STEAM Education: Technological Skills, Students’ Cultural Background and Covid-19 Crisis

Abstract We present an initial description of an ongoing research project. Students are attracted to learn mathematics, not only for its application but also for their cultural interest. The students’ cultural backgrounds are used, and situations are analyzed and modeled using technology. This first step has been instrumental in making the transition to distance learning necessary due to the Covid-19 crisis. We focus on a specific population of students who had to overcome, within a short time, two important transitions in the learning processes.


Introduction
developed Ethnomathematics, i.e. the study of cultural influences on mathematics education in various ethnic groups, focusing on the social context of students, involving their language, behavioral norms, and cultural background. Extensive studies have been conducted for mathematics education among the Roma, Inuit, Bedouins, etc. In fact, every population group has its own cultural characteristics. For decades, European countries have made efforts to unify the continent, but cultural differences between them are still present. This has been made apparent even more during the Covid-19 crisis, as different countries reacted in different ways, adopting different policies. When restrictions were loosened after the initial lockdown, the behavior of different populations in different countries has shown major differences.
We wish to emphasize that the "ethno" of mathematics has nothing to do with the kind of studies which have been conducted in the 19 th and early 20 th century. Ethnomathematics studies the ways of learning and teaching mathematics and conveying mathematics knowledge and skills among different populations, with regard to their respective cultural background.
As an example, coming from another domain, it is well known that the Inuit have about 30 different words to describe snow and ice. No need to explain why. And no need to explain why this would be useless for Saharan inhabitants.
A nice example of teaching a mathematical topic, when relying on the students' everyday life, is given by Barton (2017). As a mathematics teacher in New Zealand, a country well-known for its surfing spots, he used to motivate his students to study trigonometry as follows: waves arriving on beaches come from more than one storm ( Figure 1 shows successive waves; it is possible to identify that they have different amplitudes). Each storm creates its own waves, the wavelengths being generally not quite similar. If we add two such sine functions, we obtain a curve with three peaks. Common knowledge among surfers is that waves arrive in groups of three. They know also that every 7 th wave is bigger than the others.
We illustrate this with an activity using GeoGebra, a Dynamic Geometry System (DGS), freely downloadable from www.geogebra.org. Using slider bars both for the amplitudes and for the frequency of the sines, it is possible to check when the ternary structure of waves appears. See Figure 2: the upper plot shows the ternary structure, the lower one does not.
Of course, not every country has surfing spots, but every country has its own cultural references. The rosette of the Dohany Synagogue in Budapest, Hungary, has been used by the authors (Dana-Picard and Hershkovitz, 2019) as the basis of an interactive activity for undergraduates: "Using analytic geometry and your newly acquired ICT skills (mostly with a Dynamic Geometry System), build a model of the rosette". It required an initial analysis of the geometrical shape and enhanced fundamental notions, such as rotations and reflections learnt in Linear Algebra. It was also a 1 st encounter with augmented reality and building a model. In Figure 3, a student shows his peers a way to fulfill the requirements: (i) First, he requested help from a friend to check using a suitable software that the picture had been shot perpendicular to the plane of the rosette, so that it did not suffer from distortions. (ii) He analyzed the picture for symmetries, either axial or rotational. He discovered that there exist numerous symmetries, whence the necessity to make a choice which are the basic symmetries he will use. (iii) He translated the geometric data into algebraic data, mentioning that this is possible by hand and with a DGS. (iv) He explained on the whiteboard the main equations and plane transformations. (v) Finally, he showed the computerized output of his work.
In this paper, we are concerned with the mathematics studies of a population of so-called Jewish orthodox students, who came to the academy after years of Higher Talmudic studies only. The groups of students are composed of pre-service teachers in mathematics, some of them in-service teachers studying for an advanced degree, and of undergraduate students studying for a degree in Engineering. The differences between the curricula do not have a great influence on the issues that we discuss. This paper is part of ongoing research performed by the authors with students from different institutions.

Mathematics and cultural background
The students in the group began Higher Education at an age between 23 and 35-40 years. Until then, they had studied in Talmudic Institutions, and their mathematics education relied on elementary arithmetics and geometry. The texts with a mathematical flavor in the Talmud1 and the rabbinical literature did not draw special attention. As we said previously, the mathematical background remained elementary.
1 Based on a Wikipedia entry (https://en.wikipedia.org/wiki/ Talmud): The Talmud is the central text of Rabbinic Judaism and the primary source of Jewish religious law (halakha) and Jewish theology. The term "Talmud" normally refers to the collection of writings named specifically the Babylonian Talmud (Talmud Bavli), although there is also an earlier collection known as the Jerusalem Talmud (Talmud Yerushalmi. It may also traditionally be called Shas, a Hebrew abbreviation of shisha sedarim, or the "six orders" of the Mishnah. The Talmud has two components; the Mishnah (c. year 200), a written compendium of Rabbinic Judaism's Oral Torah; and the Gemara (c. year 500), an elucidation of the Mishnah and related writings from the same period, which often ventures onto other subjects and expounds broadly on the Hebrew Bible. The term "Talmud" may refer to either the Gemara alone, or the Mishnah and Gemara together. The entire Talmud consists of 63 treatises called "tractates", and in the standard print, called the Vilna Shas, it is 2,711 double-sided folios. It is written in Mishnaic Hebrew and Jewish Babylonian Aramaic and contains the teachings and opinions of thousands of rabbis (dating from before the Common Era through to the fifth century) on a variety of subjects, including halakha, Jewish ethics, philosophy, customs, history, and folklore, and many other topics. The Talmud is the basis for all codes of Jewish law, and is widely quoted in rabbinic literature.
The Bible contains numerous chapters with mathematical elements. Most of them are geometric: the dimensions of Noah's Ark (Genesis VI, 15), the dimensions of the Holy Ark and other objects in the Tabernacle (Exodus XXV), etc. As well as these examples, mathematical notions and mathematical thinking are ubiquitous in the Talmud: of course there is formal logic everywhere, often based on analogy (both external and internal), trigonometry and integral calculus (computation of the slope of a path, or of the length of an arc of a curve, in Tractate Eruvin), probabilities, geometry, etc.
The strength of these students is elsewhere: they are object-oriented and accustomed to extensive efforts in learning, spending hours and hours on the texts they have to scrutinize. Some of the main characteristics of their learning are as follows: (a) A personal analysis of unseen texts. Generally, the students receive, at the beginning of the week, a sheet of questions as a guideline for their work. An important feature is that the questions do not point towards a specific answer, but freedom is left to the learner. (b) The learner is encouraged to compare the text under scrutiny with other texts. When studying a text in one tractate of the Talmud, learners are asked to compare it with other parts of the Talmud. Analogy is the main word for this, as the topics may be very different, but the students can discover that their internal logic is identical. (c) Learning is generally organized on a weekly basis. On the first day, the learners receive a sheet of leading questions. Together with them, a list of references may be given. This list includes commentators living at other historical periods. Their study may help the learner to acquire a more profound understanding of the text, and also to discover the development ways of Talmudic thinking. The expected "output" of this learning process is not a reconstitution of what has been already said or written in previous generations, but rather the personal understanding of the learner. If this fits the explanation of a classical commentator, the educator will point this out as positive. A new understanding of a classical text, taking into account recent developments in science, technology, or social sciences (depending on the central topic of the text under scrutiny) may be important. (d) We should mention that the socio-cultural context in which a specific commentator lived has often a great influence on his or her point of view. The differences between comments written by an author living in an almost closed medieval ghetto and the comments written by an Italian commentator living in a more open environment at the Renaissance are sources of important intellectual developments. We may compare this kind of study to what is described in Ethnomathematics. No matter what field of study, the cultural background of the learner has an influence. The students in our study also understand these commentators according to their own socio-cultural background, where modern science may not have a central place. (e) The learner is not left alone. From the beginning, the educative team analyzes the personal skills of all the students, and they pair them according to what is called a "chavruta". This Aramaic word says friendship, but more than that. The educators try to compose pairs (should we call them binomials?) of students of a similar study level, and who are able to communicate with each other without using authority arguments. They will share their understandings, ask each other new questions and apply their own skills to explain and convince each other. (f) The "chavruta" is not alone. All the pairs learn in the same environment, in the same location. The educative team is present and provides the necessary scaffolding. Slowly, this scaffolding is removed, and the learners acquire autonomy.
The transition from the yeshiva environment to the academy may present an important and difficult gap, socially, educationally, etc. Some academic institutions enable a smoother transition, as they offer a double trend: a student who wishes, can devote half of the time to Talmudic studies, in a setting similar to yeshiva, the second half being devoted to academic studies. This is the model of studies at JCT for hundreds of students. What we described above is an application of what is called nowadays the 4 C's of Education (National Research Council, 2010): Communication, Collaboration, Critical Thinking and Creativity. The four C's are easily identified in points (a)-(f) above.
When arriving at the academy, in particular to learn mathematics, these are the skills that these students have already developed. Now they try to apply them to mathematics. Of course, the best situation is to have them guided by a mathematics teacher who has a similar cultural background. This will help to establish a fruitful teacher-learner communication.
A problem may appear when the teacher and the learner do not give the same meaning to a specific notion. As an example, for a student with a strong Talmudic background, the word "infinity" has a totally different meaning from the mathematical meaning. If the teacher's mathematical discourse takes this into account, then progress may be quick. The teacher may even take advantage of this fact, and his students will arrive quite fast at an understanding of the difference between potential infinity and actual infinity (Fishbein, 2001).
Moreover, despite a lack of theoretical background, technology has a great appeal for the students of the orthodox population. Therefore, these students' educators may have the benefit of a technology-rich environment for activities built around topics with a Jewish-Talmudic flavor: the geometric structure of Judaica objects, or of buildings such as synagogues. This has been the topic of the activity whose output has been briefly shown in Figure 3: the students used notions and methods from analytic geometry and plane transformations, together with GeoGebra.
We said that technology has a great appeal. Actually, the new situation of the Covid-19 crisis implied an important transition for the orthodox population at large, and sometimes introduced some dissonance. Until now, many of these students used standalone technology, for moral and social reasons: cellphones but no smartphone, computers but without an internet connection. With the Covid-19 crisis and the switch to distance learning, internet became an essential tool2. The dissonance was double. Students who used not to be connected needed now to connect. If these students are married and have children, 2 We should mention that for a fringe of the ultra-orthodox population, the switch to internet connection has still not been done. The educative institutions developed specific communication on the phone, with devoted lines. This is not the population in our study. their children also have to spend hours communicating either on the phone or with the computer with other children (rarely) and with their teachers (every day). Exactly the contrary of what was a fundamental element of their culture and education.

Inserting the students' cultural background into their math learning
The example shown above has been chosen for students from the so-called Jewish Orthodox population, for whom a synagogue is a central part of life. Analyzing and building models of such a central element of their life connected them to the mathematics they had to learn. It is well known that motivation is essential to efficient learning.
For other students, octagons and other polygons have been studied, enabling the development of new DGS skills, based on an Italian 12 th century castle. Fig. 4 shows an aerial photo of a castle, and a snapshot of a GeoGebra session to check (ir)regularity of octagons.
The orthodox students of the class mentioned above were more motivated by the Rumbach synagogue in Budapest than by the castle; the octagonal structure is visible on Fig.5a and a snapshot of a computerized activity is shown on Fig. 5b.
According to the specific cultural background of the students, a vast choice for examples is available for almost any mathematical topic. For example, Dana-Picard et al.
(2020) show how to use different buildings for European students and for Asian students for the same mathematical topic, namely Geometry and Golden Ratio. Of course, in each topic, some examples are internationally accepted.

Sudden switch to distance learning
In the spring of 2020 like all the world (NCTM, 2020) they had to switch to distance learning at once, because of the Covid-19 crisis. The main accent has been put on the technical aspects of this switch: "More attention has been given to ensuring the continuity of academic learning than to the socio-emotional development of students, and there is agreement that not all students have been able to engage consistently with their education as provided under these emergency strategies." (Reimers and Schleicher, 2020). One of the main goals of this study was to follow how this switch, the second one in a row for the orthodox students, has been managed and eased. Our study is based on questionnaires that we dispatched among students in two institutions. After having analyzed the answers, we also decided to interview a couple of teachers.
The 1 st ICT skills acquired by these students helped them move to the new skills. Suddenly, they had to master new technologies:  In many academic institutions, Zoom became the main communication tool and became within days an integral part of the institutional culture (Artigue (2002). Reimers and Schleicher (2020) mention the large "disparity in access to technology, connectivity and skills to engage with technology faced by students from different socioeconomic groups." For our students it was also necessary to use the internet at home. This was no small matter because of their culture. Adding the teachers to the population under study makes these disparities bigger. If, generally, some distance training had been organized for the teachers enabling them to learn the new technologies by using them, nothing had been offered to students. They had to acquire new skills almost alone and to re-invent their learning environment and their communication channels between other students and between students and teachers. Actually, this second process has been a clear example of the mutual influence of teachers on students and of students on teachers.
We must mention that, either because of previous usage and mastering of the technology, or because of the security drawbacks of the communication software chosen by the institution, some lecturers chose a different communication technology. At the beginning, this made the switching process from standard academic learning to distance academic learning harder for many students3.
Most students had already some CAS and/or DGS literacy, but some of these communication technologies were brand new for them. Different students may have used different CAS, but they were able to understand each other. This made the transition from face-to-face lectures to virtual classroom easier, at least for its technological part, but the students had to overcome their cultural norms. We prefer to speak about face-to-face lectures instead of frontal lectures: -In a frontal lecture, a lecturer conveys information in front of a passive audience. -A face-to-face lecture enables students to ask questions and to discuss the learnt topic with the teacher in real time. All the students can listen and have benefit of the exchange. This is the prevalent situation in the institutions of Higher Education to which the population we describe belongs.
Nowadays STEAM education develops fast. STEAM is an acronym for Science, Technology, Engineering, Arts and Mathematics. Roughly speaking, STEAM sees these fields of knowledge as connected to each other. As STEAM education teaches linkage of more than two domains of knowledge, and some of them may be quite new for the students in our study, changes in their socio-cultural background are made richer. For the implementation of a CAS in mathematics teaching, Artigue (2002) says that the new technological skills are an integral part of the new mathematical knowledge. Here the new technological skills are more complex: all the technologies had to be quickly used together, transforming the teacher into a kind of octopus (laptop, with a DGS and a CAS, communication software with screen sharing, maybe an iPad as white board, etc…). The same applies to students. Because of the Covid-19 crisis, all the teaching/ learning structures changed overnight. Both teachers and students had to go through a speedy instrumental genesis (see the papers by Lagrange, 2000;Trouche, 2002, Artigue, 2002 and the book edited by Guin, Ruthven and Trouche, 2010). This is generally a very personal process, but here the instrumental genesis of students and teacher are intertwined: the teacher tries to share with the students' skills with CAS and DGS, and students may use their experience with other teachers to help the educator to master the new communication technologies.
The traditional learning experience of Orthodox students, in Higher Talmudical Institutions (called Yeshiva), before arriving at the academy, was different, based mostly on personal interaction with collaborative learning of fundamental texts by analyzing them, finding analogies in other texts and critically exploring them for deep understanding of fundamental texts. They were used to face-to-face discussion, and rare intervention of the educator. Even if computers were available, generally to enable data mining and text writing, these are not a central item at home. Sometimes, they had no computer and no internet at home. Neither smartphones. The interpersonal relationship was the most important in their education. The switch to the academy changed the pace and structure of learning. The ICT based "regular" teaching (if this makes sense) helped to make the great change to distance learning in this crisis era. Now, at least the classes under study use all these technologies, plus other communication technologies (WhatsApp, Skype, etc.), making them learn in parallel pathways.
As educators, we have to take into account the possible usages of technology (data mining, computation, visualization, communication, etc.). We must also monitor and analyze the adaptation processes required from the students (and from the educators), with such a sudden switch not only in the learning content, but also, possibly more importantly, in the teaching methods and the learning processes. All this occurs in a new pedagogical and a new technological environment.
After a few weeks of almost total confinement, the Israeli government decided to open most of the country to more normal life. Higher education was not part of this opening, and the teaching remained distanceteaching and learning. Nevertheless, at JCT (recall that it is an engineering school), a mixed framework has been established for very specific domains: labs for physics, electronics and other applied domains have been re-opened. What can be done using computerized simulations is done via such simulations. Only after that, for the activities which are "hands on", have the labs been re-opened, but re-organized for small groups only, respecting social distancing. Of course, students and educators have to wear masks.
This had no impact on mathematics courses. They continued and are still based on distance-learning.
Interaction between educators and learners, and between learners is totally different in the new setting imposed by the Covid-19 crisis. Of course, we see that situation as an exploration of the students' Zone of Proximal Development (ZPD); see (Vygotsky, 1962) Maybe also an exploration of the educator's ZPD. In reality, the 4 C's of Education have to be revisited and re-invented.

The social environment: a brief description
With the sudden explosion of the Covid-19 pandemic, most (if not all) of the education system locked down. Many working places locked down also. As a consequence, entire families found themselves confined at home. The parents may have had to work from home and all the children changed to distance learning.
The characteristics of the situation include the following points: -Everyone must work using a computer. How many computers may be available in a standard family? -Do the family enjoy a wide enough bandwidth? After all, the children have to use the computer to learn, but they also wish to use it to play and to interact with cousins and friends. -The entire world went to internet. Is the network strong enough in the family's area?
Among the students in the population that we describe, many of them belong to large families and live in a small apartment, with parents, brothers and sisters. Before the Covid-19 crisis, their usage of computer communication was quite low. Moreover, if in normal times, the children between the ages of 13 and 18 learned at boarding schools, now all of them are at home. Everyone needs not only computer time, but also a more elementary requirement: a place to sit and study. We did not mention the necessary calm atmosphere for learning. One of the students whom we interviewed said: "the only place where I can learn is sitting on my bed with my computer on my knees and wearing earphones." Moreover, if before the crisis, the family used to keep young children far from electronic communication, now the same children have to use the technology for hours, and "worse", to see their older siblings and their parents almost all day long in front of the keyboard and the screen. The most important issue has been described by one of the students. He said: "We could have chosen to register with the Open University, where all the learning is distance learning, but we decided to register with this specific institution because we want face-to-face contact with educators and with our peers. In our previous life, we learnt in Talmudic institutions according to the chavruta framework, and we wish to continue that way. We wish also to learn mathematics and other disciplines that way." Another student said: "We have no choice now but to be online, but please try to be as close as possible to our natural environment and culture".

A huge opportunity to develop new pedagogies
As mentioned in a previous section, the most urgent task taken over by the directors of institutions and by the academic staff with the "explosion" of the Covid-19 crisis was to ensure the continuity of the academic learning. The answers were mostly technical: -A communication technology had to be chosen and imposed on all the teachers and learners -Lectures had to be delivered according to the originally planned schedule. -Homework assignments had to be uploaded according to the original syllabus -Regarding exams, a decision will be made later whether to request physical presence on the campus or to have them online. The decision will be made later, taking into account the evolution of the pandemic and complying with the governmental decisions.
We decided to address a more human aspect of the situation: how a special population of students' lives and learns in this situation. We discovered an important disparity between them and the general population. We discovered also that from this study we may have guidelines to invent a new pedagogy. The respective roles of the STEAM components have to change. The questions belonging to SEA may remain the same questions aimed at developing M knowledge and understanding, as they are chosen according to the specific curriculum and to the cultural background of the students. The T component will change: the role of communication technology will increase, and as byproduct new technologies will be used instead of the traditional chalk on a blackboard frame. Interactivity in two directions will increase (the way Google Docs are used, for which more than one user can work at the same time on a common document), and other possibilities already exist. In our eyes, it is not enough (more than that, it is not desirable) to simply transfer standard teaching from a whiteboard to an electronic tablet shared with Zoom, not changing an iota to the discourse. The world has a unique opportunity (of course, we wish not to have it based on a pandemic) to invent and develop genuine 21 st century pedagogy.