We have long been unable to understand what it is meant to communicate because we have been studying maths in a dehumanised manner so that we have no idea how it can be useful in our everyday life. Therefore, maths needs to be put in a new light with the help of non-formal methodologies. Trying new fun ways of learning will boost the confidence of children who struggle with maths, as well as low-skilled adults, thus proving that anyone can achieve a good level of maths. However, the goal is not to make maths experts out of them but to teach them life-long numeracy skills. This is the mission of the Numeric[All] project.

^[1] Hart, S. A., & Ganley, C. M. (2019). The Nature of Math Anxiety in Adults: Prevalence and Correlates. Journal of numerical cognition, 5(2), 122–139. https://doi.org/10.5964/jnc.v5i2.195

^[2] OCDE (2013), « Mathematics Self-Beliefs and Participation in Mathematics-Related Activities », dans PISA 2012 Results: Ready to Learn (Volume III) : Students’ Engagement, Drive and Self-Beliefs, Éditions OCDE, Paris, https://doi.org/10.1787/9789264201170-8-en

^[3] Hart, S. A., & Ganley, C. M. (2019). The Nature of Math Anxiety in Adults: Prevalence and Correlates. Journal of numerical cognition, 5(2), 122–139. https://doi.org/10.5964/jnc.v5i2.195

^[4] Hyde, J. S., Lindberg, S. M., Linn, M. C., Ellis, A. B., & Williams, C. C. (2008). Gender similarities characterize math performance. Science, 321(5888), 494-495.

^[5] Spencer, S.J.; Steele, C.M.; Quinn, D.M. Stereotype Threat and Women’s Math Performance. J. Exp. Soc. Psychol. 1999, 28, 4–28.

On the third transnational meeting in Athens, the partners came together to try out the 16 prototypes created under the second project result, the gamified mobile museum. We are excited to share with you some pictures from our experience testing the prototypes, as they say, one picture is equal to a thousand words.

After testing out the prototypes and deciding on the final modifications of the exhibits, we extensively discussed how to bring the interactive exhibits to life through 3D printing and simple materials. Under the context of the third project result, we are developing a 3D Module along with its accompanying Laboratory Manual to provide adult trainers and educators with knowledge on how to employ 3D modelling and printing in their educational settings. The DIY Creation Kit is also a part of this project result, and it will explain in a step-by-step process how the interactive exhibits can be recreated in 3D software.

What you can expect in the next few months

We are going to be working on finalising the blueprints of the exhibits and the 3D Module, as well as, developing the DIY Creation Kit that will be tested in Barcelona in May 2023. The next few months are going to require extensive testing from each partner and preparation for our upcoming training activities.

Numeric[All]’s consortium is dedicated to working together to produce inclusive and high-quality materials for adult learners as a way to boost both numeracy and literacy skills through non-formal mathematics museum methodologies. There is still a long way to go until the project wraps up in 2024, so stay tuned!

Despite the fact that numeracy and literacy are considered to be basic skills for achieving social and labor success, Information and Communication Technology has been the third most important skill, along with the before-mentioned capacities[ii] that enables the personal growth. According to Jeannette Wing and Peter J. Denning,” computational thinking is a way of thinking about processes and solutions to problems that can be solved with the help of computers”[iii].

When it comes to illiterate adults, the process of education demands the exploitation of formal and non-formal methods. There is a numerous list of existing programmes that have attempted to educate adults lacking numeracy and literacy skills, through the use of information and communication technologies. For instance, National Education Programme for Illiterate Youth and Adults through Information and Communication Technologies (or PNEBJA-TIC, its abbreviation from French), launched in 2012 by the Government of Senegal is a programme that enables the provision of literacy and everyday life skills for people who have never been to school or who have left early[iv]. Digitalization has been proved as one of the most important technological trend that enables societal transition and development. The transformative potentials of digitalization in the field of education offer many opportunities to people that seek better educational perspectives.

With exception to digitals skills, non-formal education may be defined as a learning methodology that promotes the organization of activities outside of the formal educational context. The main objective of providing non-formal means of education is the introduction of new ways of living as well as the acquisition of upgraded potentials that can stimulate the obtaining of individual skills and personal growth in general.

Based on the above, ‘Numeric[All]’ mainly prioritizes the strengthening of illiterate adults’ inclusion and the improvement and extension of the supply of high-quality learning opportunities tailored to them through the development of gamified, non-formal mathematical tools, consisting components of a mobile museum, with the ultimate aim of cultivating and bolstering basic educational and professional skills of illiterate adult learners. Our project sets as a priority the achievement of transformation through developing innovative digital tools to support the fast-changing needs of our digital society.

[i]Shala, Arif & Grajcevci, Albulene. (2016). Formal and Non-Formal Education in the New Era. 119-130.

[ii]Jimoyiannis, Athanassios & Gravani, Maria. (2010). Digital Literacy in a Lifelong Learning Programme for Adults: Educators’ Experiences and Perceptions on Teaching Practices. IJDLDC. 1. 40-60. 10.4018/jdldc.2010101903.

[iii] ”Digital illiteracy: a phenomenon that can only be fought at school”, worl.edu. Retrieved from: Digital illiteracy: a phenomenon that can only be fought at school – World leading higher education information and services

[iv] ”National Education Programme for Illiterate Youth and Adults through Information and Communication Technologies, Senegal” (2017), UNESCO Institute for Lifelong Learning. Retrieved from: National Education Programme for Illiterate Youth and Adults through Information and Communication Technologies, Senegal | UIL (unesco.org)