2. Teachers’ Perceptions about the PDP and STEM tasks implemented in two 6th grade classes in the context of Covid-19 pandemic 

An integrated approach of STEM education based on real-life scenarios was developed in the context of a collaborative Professional Development Programme (PDP), targeted to primary school teachers (6 to 10 years old). Because of Covid-19 pandemic, the PDP was implemented in an exclusively online context through the Zoom platform, from October 2020 to February 2021. By “exclusively online” it is meant without face-to-face meetings.

To guide the study, the following research questions are addressed:

What are teachers’ perceptions about an online STEM hands-on PDP?

What STEM teaching strategies favoured students’ understanding of a real-world problem?

At the last workshop of the PDP, a short and simple questionnaire was applied to teachers using Google Forms with four Likert items with a five-point scale (these items were previously assessed and validated by one of the authors not involved in the construction of the questionnaire).

Table 1

Table 2, the results of the answers to the questions (n = 13).

The theme is too important to update the trainee’s knowledge as a teacher at the 2nd cycle of elementary education, making this PDP a real training opportunity.

(…) the trainee’s initial expectation was that she would certainly enjoy different and innovative experiences, as is typical of the activities promoted by most higher education institutions.

(Elisa, Final report, 2021 January)

In the above citation, it is possible to understand that Elisa recognizes the importance of the contents approached in the PDP and that she had high expectations about “different and innovative experiences” because the PDP was implemented by a higher education institution. Concerning the online format of the PDP, she refers that:

(…) all contents were fully complied with, the different scheduled workshops were developed in synchronous sessions, via the Zoom platform, and no constraints resulted from this.

There is no question that certain face-to-face experiences would be more fruitful. However, the content approach, in the different sessions, was completely appropriate to the context in which rwesearchers are are living.

(Elisa, Final report, 2021 January)

As referred above, although Elisa considers that face-to-face activities are more fruitful, she also considers that the approach used by the educators on the online workshops of the PDP “was completely appropriate” and “no constraints resulted from this”. In summary, regarding the context of the PDP, despite being an online format, it was verified that teachers recognize the importance of the contents and the approach introduced in the workshops with live demonstrations and interactive computer screensharing activities. Furthermore, the PDP contributed to new knowledge and innovative practices in the classroom that motivate students to learn.

3. Teacher Elisa Case Study: Tasks Implemented in Two 6th Grade Classes in the Context of COVID-19 Pandemic

Teacher Elisa  discussed with the facilitator of the PDP (first author of this paper) several possibilities of activities that could be implemented in her class. She mentioned several times that she wanted the activities to be within the curriculum she was teaching and to have meaning for her students. After several proposals by the educators and discussion, she finally opted for one of the proposals with an interdisciplinary approach in the context of the COVID-19 pandemic. One goal was to use mathematics to help interpret and predict the evolution of the pandemic according to various possible contagion scenarios. Inspired by the ^[25] paper, Elisa planned and developed several tasks to be implemented in classes with different curricular unities: Natural Sciences, Mathematics and Information and Communication Technologies (ICT). In a first stage, she started by introducing the COVID-19 theme in the Natural Sciences class because the virus context is part of the curricular contents of this discipline, in the field of Environmental Aggressions and Integrity of the Organism. However, Elisa felt that her students did not fully understand how the virus spread and why this pandemic had such an impact on our lives that isolation measures had to be taken. In a second stage, she developed several tasks to be implemented in the Mathematics classes. Table 3 describes some possible scenario of infection proposed to the students to help them understand the reason for the need of confinement isolation situations.

Table 3. Tasks implemented in the Mathematics classes.

Tasks	Scenario of Infection	Basic Number of Transmission
Q1				2 (15.4%)	11 (84.6%)
Q2				1 (7.7%)	12 (92.3%)
Q3			1 (7.7%)	2 (15.4%)	11 (76.9%)
Q4			1 (7.7%)	3 (23.1%)	10 (69.2%)

As can be seen in both tables, all teachers responded positively to all the questions. For example, in Q1, all teachers agree that the approach proposed in the workshops is more motivating for students’ learning. This approach is related to hands-on experiments implemented promoting interdisciplinarity with STEM contents, which is in line with the literature that recommends it (e.g., ^[22]). Regarding the importance of obtaining training in this area, all the teachers recognize that it is “High” and “Very High”, with 92.3% for “Very High”. This means that they find this PDP important and that they need to have guidance related to STEM education. Besides recognizing the importance of promoting STEM education, it also means that teachers understand the need to acquire knowledge and skills to implement STEM hands-on practices in class. These results are in line with Margot and Kettler ^[23] who report that teachers suggest the need for effective professional development that provide them with learning opportunities to increase their knowledge and ability to effectively integrate STEM content. Question Q3 is related to the usefulness of the PDP in teachers’ practices and question Q4 with the online format. All teachers responded positively to both questions. However, the results are not as enthusiastic as in the previous questions. This may be related to their confidence on knowledge and skills about implementing hands-on practices in class and, regarding question Q4, on the preference for face-to-face workshops. BasNed on xt, excerpts from teachers’ final reports, presented in February 2021, researchersare discussed in order to bring more light to the discussion. In this table, we highlight the following dimensions: Motivation and expectations, Online format, Workshops and curricula contents, Impact of the PDP in teachers, Innovative practices, Collaborative environment among teachers and educators, and Impact in students.

1	Each student infects two colleagues	R0 = 2
2	Each student infects three colleagues	R0 = 3
3	Each student only infects one colleague	R0 = 1
4	Probability to infect someone is less than one	R0 < 1

In task 1, Elisa explained that it would be considered the scenario where “Each student infects two colleagues” and that “Sick students are isolated at home and no longer infect colleagues”. She also constructed a grid with 12 lines and 12 columns, where each square represents one student from a school (Figure 1). In addition, a table with the “Day” in the first column, the “Number of students who gets sick” in the second column and the “Total number of sick students” in the third column was constructed (Table 4). After, she asked the students to start painting the number of sick students on the grid:

Figure 1. Grid where each square represents one student at a school.

Table 4. Each student infects two colleagues.

Day	Number of Students Who Gets Sick	Total Number of Sick Students
0	0	0
1	1	1
2	…	…

Imagine that each square on a grid (Figure 1) represents a student from a school. One day, which rwesearchers will call day 1, one of the students becomes sick with COVID-19. Represent him, painting a red square on the grid.

She also asks students to fill in Table  4 with the following information:

Fill in the table, with the information about the “Number of students who gets sick” (Column 2) and the “Total number of sick students” (Column 3). For example, on day one, you write one on both columns.

Next, she gives information about how the sick student infects the others:

Let us now assume that each sick student will infect two students on average (To say that it is on average means that it may be that only one person infects one colleague, but there is another that infects three, and therefore, on average, each person infects two colleagues). So, the next day, day 2, there are two more students with COVID-19 who were infected by the first student with this disease; in all, there are already three sick students. Therefore, paint two more squares on the grid, and fill in the table with this information: on day two, two in column two and three in column three.

Elisa asks students to continue:

Again, sick students are isolated at home and no longer infect colleagues. Now, each of these two students is going to infect two other colleagues, and on the third day, there are four more sick students. Therefore, paint four more squares on the grid, and fill in the table with this informatio

Next, she asks several questions:

(a)

If each of these students now infects two more colleagues, how many new students will be infected on the 4th day?

(b)

And what is the total number of sick students?

(c)

In what day is everyone sick?

(d)

What if the school had 1000 students, after how many days would all students be sick?

(e)

Can you write the numbers of column two in powers of two?

Af

Table 5 is filled with the numbers until the day where all the squares on the grid (Figure 1) are red, which means that all 144 students are sick. As can be seen, on the 8th day, all students will be sick with COVID-19, in a school with a number of students bigger than 127 and smaller or equal to 255 students.

Table 5. Each student infects two colleagues.

Day	Number of Students Who Gets Sick	Total Number of Sick Students
0	0	0
1	1	1
2	2	3
3	4	7
4	8	15
5	16	31
6	32	63
7	64	127
8	128	255
…	…	…

From 45 students from two classes of teacher Elisa, almost all presented the results as stated on Table 4. Only two students, one from each class, considered that the school only had 144 students, and for this reason, on the 8th day, only 17 students get sick, and the total number of sick students is 144 (Figure 2, table on the left).

Figure 2. Each student infects two colleagues.

Below follows the answer of one of these two students:

On the 8th day, only 17 students get sick because in total there are only 144 students and 127 students are already infected, so only 17 students are missing.

[Student A]

The same student also presented the table on the right of Figure 2 to answer that on the 10th day, all students from a school with 1000 students would be sick. Another question asked by the teacher was to write the numbers in column two in powers of two. A power of two is a number of the form 2ⁿ where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. Based on this question, she explained to the students that “the growth of students sick with COVID-19 was exponential”. The following figure gives examples of answers given by the students. On the left, the result given by most of the students and on the right one of the students who considered the total number of students on the school as 144. On Figure 3, the powers on the right were written by the second student who had in account that the school had only 144 students. Next, his explanation is presented:

Figure 3. Writing ther implementing t numbers in column two in powers of two.

The double of 64 is 128 and thus only 17 non-infected students are left, so it is not possible to obtain a double of 128, so the remaining ones are infected (17 people).

The last student understood that, in column two, on each day, the number of students who gets sick is the double of the previous day but in the case of a school with 144 students, on the 8th day, it was not possible to consider the double because there only were 17 students left. This explanation means he has critical thinking. However, he could consider the example with more students as presented in the left. After ending task 1, teacher Elisa introduced the next task as stated on Table3:

You can think of a different situation. Imagine that each student infects three colleagues. After how many days are all students sick?

Use the previous procedure to make your observations and record them in Table 1.

The following figure gives examples of answers given by the students considering the scenario of infection presented in task 2 (Figure 4). On the right, the Table belongs to one of the students who considered the total number of students equal to 144, as stated by teacher Elisa, the student “remained faithful to the line of reasoning he had applied in the development of the previous task”.

Figure 4. Each stude tasks based on the first scenarios,nt infects three colleagues. During this task, teacher Elisa refers that:observed some excitement in her students.

At this stage, at least in the 6th B class, a high point of motivation of the students was visible in solving the task. The students were generally and visibly excited because they understood the situation they were experiencing.

(Elisa, Final report, 2021 January)

She continues, exemplifying students’ discourse:

“Now I understand, now I understand everything, this is so fast, contagion, … and rwesearchers are not counting everyone, families are missing and other people who have contact with them!”

[Student C]

The student was immediately supported by his colleagues….

(Elisa, Final report, 2021 January)

The above citations show that the students did understand the “situation they are experiencing”, which is the COVID-19 pandemic, and recognized the problem of spreading the decease so fast. On the work sheet of task 2, Elisa asked several questions. Next, rwesearachers present answers that students gave to the following question: Compare this result with the result you got when each student infected two students. What do you conclude?

I can conclude that the contagion of the students was faster in this situation, so much that they were all sick on the sixth day, two days earlier than in the past situation.

[Student D]

I conclude that if each student infects one more student, then the results would be drastic; for example, on day 5, in Table 1, there are 31 sick students. However, in Table 2, that same day, there would be 121 sick students.

[Student E]  (Here, Table 1 is on Figure 2, and Table 2 is on Figure 4)

When each student infects three, there are many more infected students, and the growth is much more exponential.

[Student F]

Based on her observations, Elisa concludes about students’ perceptions:

Overall, the students realized the dimension of the problem, became more informed about its magnitude, and realized that, in reality, the processes are much worse than in the model studied.

(Elisa, Final report, 2021 January)

This conclusion is in line with one of her goals, which was to raise awareness and understanding about the need for confinement in the context of the COVID-19 pandemic. To reinforce this perception, she introduced the following task:

You certainly understood the evolution scenarios of COVID-19, which you analyzed in the previous tasks. Point out three reasons, of a social nature, for which confinement was necessary.

Next, some students’ answers are presented:

A person can infect more than one person and the disease will spread more easily. If everyone gets infected, doctors cannot treat everyone. RWesearchers  were confined to allow time for the vaccine to be made.

Confinement is important for the virus to infect fewer people in order not to infect more people. If rwesearchers become contaminated, hospitals will be full. If researcherswe are confined, scientists will have more time to produce the vaccine.

The reason was because if reswearchers continued to live together, COVID would spread and the hospitals would be full, and they would not be able to treat everyone.

Prevent the disease from spreading further. Prevent further deaths. Hospitals would run out of beds.

Confinement is important to ensure social distance, that is, it avoids physical contact through kissing, hugging or even the simple touch and thus rwesearchers control the spread of the virus. On the other hand, the fact that researcherswe are confined will greatly reduce large clusters of people, whether at work, in transport or in social gatherings.

In her report, Elisa explains the reflection with students on measures to be taken to prevent the COVID-19 pandemic:

In this task, the students reflected on the objectives pursued with confinement and social isolation as well as all the other rules that are suggested for the control of the pandemic.

In fact, based on students’ answers, it is possible to conclude that they understood the reasons for confinement, as intended by teacher Elisa. Besides task 2 from Table 3, Elisa conducted tasks 3 and 14 from the same table. Next, we present how she introduces task 4:

To keep the situation under control, the likelihood of infecting someone must be less than one.

What does it mean “less likely to infect someone less than one”? After all, we cannot infect only half a person… You must think about the average again. It means, for example, that if there are ten sick people, they will infect less thand 2 fr ten other people, that is, every day the number of people who get sick is less than the number of people who got sick the day before.

Do the following experiment and proceed to the records in Table 34: it assumes that the probability of contagion remains always less than one and that, each day, Ethe number of students who become ill is equal to the number of students who became ill the day before one lisa cess. Suppose that on the first day there are 10 sick students.

After how manductey days are there no students getting sick? (…) How many students became ill? (…)

The following figure gives examples of answers given by the students tasks 3considering the scenarios of infection presented in tasks 4, where “Probability to infect someone is less than one” (Figure 5).

Figure 5. Probability to infect someone is less than one.

Next, we present the answers that a student gave to the questions asked by Elisa:

There are nd 4 fro students falling ill after 11 days.

55 students became ill.

And Elisa comm thented this task:

In this task, the students contame tablected with the term “probability” which became a concept of the 3rd cycle of elementary education. 

Most students understood the situation in question. “Teacher, when will this happen”?

Elisa also used Excel files to illustrate what happens in the different scenarios over the days, which allowed the students to observe how quickly the numbers grew in cases where the probability of infecting someone was greater than one. On the other hand, when it was less than one after some days, no one else will be sick (Figure 16).

Figure 26. Examples of Excel files.

Elisa decided to end this theme consolidating knowledge of Natural Sciences that she thought had not been well assimilated at the beginning of the school year:

To complete the task around Dr. Providência’s article ^[25], students completed a text of gaps mobilizing knowledge on the topic “Microorganisms” that were the target of exploration, in the Natural Sciences classes and evaluated in tests and where some weaknesses had been seen. In this way, it functioned as a moment of knowledge recovery/consolidation.

(Elisa, Final report, 2021 January)

Figure 7 shows the text with the gaps filled in by one of the students.

Figure 7. Text of gaps, filled by one student, on the topic “Microorganisms” explored, in the Natural Sciences classes.

Translation of the text:

COVID-19 is a disease caused by a virus called Sars-CoV-2. In order to reproduce, it needs to infect a host cell. The details of this microorganism were only possible to know, thanks to a device that physicists developed to see the infinitely small, called an electron microscope.

Table 56 shows STEM contents included in the tasks developed and implemented by teacher Elisa.

Table 56. STEM contents of the tasks implemented by teacher Elisa.

Science	Technology	Engineering	Mathematics
Natural Sciences Microorganisms Disease spread Pandemic	Computer Internet Wikipedia Power Point Excel.	Planning, designing and performing the activities.	Powers Exponential growth Mathematical model Variable Iteration Functions Graphics Organization of tables and data visualization.

With regard to implications on her future practices, Elisa refers that:

The trainee considers that the frequency of this training, from now on, will have implications for the preparation of her classes. She will seek to intensify her teaching practice with experiences that require the mobilization of different areas of knowledge and will lead her students to a better articulation of knowledge, promoting as much as possible the development of the ability to reason, communicate and defend points of view in all students.

(Elisa, Final report, January 2021)

In her final report, Elisa referred to the impact on her classes and on the students:

The trainee feels quite satisfied with the work she developed, firstly, because she realized that her students were very motivated, that they adhered to the proposed tasks, there was even an unusual frenzy, especially in class B and some students verbalized that the task allowed them to understand the frightening spread of the virus that plagues us.

In fact, Elisa recognizes motivation in her students who finally understood “frightening spread of the virus”. Although she already introduced this theme previously, she reinforces that it was with these tasks that students understood the need for measures to prevent propagation of the disease:

It should be noted that the trainee at the time of application of the activity had already taught the content of “Microorganisms” and obviously had contextualized and integrated the whole problem of the pandemic, but it was with the activity “When will everyone be sick?” that students understood the reason for the rules to which rwesearchers are/are subject to limit the spread of the disease.

Additionally, the teacher highlights the interdisciplinary approach provided in the tasks she implemented in class:

On the other hand, the interdisciplinary aspect of the task allowed the articulation of the disciplines of Natural Sciences, Mathematics and Information and Communication Technologies and, thus, to participate in the Domain of Curricular Autonomy and Flexibility, as well as in the School Project.

Finally, Elisa identifies the importance of implementing this approach with students to better prepare them to the real-world challenges as stated in the literature. Moreover, she intends to keep participating in this type of PDP:

In today’s world, full of complex challenges, the development and integration of multiple literacies, inspired by real situations, will certainly allow for more meaningful learning in which talent, individual qualification, the scientific system and democratic citizenship are strengthened. rWesearchers are grateful for the opportunity, and researcherswe await other formative moments of undeniable value.

In summary, the teacher Elisa case study exemplifies the implementation of interdisciplinary tasks related to STEM (Table 10), with real-world problems such as the COVID-19 pandemic.

34. ResultsDiscussion and conclusions 

Although some teachers mentioned their preference for face-to-face workshops, they also recognized the relevance of the online format, where the hands-on experiments were exemplified through videos and live sessions with the teachers. In addition, they referred that the programme corresponded and exceeded their expectations concerning its structure, contents, creativity, collaboration, innovation, and improvement in teachers’ practices. Moreover, teachers revealed interest, enthusiasm and motivation regarding the contents provided in the workshops of the PDP and referred that they gained new knowledge that will have impact in their practices. Furthermore, they mentioned that promoting interdisciplinarity with several subject matters and resorting to real-world scenarios is more motivating to students and contributes to promote their interest to learn. This is in line with the literature that recommends that this approach improves students significative learning and consequently their learning achievement. These Teachers’ beliefs and perceptions are important because, as referred by Margot and Kettler ^[24](2019), they will influence teachers STEM instruction.

Therefore, an exclusive online PDP can provide teachers with knowledge, and also can engage and motivate them to innovate their practices as required in an effective PDP (Darling-Hammond et al. , 2017). Moreover, several teachers, who participated in this study, developed interdisciplinary tasks related to STEM contents and implemented them in class. Because of the current scenario of Covid-19 pandemic, teacher Elisa case study was chosen to exemplify the implementation of STEM integrated tasks based on a real-world scenario. It was verified that she did develop STEM practices within an authentic context for the purpose of connecting these subjects to enhance student learning as stated by Kelley and Knowles^[15] (2016). In fact, she used the real scenario of COVID_19 pandemic with the aim of introducing tasks with meaning for her students and related to the curricula of Natural Sciences, Mathematics, and Information and Communication Technologies. Moreover, the teacher achieved one of her initial objectives, which was to make students understand the dissemination of the decease and to be aware of the need for measures to face the pandemic. Furthermore, Elisa recognized that it was based on this approach that students finally understood the problematic of exponential grow of infection and the impact on real life, and consequently the need for isolation or vaccination measures. Also, she identified critical thinking skills and significative learning because of this initiative. Her conclusion is in line with Stohlmann et al.^[24] (2012), who states that a strategic approach of STEM education provides students with higher levels of critical thinking skills, improves problem solving skills, and also increases learning retention. Moreover, relevant interdisciplinary learning environments were provided as recommended by some authors (Bes. Indeedwick & Fraser, 2019; Geiger, 2019). In fact, Elisa case study highlights the interdisciplinary tasks she implemented in class and the importance of implementing this approach with real life scenarios that provides students with meaningful learning and better prepares them to the real-world challenges. In factsummary, teacher Elisa case study exemplifies the implementation of interdisciplinary tasks related to STEM (Table 10), with relevant real-world problems, such as the COVID-19 pandemic, as recommended in the literature^[15] (Kelley & Knowles, 2016).

Furthermore, based on Aguilera et al. (2021) and Vasquez et al. ^[8][12](2013) theoretical framework for STEM education, tasks developed by Elisa are between the second and third level. In fact, the learning goals transcend the individual disciplines, are curriculum oriented (interdisciplinary) and, also, focus on a real-world problem and are oriented towards social implications (transdisciplinary). Indeed, the real real-world problem of COVID-19 pandemic, caused by coronavirus SARS-COV-2, was approached, in order to make students understand the phenomena, namely several scenarios of infection. In addition, social implications were discussed such as the need for measures to prevent or minimize the problem. Elisa was able to prepare and implement STEM tasks highlighting the role of mathematics for her students to understand this problem, which was successful, because it was based on these tasks that students finally understood the pandemic, which did not happen before when the subject was approached in the science class. Therefore, it was the STEM approach that promoted meaningful learning in students.

Based on this research, it was verified that it is possible to operationalize an exclusive online PDP in STEM education that motivates teachers and improves their knowledge and skills to implement STEM hands-on practices in class. In addition, teachers recognize the importance of resorting to relevant real-world scenarios because it increases students’ motivation to learn. Finally, teacher Elisa case study exemplifies a strategy to implement integrated STEM hands-on tasks in class, based on real-world scenarios, as is the case of COVID-19 pandemic, which is an approach that promotes students’ meaningful learning.

Regarding the limitations of this study, more research needs to be provided about the efficacy of online PDP formats regarding hands-on STEM education approach, namely in other levels of school such as secondary school.