Study visits as a part of mathematical project work in Finnish basic education

Abstract

The article focuses on study visits from the perspective of mathematical project work. Project work means a systematic organizing method of teaching that is based around a project. The research questions are the kinds of study visits students made, the meaning(s) of those visits, the mathematical content in the visits and how such study visits should be developed. The research material consists of two questionnaires (one for teachers and one for companies) and a case study of a student group that carried out two study visits as part of their mathematical project work. The results show that both teachers and companies considered study visits to be significant from their own standpoints. The teachers organize study visits, but the content of the visits is not usually connected with activities in the classroom.

KEYWORDS:

• Study visit
• project work
• mathematics
• basic education

1. Introduction

A variety of projects and out-of-school learning environments are part of high-quality education in Finland and all over the world. This topic is relevant because the most recent Finnish national core curriculum for basic education (2016) requires the inclusion of at least one multidisciplinary learning module in each school year. A study visit is one option for such a module and fulfilling that mandate. However, the goal is not simply to connect study visits to schoolwork. Morag and Tal (2012) identify several challenges with study visits: (1) students’ minuscule preparation before the visit, (2) communication between the teacher and the instructor at the company, (3) weak connection to the curriculum, (4) incomplete clarification of goals, (5) using students’ immediate surroundings, (6) the lack of connection to everyday life and (7) social interaction. These challenges are not isolated but interrelate with one another. The article considers these challenges and the solutions of them from the perspective of Finnish schools.

Technology Industries of Finland, which is the country’s lobbying organization for technology industry companies, piloted its MyTech program in spring 2017. MyTech is a multidisciplinary learning module for Finnish lower and upper secondary schools that provides schools a free, functional visit to a member company and a university. One objective of the program is to provide information on technology industries and show young people who are interested in mathematics, natural sciences and technology the jobs that are available in those fields (MyTech, 2021).

The present study examines Finnish students’ study visits to technology industry companies as part of project-based learning (PBL) in mathematics. While the focus is on study visits by Finnish comprehensive school¹ students, there are also references to visits by upper secondary school students. The study is divided into two parts. The first consists of two questionnaires, one for companies and one for teachers. The second part is a case study of the MyTech pilot. The following research questions are posed:

1. What kind of study visits have schools made to technology industry companies?

2. Why are schools’ study visits meaningful for schools and for companies?

3. How should study visits be developed?

   1. What challenges are there with study visits?

   2. How should a teacher organize study visits?

   3. How should a company organize study visits?

4. What mathematics, in accordance with the Finnish core curriculum, do workers at technology industry companies need?

5. How are the results of research questions 1–4 reflected in the MyTech project?

In Finland, the nine-year compulsory basic comprehensive school starts at age seven, comprising primary school (classes 1–6) and lower secondary school (classes 7–9). Upper secondary school contains three grades. Class teachers provide instruction for all school subjects in primary school, whereas subject-specific teachers are used in lower and upper secondary schools.

Research questions 1–3 are addressed from the perspectives of both in-service teachers and companies. Answering research question 4 will help teachers to plan mathematical projects that include study visits. Research question 5 combines the results of the first four questions and synthesizes them by way of a practical example.

2. Theoretical framework

2.1. Project-based learning

The concept of project work treated in the article means an organizing method of teaching that is adapted from PBL. The literature (Capraro & Slough, 2008; Grossman et al., 2019; Krajcik & Blumenfeld, 2006; Larmer et al., 2015) uses different words to define PBL, but the basic meaning is consistent. The points of emphasis can differ (Erdogan & Bozeman, 2015). The central, intertwined elements of PBL are as follows: (1) driving questions (Grossman et al., 2019; Krajcik & Blumenfeld, 2006), (2) creating artefacts (Krajcik & Blumenfeld, 2006), (3) collaborating (Grossman et al., 2019; Krajcik & Blumenfeld, 2006), (4) reflecting (Grossman et al., 2019; Larmer et al., 2015) and (5) sustained working, disciplinary learning and scientific practices (Grossman et al., 2019; Krajcik & Blumenfeld, 2006; Larmer et al., 2015).

Krajcik and Blumenfeld (2006) regard driving questions as a key feature of PBL. Usually, driving questions are the starting point for a project and provide a context in which students can see the connection between the project’s learning goals and real-world situations. Driving questions should guide the learning process throughout the project. Larmer et al. (2015) and Grossman et al. (2019) use the word ‘authenticity’ to describe the same thing. Additionally, Larmer et al. (2015) emphasize a challenging problem as the basis of a project.

An essential part of any project is the creation of artefacts, which are external representations of students’ constructed knowledge (Krajcik & Blumenfeld, 2006). The artefacts are the project outcomes and result from students’ investigations into the driving questions (Blumenfeld et al., 1991). An artefact can be a tangible product, a solution or a report, among other things. Larmer et al. (2015) present a public presentation and a final product.

PBL provides opportunities for students, teachers and actors outside schools to collaborate with one another (Krajcik & Blumenfeld, 2006). At the same time, the project should support students in making their own choices and in collaborating Grossman et al., 2019. Larmer et al. (2015) use the expression ‘student voice and choice’. Voice means that teachers are to allow students to speak in their own way rather than in the way they think the teacher wants. Student choice means that students have an influence on decisions about, say, driving questions and methods.

The teacher should support students to give and receive feedback and reflect on their own working process (Grossman et al., 2019; Larmer et al., 2015). Rather than standing at the front of the classroom, the teacher should move around among groups to assess students, give feedback and help students take the next steps in their learning (Grossman et al., 2019). In addition, the teacher supports students to reflect informally during their work and provides an opportunity to discuss scheduled formative assessment and project checkpoints formally. On the other hand, Larmer et al. (2015) include critique and revision as part of a project, by which they mean giving and receiving constructive feedback.

The idea of critique and revision is reminiscent of general scientific practices. Krajcik and Blumenfeld (2006) use the term ‘situated inquiry’ when talking about scientific practices. In PBL, students investigate their driving questions during project time, whereas students in traditional classroom work tackle short-term problems that are not situated in an overall process of inquiry. Larmer et al. (2015) offer the same formulation of sustained inquiry, while Grossman et al. (2019) try to engage students in practices of academic disciplines, noting that teachers ‘don’t teach students about science – they get them to do science, engaging them in problems or questions that are specific to a discipline, using its methods’ (Grossman et al., 2019, p. 46)

In addition to PBL’s central elements, it is important to understand that the objective of PBL is to assist students in developing not only their knowledge and understanding of subjects but also twenty-first-century skills, also known as success skills (Larmer et al., 2015). These are the skills that are necessary for success in everyday life, both at school and in the modern workplace; they are also known as transversal competences (Finnish National Board of Education, 2016). The specifics of twenty-first-century skills differ depending on the source. Larmer et al. (2015), for example, define twenty-first-century skills as critical thinking, collaboration and self-management, while the P21 network (Partnership for 21st Century Skills, 2021) defines them as learning and innovation skills, information, media and technology skills and life and career skills. In mathematics education, PBL offers opportunities to practice twenty-first-century skills together with mathematics (Viro & Joutsenlahti, 2018).

2.2. Non-formal learning and study visit as teaching

Learning can be classified into three types: formal, informal and non-formal (Eshach, 2007). Formal learning is organized, structured and located in an established institution like a school; the role of learning objectives designed by the teacher is central (Garner et al., 2015). Informal learning is spontaneous and voluntary; it is never organized and does not follow a curriculum (Eshach, 2007; Garner et al., 2014). Examples include visiting a museum or watching a documentary on television.

Non-formal learning is situated between formal and informal learning and connects an authentic learning environment and curriculum-based learning (Bjornavold, 2000). Non-formal learning has a certain structure and explicit learning objectives but is more flexible than formal learning (Garner et al., 2014). It can also be connected to formal school activities (Eshach, 2007). Table 1 presents the differences between formal, informal and non-formal learning.

Table 1. Differences between formal, informal and non-formal learning (adapted from Eshach, 2007).

	Formal	Informal	Non-formal
Place	At school	Everywhere	Institution outside school
Organization	Structured and prearranged	Unstructured and spontaneous	Structured and prearranged
Compulsion	Compulsory	Voluntary	Usually voluntary
Teacher’s role	Teacher-led	Learner-led	Guided
Evaluation	Evaluated	Not evaluated	Usually not evaluated
Orientation	Goal-oriented	Free	Goal-oriented

Study visits to an out-of-school learning environment like a company, library or university are one way to realize non-formal learning (Ikävalko, 2017; Räsänen et al., 2018). Such visits have long been linked to education in the natural sciences (Garner et al., 2015; Ikävalko, 2007), but have thus far played only a minor role in mathematics.

Study visits are reported to have several advantages (Bell et al., 2009; Olson et al., 2001). Specifically, they generally provide a more authentic learning environment than a traditional classroom (Olson et al., 2001), support the development of an overall picture of science and technology (Hofstein & Kesner, 2006) and increase students’ motivations toward and interest in a given subject (Bell et al., 2009).

Study visits have different objectives depending on school subject and viewpoint. Teachers highlight the development of their own teaching and obtaining new teaching materials (Garner et al., 2015). Additionally, they are a natural way to provide experimental work experience and vocational orientation for students. Teachers also see visits as tools that can motivate students. From the student perspective, visits provide new experiences and better working conditions than those found in schools (Garner et al., 2015). The learning objectives of study visits in a non-formal learning environment can be achieved through good planning (Morag & Tal, 2012). Table 2 presents the basic structure for a study visit, including activities before and after the visit.

Table 2. Basic structure for study visits, according to Orion and Hofstein (1994).

Before the study visit	Students’ preparation in classroom, including the goals of the visit (Morag & Tal, 2012)
	Collaboration between teacher and the organization visited (Morag & Tal, 2012)
	Connection between content and difficulty level of visit and curriculum (Morag & Tal, 2012)
During the study visit	Wide exercises (Mortensen, 2011)
	The facilitator’s performance (Morag & Tal, 2012)
	Student activities (Morag & Tal, 2012)
After the study visit	Recalling central themes (Eshach, 2007)

The content and difficulty level of a study visit must link with the core curriculum (Morag & Tal, 2012; Orion & Hofstein, 1994). This demands close collaboration between the teacher and the organization visited, with all parties establishing clear aims of the visit (Morag & Tal, 2012). It is also important that students prepare and orient themselves for the visit (Morag & Tal, 2012) and work on the same subject after returning to school (Garner et al., 2015). Of course, it is essential to invert activities during the study visit: wide exercises (Mortensen, 2011), an active role for students (Morag & Tal, 2012) and a good facilitator (Morag & Tal, 2012).

2.3. Study visits in the Finnish core curriculum

Finland’s national core curriculum for basic education emphasizes a range of learning environments inside and outside schools. The curriculum brings out ‘active cooperation with communities or experts outside the school’ (Finnish National Board of Education, 2016). The curriculum notes that ‘the students also learn new knowledge and skills outside the school is taken into account in the development and selection of learning environments’, such as ‘libraries, sports, art and environmental centres, museums and many other partners offer diverse learning environments’ (Finnish National Board of Education, 2016).

In addition to a variety of learning environments, the Finnish national core curriculum highlights multidisciplinary working methods, in which study visits are included:

A precondition for integrative instruction is a pedagogical approach to both the content of instruction and working methods where phenomena or themes of the real world are examined as wholes in each subject and, especially, in multidisciplinary studies. The manner and duration of integrative instruction may vary depending on the students’ needs and the objectives of the instruction. For example, integrative instruction may take place by: [–] functional activities, including theme days, events, campaigns, study visits and school camps, longer multidisciplinary learning modules, which are planned and implemented in cooperation between several subjects and which may contain some of the aforementioned integrative instruction techniques, selecting content from different subjects and shaping it into integrated modules [–]. (Finnish National Board of Education, 2016)

In grades 1–9, one objective of mathematics education is to guide ‘the students to understand the usefulness of mathematics in their own lives and more broadly in the society’ (Finnish National Board of Education, 2016); the teaching of mathematics should be concrete in every grade (Finnish National Board of Education, 2016).

3. Materials and methods

In this chapter, I describe the data material that was used in this study. First, I introduce the two questionnaires and then a case study. The first questionnaire was addressed to companies in the technology industry and the second to basic education teachers. The case study concerns the project work of seventh-grade students, which included two study visits.

3.1. Questionnaires

In autumn 2017, the lobbying organization for technology industry companies, Technology Industries of Finland, sent the questionnaire to its member firms that had expressed an interest in school study visits. Of 63 such companies, 29 responded, of which 23 had experience with study visits. The individual respondent was usually the company’s CEO or HR manager. The size and branch of the companies varied, but every company was linked with technology in one way or another.

As to teachers, answering the questionnaire was a voluntary part of an online course about mathematical project work in autumn 2018. Teachers in the course were pedagogically active on average and wanted to develop their teaching. Of the 24 teachers in the course, four mathematics teachers in lower secondary school and four class teachers in primary school answered the questionnaire. Overall, three of these teachers had made at least one study visit with their students.

Table 3 summarizes the questions in both questionnaires. The questions concerned the structure, organization, significance and development of study visits. Additionally, there was a question about useful types of mathematics for technology workers on the company questionnaire. Teachers’ and companies’ answers to the open questions were categorized via content analysis that was largely data driven. Because the sample was small, I calculated only frequencies and relative frequencies for the multiple-choice questions.

Table 3. Questionnaires for companies and teachers; all items translated from Finnish into English.

Theme	Companies	Teachers
The structure and organization of study visits	Describe the content of a typical study visit to your company.	Describe the content of study visit(s) you have been on with students. Additional multiple-choice questions
	How does your company usually plan a study visit program? Additional multiple-choice questions
The significance of the study visits	Why are study visits significant for you?	Why are study visits a significant part of your teaching?
The development of the study visit	What challenges do study visits pose?	What challenges do study visits pose?
	How would you develop the study visits?	How do you develop the study visits?
Mathematics at the companies	What mathematics do workers at technology industry companies need?

3.2. Case study

In spring 2017, 19 seventh-grade students and their teachers undertook a robotics project as part of the MyTech program pilot. The students were in a technology-oriented class and thus had grades in mathematics that were higher than usual (mean 8.58). They were also explicitly interested in technology and natural sciences.

In the class, the students worked in groups of three or four. A mathematics teacher, an art teacher and the present study’s researcher instructed the groups. Every group had responsibility for a given area of robotics, such as industrial or service robots. The groups were not allowed to choose their topic. They had to prepare a presentation and solve a mathematical task linked with the area. The mathematical task might be for example to study the path of a robotic vacuum cleaner of the movements of an underwater robot. The task was an authentic real-world problem. They tested their mathematical solutions by programming Lego Mindstorms robotics. The project instructions were quite closed, but there were many possibilities to solve problems. Teachers had a checklist which tell the minimum requirements to pupils. Pupils were allowed to expand the subject and to find new viewpoints. The content objectives of the project were linked with mathematics and programming, physics, art and guidance counselling, but each group had its own objective. The mathematical objectives, for example, involved familiarity with the 3D coordinate system, the Pythagorean theorem, the basics of graph theory, algorithmic thinking and programming. The objective in physics was to calculate average velocity. In the art lessons, students planned a marketing poster for their robots. The project included two study visits, the first to a university and the second to a company. The study visits were linked with both the guidance counsellor and the mathematical content. The purpose of the visits was to concretise the theory studied at the school. Additionally, pupils saw real robots in action.

The research materials for the present study were collected during the pilot project. The material about the structure of the study visits is based on the researcher’s diary and videos about project work at school, at the university and at the company, along with the notes from a planning meeting. The researcher observed students’ project work as an active observer (Metsämuuronen, 2006). In the final questionnaire for students, there was a multiple-choice question about the most meaningful part of the project, an open question about the targets for development in project work and a self-assessment question about their learning of mathematics. Additionally, students participated in a brief final test. The teacher’s views on targets for development were asked in a standardized, open-ended interview. Not all the collected material was used in the research.

Table 4 summarizes the connection between the data and the research questions. Researcher notes, diary and videos were used to develop and present the overall view of the structure and planning of the visits and were not intensively examined.

Table 4. Summary of all data in the present study.

Part of the study	Data	Research questions
1	Questionnaire for companies	1–4
1	Questionnaire for teachers	1–3
2	Researcher’s notes from a planning meeting	Primarily 5, secondarily 1
2	Researcher’s diary and videos about project work at the school, university and company	Primarily 5, secondarily 1
2	Interview of teacher	Primarily 5, secondarily 3
2	Final questionnaire for students	Primarily 5, secondarily 2, 3, 4
	Final test for students	Primarily 5, secondarily 4

4. Results

Sections 4.1–4.4 cover only the questionnaire results, while section 4.5 uses a case study approach to examine the study visits.

4.1. The structure and organization of study visits

Of the 29 responding companies, 27 (93%) answered the question about planning study visits. Four of these respondents were planning their first study visit, but the other 23 companies had all hosted at least one study visit. Figure 1 presents more detailed information of the visits to these companies. The visiting groups were most commonly from secondary schools, especially lower secondary schools. The number of study visits per company varied between 1 and 15 over the previous two years. Almost all the companies said that they could take more groups for study visits in the future.

Figure 1. The upper graph shows the number of the student groups that had visited companies that answered the questionnaire in the previous two years. The lower graph describes how many companies had received students from upper secondary, lower secondary and primary schools.

The examination that follows deals only with companies that student groups had visited or would soon visit. Figure 2 shows the structure of project planning in the companies. Seven of 27 companies (26%) did not have a single person responsible for visits and did very little planning. at 20 companies (74%), there were designated individuals who organized the study visits. At more than half of these companies, this person had a multi-professional group for support. Only six companies (22%) had a standard structure for the study visits. About 70% of firms with a designated individual did not use a standard structure when planning the visits. Some asked for the schools’ wishes (f = 5) or operated according to the situation or feeling (f = 9).

Figure 2. The structure of study visit planning at the companies.

Per the companies, suggestions for study visits were usually made by teachers (20 of 27), with only four of the companies suggesting them. Sometimes, another individual, like the researcher or a Technology Industries of Finland staffer, proposed a visit.

The visit structure varied between companies. At five firms (19%), there were only presentations about the company. The study visits to 13 companies (48%) included both presentations and a tour of the factory. Only two companies (7%) offered the possibility for students to work with a concrete task, along with a presentation and a tour. Finally, a single company (4%) organized a presentation and concrete task without a factory tour.

Table 5 presents the companies’ answers to the closed questions about their study visits. Only 9 of 23 (39%) usually receive groups that had prepared for the visits, and half a dozen (26%) knew that students worked with the visit subject after the visit. Four companies (17%) provided some materials before the visit, but only five (22%) planned the study visit jointly with teachers. Overall, students rarely played an active role during visits; only two companies (9%) organized hands-on work for students, and students asked questions at six companies (26%). Companies were generally satisfied (74%) with the visits, but fewer than half (39%) received feedback from students regarding the visits.

Table 5. The students’ work before, during and after a study visit, from the viewpoint of the companies (N = 23).

		No (all or nearly all groups)	Yes (all or nearly all groups)	Don’t know
Before study visit	Preparation at school	13 (57%)	9 (39%)	1 (4%)
	Company provided materials before visit	18 (78%)	4 (17%)	1 (4%)
	Planning with teacher	17 (74%)	5 (22%)	1 (4%)
During study visit	Hands-on work for students	21 (91%)	2 (9%)	0 (0%)
	Questions from students	16 (70%)	6 (26%)	1 (4%)
After study visit	Exercises after visit	9 (39%)	6 (26%)	8 (35%)
	Feedback on visit from students	12 (52%)	9 (39%)	2 (9%)
Overall	Experience of a successful study visit	6 (26%)	17 (74%)	0 (0%)

Three of eight teachers who answered the questionnaire had been on at least one study visit. Each such visit consisted of a presentation and a tour of the company. All these teachers prepared for their visits, but only two required their students to work with the topic after returning to school. One teacher was planning a visit with the company; only this teacher’s students were to conduct concrete activities during the visit.

Overall, the challenges cited by Morag and Tal (2012) were visible. Most groups did not work with the company’s theme before or after their visits; the visits were often an isolated event that was not linked with the curriculum. Although most companies had a designated individual with responsibility for visits, they did not a standard structure for visits in which students played an active role.

4.2. The significance of study visits

Both companies and teachers reported on the significance of the study visits; those results are presented in Table 6. The most important reason for the companies was influencing students’ career choices (f = 22, 83%), future studies (f = 13, 50%) and future jobs (f = 9, 35%). For the companies, it is also essential to paint a positive picture of the technology industry (f = 19, 73%). They wanted to highlight cleanliness, safety and the lack of physical demands. Of course, the companies (f = 8, 31%) understood that the visits were an opportunity to advertise themselves for students and their families:

Generally, we need more primary applicants for education in technical sector. At this moment, the image of the industry does not attract gifted students. This situation will influence recruitment in the future. Hopefully, we can create more positive impressions through study visits. (Company 1; all quotations translated by the author from Finnish)

Table 6. The significance of study visits from companies’ (N = 26) and teachers’ (N = 8) perspectives.

Companies’ perspective	f	Teachers’ perspective	f
Controlling of students’ career choices (studies, job)	22 (83%)	More concrete teaching	3 (38%)
Positive picture of the technology industry	19 (73%)	Familiarization with working life	3 (38%)
Marketing of the company in its own municipality	8 (31%)	Authentic learning environment	3 (38%)
		Motivating	2 (25%)

On the other hand, teachers highlighted the significance of study visits as a method of concrete teaching (f = 3, 38%) and using working-life based (f = 3, 38%), authentic (f = 3, 38%) learning environments. They also used study visits to increase students’ motivation (f = 2, 25%):

Via study visits, students have a conception of working life generally and the skills that they will need in the future. The study visits are also motivational, and it is nice to leave the classroom. (Teacher 1)

4.3. The development of the study visit

The companies described the greatest challenge as arousing curiosity among students (f = 9, 31%). They did not know how to motivate students to listen or be active during visits:

The biggest challenge is to create contents that is interesting in the students’ opinions and to find the correct difficulty level. (Company 2)

The companies’ concern is well founded. Only one of three teachers who had been on a study visit said the students seemed active and asked questions. The teachers did indicate that ensuring an active role for students was a development target for the visits (Table 8).

The other significant problems faced by companies were a lack of time (f = 7, 24%) and limited physical facilities (f = 6, 21%). On the other hand, teachers considered travelling to the company to be a problem (f = 6, 75%) and even a waste of time and money. Some companies (f = 5, 17%) and a couple of teachers (f = 2, 25%) said that they found it challenging to collaborate and communicate with one another. Table 7 presents the challenges faced by both companies and teachers.

Table 7. Study visit challenges from companies’ (N = 29) and teachers’ (N = 8) perspectives.

Companies’ perspective	f	Teachers’ perspective	f
Motivating students	9 (31%)	Travel	6 (75%)
Lack of time	7 (24%)	Collaboration with companies	2 (25%)
Facilities	6 (21%)	Time to plan study visit	1 (13%)
Collaboration with schools	5 (17%)	Large groups	1 (13%)
Security	2 (7%)

The companies (f = 14, 48%) consider closer collaboration with schools to be an important development target (Table 8). The teachers targets for development in greater detail, but they had the same message: they hoped that the companies would take account of students’ level in mathematics (f = 3, 38%), the connection between study visits and teaching at school (f = 3, 38%) and ensuring an active role for students during the visit (f = 3, 38%). These results suggest that if teachers and companies communicated more before the visit, it would be possible to solve many issues:

When a study visit has been agreed on, we do have not any problems. It is challenging to inform teachers of the possibility of visiting our company finding suitable student groups. (Company 3)

The biggest challenge is to find a company and program that take the students’ age into account. (Teacher 1)

Teachers also highlighted good planning (f = 2, 25%), prepared programs from which a teacher could choose (f = 2, 25%), flexible timetables (f = 2, 25%) and a fluent facilitator at the company (f = 3, 38%) as factors that would improve study visits. A few companies felt that it would be easier to systematize study visits (f = 4, 14%) so that they did not have to be planned from scratch each time. Both companies and teachers considered smaller groups to be better.

Table 8. The development targets in study visits from the perspectives of companies (N = 29) and teachers (N = 8).

Company perspective	f	Teacher perspective	f
Closer collaboration with schools	14 (48%)	Connection to subject curriculum content	3 (38%)
Systematization of study visits	4 (14%)	Correct difficulty level	3 (38%)
Small, motivated student groups	4 (14%)	An active role for students	3 (38%)
		Good facilitator performance	3 (38%)
		Flexible timetable	2 (25%)
		Good planning	2 (25%)
		Work after visit	1 (13%)
		Prepared programs from which teachers can choose	1 (13%)
		Small groups	1 (13%)
		Audio equipment	1 (13%)

4.4. Mathematics at the companies

The questionnaire for companies asked respondents to specify the content areas of mathematics that workers need to carry out their duties. These multiple choice questions allowed respondents to choose several options; they were also asked to give an example of each content area. Table 9 presents their responses.

Table 9. Companies’ views of types of mathematics needed by their workers; the percentages refer to how many companies indicated that their workers needed the content area (N = 29).

Content area	f	Example
Numbers and operations	26 (90%)	Tender calculations
Thinking skills and methods	24 (83%)	Design of new products
Statistics	22 (75%)	Monitoring of office hours and machine time
Geometry	21 (71%)	3D modelling
Programming	20 (69%)	Machining
Functions	12 (41%)	Calculation with heat transmission
Probability	11 (38%)	Fatigue
Equations	10 (34%)	Strength calculation
Producing of written mathematical text	9 (31%)	Reports

Every key content area in mathematics (C1: thinking skills and methods; C2: numbers and operations; C3: algebra; C4: functions; C5: geometry and C6: data processing, probability and statistics) in degrees 7–9 in the Finnish core curriculum (Finnish National Board of Education, 2016) are useful at least in some companies. Specifically, programming and producing written mathematical text are an essential part of the workers’ competence. The most general area of mathematics referred to by the companies was numbers and operations (f = 26, 90% of companies). This content area is useful, for example, in tender calculation, pricing, financial administration and production. Thinking skills and methods (f = 24, 83%) are especially important for company management and the design of new products. Statistics (f = 22, 75%) and geometry (f = 21, 71%) provide tools to work in many units. It is important to be able to make decisions based on statistics and to understand technical drawing. More than half of the companies named programming as part of their workers’ duties. Machining, automation designing and embedded system are a commonplace need at many companies. Functions and probability are used by workers at about one-third of companies.

4.5. Reflection about the MyTech project as a case study

This subsection presents a case study about the MyTech pilot project and project study visits from the viewpoints of structure, relevance, targets for development and mathematical content. In the MyTech program pilot, Technology Industries of Finland offered a school class the opportunity to visit a technology company and a university as part of their project work. The planning of the robotics project started with a meeting in which the mathematics teacher and the guidance counsellor of the test class, the researcher and a representative from the study visit laboratory at the university discussed the targets, schedule and structure of the project. The contact person at the company participated in the planning only over e-mail.

Figure 3 presents the structure of the visits. The size of the entire student group was 19, divided into two for the university visits. The university researchers split up these groups into two even smaller groups that were comprised of only four or five students; consequently, every student was able to work with two different robots. All the students went on a single company visit. One group of ten students started with the company presentation and a tour of the factory while another group of nine worked with robots. The groups then switched tasks.

Figure 3. The structures of the visits to the university and the company.

The researcher observed that the students were prepared for the study visits due to their project work in school and that the work continued after the visits. Thus, the study visits were not unconnected to the curriculum. Because the group size was small, it was possible for the students to be very active during the study visits. They worked concretely with industry robotics. Additionally, the study visits had a clear focus and goal.

In an interview after the entire project, the mathematics teacher emphasized the meaningfulness of the study visit from the perspective of guidance counselling and practical work. The entire project, including study visits, developed students’ competence for working life in areas like teamwork and time management skills. Additionally, the teachers considered the project’s mathematical problems to be important because the exercises forced students to think instead of using information learned by rote.

Students were also asked their opinions of the project and especially emphasized that the visits were meaningful. Their attitude toward study visits was very positive (Figure 4), but their view of the work at school was more neutral.

Figure 4. Students’ views on parts of the project work (N = 19).

Based on the interview with the teacher, the biggest problem was instructing. The study visits were not challenging, but it was difficult to instruct students and groups during project work at school. The researcher observed that the most important development target was closer cooperation between the teacher, the company and the university. Although the parties met before the project work and the study visits, it would have been valuable to discuss more thoroughly how to create a coherent whole. The study visits were linked with the project work at school, but the visits were not an essential part of that work.

The project included lots of mathematics outside the curriculum, like graph theory and the 3D coordinate system (see Table 10). During the project, the groups also became familiar with the Pythagorean theorem and algorithmic thinking, which are parts of the curriculum.

Table 10. Achievement of mathematical learning goals. The column ‘students’ opinion’ reports the number of students who reported learning that item during the project. The last two columns describe the number of students who earned at least half points or full marks, respectively, on the test that measured learning goal achievement (N = 19).

Mathematics	Students’ opinion	At least half the points on the test	Full marks on the test
3D coordinate system	8	7	2
Pythagorean theorem	7	16	11
Graph theory	3	19	19
Algorithmic thinking	0	16	2

The depth and richness of the mathematics used varied between groups, as each group focused on the mathematics that was relevant in its project. There may be some areas where their only exposure to a given part of mathematics was listening to their classmates’ presentation.

5. Discussion

Taken together, the results suggest that study visits have the potential to be a valuable and effective part of mathematics education; both teachers and companies realize their importance. The most pressing need for companies is to influence students’ career choices, while teachers want to create concrete and authentic learning environments. Both parties understand the added value that they obtain from study visits. According to the case study, students also consider study visits to be meaningful.

The same challenges that Morag and Tal (2012) found arose in the present study. Many companies receive visitors, but there are problems in planning the visits and the connection between visits and the work done in school. Both parties hope for closer cooperation with one another; such cooperation is essential if study visits are to be meaningfully linked with the curriculum. The work at technology companies includes a great deal of mathematics, including content that is part of the Finnish core curriculum for basic education. A better dialog between teachers and companies could make an authentic learning environment for studying mathematics a reality.

PBL can be a way to find the link between working at school and at a company. In PBL, the learning objectives must be clear (Krajcik & Blumenfeld, 2006; Larmer et al., 2015); these objectives are also important in non-formal learning (Garner et al., 2014). The achievement of the objectives requires structure and advance planning.

Based on the study, the following suggestions are offered:

• There should be close cooperation between teachers and companies in planning.

• Study visits should be part of working at school (e.g. project work) before and after the visit and connected with the curriculum.

• Visits should have clear objectives.

• Students should have an active role.

• There should be appropriate mathematical content.

These suggestions are adapted from Orion and Hofstein’s (1994) basic structure for study visits and incorporate the insights obtained in this study.

It would be interesting to investigate how to increase students’ opportunities for influence without affecting the achievement of learning objectives. Now, the project instructions were quite closed. If pupils had an influence on a choice of visit place or subject, would their motivation increase?

The MyTech program of Technology Industries of Finland tries to facilitate the cooperation that is needed. Teachers choose a technology company near their school from a list in which companies indicate what they provide for schools. The companies also find support to plan the content of study visits so that students’ have an active role in the visit. The COVID-19 pandemic has increased the number of virtual study visits (My Tech). The structure of these visits may differ in important ways, an issue it is worth studying.

The most important limitation in the present study is the sample; especially among teachers, the sample size was small. The samples were also selected rather than chosen at random. The teachers and companies who answered the questionnaire were already interested in study visits or project work. The student group in the case study was technologically oriented. The data were also collected in a specific educational context in Finland, which limits the degree to which the results can be generalized.

Additionally, the study focuses on the mathematical objectives of study visits and dismisses the objectives in the twenty-first-century skills (Partnership for 21st Century Skills, 2021). Despite these issues, the work presented can be a springboard for further research.

Acknowledgements

Elina Viro would like to thank Chief Specialist Birgitta Ruuti at the Technology Industries of Finland LUMA Centre Finland, Daranee Lehtonen and Jorma Joutsenlahti at Tampere University and LUMA Centre Finland for their cooperation.

Disclosure statement

No potential conflict of interest was reported by the author.