4.2.1. Art Teacher
The first part of the activity, occurring within a two-hour art lesson, was dedicated to crafting a modular composition using plastic bottle caps of various colors. The art teacher divided the students into four groups and provided each of these groups with the necessary resources to carry out the activity: a specific number of yellow, white, and blue plastic bottle caps; a cardboard sheet; a gridded sheet where the length of each square corresponds to the diameter of the bottle caps; and glue. A brief explanatory video and the image that the different groups were supposed to reproduce on the cardboard were projected onto the interactive multimedia whiteboard (IWB). The colors of the module were chosen to recall the colors of the Ishtar Gate, which the students had recently learned about in art history. When all the groups had finished the module (an example is shown in
Figure 3a), the teacher asked the students to arrange them in different patterns to create different modular compositions, aiming to grasp their differences (an example is shown in
Figure 3b). The goal of this initial activity was to envision the repetition of the module as a “shift” and, thus, a translation. Furthermore, the properties of the geometric figure depicted allowed students to reflect on the concept of symmetry.
The art teacher included the following resources in her SRRS (
Figure 4):
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Technological resources, like the IWB for the reproduction of videos, projection of the image of the module, and projection of the YouTube video with instructions for students;
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Material resources, like caps, sheets, glue, and the art textbook;
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Human resources, like previous professional experiences as well as exchanges and sharing with colleagues.
Figure 4.
SRRS created by the art teacher for the first part of the STEAM activity.
Figure 4.
SRRS created by the art teacher for the first part of the STEAM activity.
Based on the interview with the art teacher and her SRRS, we derived a visual summary of the document that she created for the first part of the activity, with indications about the situation in which it applies, the utilized resources, the rules of action, and the operational invariants (
Table 2).
The second part of the activity took place during the subsequent two-hour art lesson and involved the creation of a symmetric figure with tempera colors. The teacher started the lesson by playing a video that addressed a fundamental geometric concept within the context of the STEAM activity, namely, the axis of symmetry. In fact, if one were to imagine folding any symmetrical object along its axis of symmetry, two mirror-image sections would result that could perfectly overlap. For a better understanding of the concept, the video presented concrete examples, such as a monarch butterfly flapping its wings, overlapping its two sides. Subsequently, the students were given a blank sheet from a sketchbook, which they folded in half parallel to the longer side. The teacher then filled three separate containers, each with tempera paint of one of the three primary colors (red, blue, and yellow), and asked each student in the classroom to choose two out of the three colors. Finally, the teacher poured a small amount of the color chosen by the student into the fold of their sheet, instructing them to close the sheet by applying pressure along the fold in order to spread the color as much as possible (
Figure 5).
The art teacher included the following resources in her SRRS (
Figure 6):
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Technological resources, like the IWB and the YouTube video on symmetries in nature;
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Material resources, like tempera colors and drawing sheets;
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Human resources, like previous professional experiences and acquired skills as well as exchanges and sharing with colleagues.
Figure 6.
SRRS created by the art teacher for the second part of the STEAM activity.
Figure 6.
SRRS created by the art teacher for the second part of the STEAM activity.
Following the interview with the art teacher and her SRRS, we developed a visual summary of the document she formulated for the second part of the activity. This table (
Table 3) encompasses details regarding the situation, the resources employed, the rules of action, and the operational invariants.
4.2.2. Technology Teacher
The third part of the activity took place during a two-hour technology lesson and focused on the creation of tiles and compositions with geometric patterns. As an introduction, the teacher presented one of the most significant figures in post-World War I architecture: the renowned designer and architect Giovanni Ponti. The teacher drew the students’ attention to the project of the Hotel Parco dei Principi in Sorrento from 1962, in which 27 tiles with different geometric combinations were used. The design featured a bicolor scheme of white and ultramarine blue, with an explicit reference to the colors of water. In
Figure 7, one of these tiles is shown, with its geometric structure reproduced. In
Figure 8, three possible compositions, each made with four of these, are presented.
After sharing the file containing the presentation of all the tiles on the classroom Google platform, the teacher asked each student to reproduce one of the tiles four times on a sheet of graph paper of specific dimensions. After drawing and coloring the four tiles, the students cut them out and placed them side by side as they pleased, observing the visual effects obtained as a result of the mutual arrangement of the tiles.
The technology teacher included the following resources in her SRRS (
Figure 9):
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Technological resources, like the IWB, the Internet, Google Workspace, and a slideshow about the work of Giovanni Ponti;
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Material resources, like pencils, colored pencils, scissors, adhesive tape, and graph paper;
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Human resources, like exchanges and sharing with colleagues.
Figure 9.
SRRS created by the technology teacher for the third part of the STEAM activity.
Figure 9.
SRRS created by the technology teacher for the third part of the STEAM activity.
Based on the interview with the technology teacher and her SRRS, we derived a visual summary of the document that she created for the third part of the activity, with indications about the situation in which it applies, the utilized resources, the rules of action, and the operational invariants (
Table 4).
4.2.3. Music Teacher
The fourth part of the activity was conducted during a two-hour music lesson and consisted of a performance of a canon song.
Because the art teacher had introduced the concept of the axis of symmetry in a previous part of the activity, the music teacher began her session by projecting some images of very generic objects onto the interactive whiteboard and asking students to identify any symmetric figures within them, along with their corresponding axes of symmetry. Subsequently, to delve further into the discipline of music, the teacher showed the students a guitar, asking them if they could identify any symmetries within it. The students were then divided into two groups, and the teacher handed each group a small keyboard. Each group was required to observe the keyboard and identify any symmetries, marking a pencil on the key that could represent the axis of symmetry, as shown in the following figure.
Upon completion of this initial preparatory activity, the teacher explained the meaning of a canon song. The canon is a polyphonic musical form that originated around the 13th century and is based on the concept of imitation, i.e., the same melodic line is presented by multiple voices or instruments, progressively overlapping each other. A classic example of a melody with a canon structure is the famous “Frère Jacques”, known in Italian as “Fra’ Martino” or “Fra’ Martino campanaro”, a nursery rhyme and popular French song dating back to the 18th century. It is a simple and easily performable song, which is why the music teacher used it in her activity.
The teacher asked the students to sing the melody of “Fra’ Martino” in unison, reading from a score projected on the IWB. From a mathematical perspective, this unison singing activity can be likened to activities in art using mosaics and in technology using tiles.
Subsequently, the students were divided into two groups with the aim of singing the canon in two voices. The first group represented the first voice, and the second group represented the second voice. Students in the second group were instructed to imitate the singing of the first group after a two-beat delay, creating a “shift” or translation of the melody.
Following this, with the assistance of the math and support teachers present, the students were challenged to sing the canon in four voices. Two additional groups were introduced, each representing a third or fourth voice. Before replicating, or imitating, the song sung by the first group, the second group had to wait for two beats, the third group for four beats, and the fourth group for six beats, as shown in
Figure 10. At the conclusion, the teacher presented two videos to the students: the first featured an instrumental canon, and the second featured the same piece but with dance, with dancers reproducing the same choreography.
Afterward, the teacher continued by projecting an image of a natural landscape on the IWB. Students were once again asked to identify symmetries and, if present, to indicate the corresponding axis that divides the figure into two equal parts. After sharing some observations and considerations about the concepts of reflection and distance, the teacher reintroduced the song “Fra Martino”, asking the students to try imagining the “reflected” melodic line. The teacher highlighted, in red lines, the “trajectory” of the notes in the “Fra Martino” melody. This way, students could more easily identify the direction of the reflected melody, i.e., an ascending line in the upper staff corresponded to a descending line in the lower staff, and vice versa. The figure below represents the reflected “Fra’ Martino” song (
Figure 11).
The axis of symmetry corresponded to the G note on the second musical staff. The teacher then asked all the students to sing the obtained melody in unison.
The music teacher included the following resources in her SRRS (
Figure 12):
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Technological resources, like the IWB, PC, YouTube videos, slideshows about unconventional music scores, and digital materials retrieved from the Web;
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Material resources, like musical instruments and pencils;
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Human resources, like students’ voices.
Figure 12.
SRRS created by the music teacher for the fourth part of the STEAM activity.
Figure 12.
SRRS created by the music teacher for the fourth part of the STEAM activity.
From the interview with the music teacher and her SRRS, we generated a visual summary of the document she designed for the fourth segment of the activity (
Table 5). It includes details about the situation, the resources employed, the rules of action, and the operational invariants.
The music teacher did not explicitly include a reference to collaboration with colleagues in her SRRS. However, throughout the entire interview, there were constant references to connections with other disciplines, demonstrating that the planning of the entire activity was conducted in collaboration with colleagues, agreeing on the connections among the different disciplines. For this reason, we inserted exchanges with colleagues as a resource on which the music teacher’s document is based.
4.2.4. Mathematics Teacher
The last part of the activity took place during a two-hour mathematics lesson focused on the construction on the Cartesian plane of geometric figures translated and symmetric with respect to the Cartesian axes. The teacher started by using the pattern of a tile design, the subject of the technology activity, as depicted in the following figure (
Figure 13).
She explained the concept of translation, prompting students to reflect on the Cartesian coordinates of the translated images and on the translation vector. The movements of the figures could occur horizontally, vertically, or diagonally, as shown in the following images (
Figure 14).
To conclude the explanation regarding translations, the teacher used the tiles already created in the technology activity. Initially, the teacher asked each student to reproduce their tile on the Cartesian plane, identifying the coordinates of the most important points. Subsequently, she asked to translate the obtained figure to the right, to the left, and diagonally, always identifying the coordinates of the points. All the rules related to translations were developed together with the students, noting reflections and considerations on the whiteboard. At various points in the activity, students were able to identify connections with modules previously constructed in the art activity and with the canon proposed in the music activity.
Regarding symmetry, the same process occurred. The teacher explained in detail the reflection of an image with respect to the x-axis, y-axis, and origin, always emphasizing the value of Cartesian coordinates. In this case as well, according to the mathematics teacher, students made interesting references to the art and music activities, particularly to the butterflies created with tempera colors.
The mathematics teacher included the following resources in her SRRS (
Figure 15):
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Technological resources, like the Internet and Google Drive;
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Material resources, like textbooks;
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Human resources, like previous professional experiences and exchanges with colleagues.
Figure 15.
SRRS created by the mathematics teacher for the last part of the STEAM activity.
Figure 15.
SRRS created by the mathematics teacher for the last part of the STEAM activity.
Following the interview with the music teacher and her SRRS, we created a visual summary of the document she formulated for the last part of the activity (
Table 6).
Notably, from the interview with the mathematics teacher, many resources emerged that were not enlisted in her SRRS, such as students’ comments and questions and the artifacts created in the previous parts of the activity.