**2. Literature review**

In order to consider the theoretical foundations of the research field, it is necessary to deal with mathematics education in Austrian elementary schools. This is constantly confronted with changes and new requirements. For example, the implementation of educational standards and competence orientation took place in 2012. Starting in the school year 2023/24, there will be new curricula that are based on the current state of research and are designed to focus on competence orientation and action orientation [3]. The current state of research and the events resulting from the necessary school closures during the COVID-19 pandemic will be discussed in detail subsequently.

#### **2.1 Mathematics instruction in elementary school in Austria**

International comparative tests [4] have shown for years that the mathematical competencies of Austrian students do not match the level of students in other countries. The question, therefore, arises as to what mathematics instruction students need in order to improve their competencies in mathematics. Research like that of Krajewski [5] emphasizes the importance of mathematical precursor skills already at preschool age and of basic mathematical competencies in the first years of schooling. For example, Krajewski [5] was able to show a connection between children's understanding of number concepts in preschool and performance in mathematics as a subject several years later. In order to be able to build up sustainable basic ideas in all mathematical areas, but especially an idea of numbers and quantities, children need many experiences with didactic materials. For Kuntze [6], it is of great importance that the children actively deal with these materials and can act with them. These materials, in turn, can be mapped in the next step, translated into a pictorial representation, and later into a symbolic representation. The connection of action, illustrations, linguistic expressions and symbolic representations enables the development of sustainable ideas and insight into mathematical laws [7, 8]. It is essential that the children develop inner conceptions of the actions through the active, acting engagement with didactic materials, which are essential for further abstractions. For Lorenz [9], mathematical learning processes are based on these actions and mathematical thought structures are precisely these internalized actions. In order to successfully build up these mental images, it is necessary to select suitable materials. As an example of didactic materials for the development of a sustainable understanding of numbers and place values, decimally structured materials can be mentioned, such as those that Montessori made available to children as early as preschool age [10].

#### *The Importance of Activity-Based Learning for Mastering Mathematical Tasks during Distance… DOI: http://dx.doi.org/10.5772/intechopen.113303*

The development and training of the child's senses was of great importance to Montessori because, with them, the child grasps its environment and learns to find its way in it. In the course of his development, the child is confronted with an infinite number of sensory impressions and objects. However, the properties of these objects are limited, which makes it necessary for the child to learn to distinguish and order these properties. For Montessori, there is a connection between this ordering of properties and the development of a mathematical understanding. Montessori refers to this need for structure and order as the "mathematical mind" [10]. She developed didactic materials to best support and encourage children's mathematical development and education. Central to these materials is that the children are given the opportunity to actively engage with mathematical content, which can lead to a deeper understanding of mathematical content.

The materials developed by Montessori cover all mathematical areas of arithmetic and geometry. They are designed in such a way that the level of abstraction increases, allowing children to eventually succeed in detaching from the material [4, 10, 11].

Current research shows that students who have the opportunity to explore mathematics with materials designed by Montessori in the mathematics classroom show positive skill development [4, 12–14]. In a longitudinal study, Apfler [4] investigated whether there is a difference in the level of competence in mathematics when students in public elementary schools are taught by teachers with or without Montessori training. At the end of the third school year, those students taught by teachers with Montessori training showed significantly higher levels of competence in the competence areas of working with numbers and communicating. Whether there is a relationship between the higher level of competence and Montessori education cannot be clearly demonstrated with this study. Nevertheless, it was found that the teachers with Montessori training used a variety of Montessori materials, especially for building a viable understanding of numbers in small number spaces and for an understanding of the decadal system.

As an example of a material for building a sustainable understanding of numbers and operations, the Golden Bead material can be mentioned. In this material, which represents the decadic system, the ones is represented as a bead. The ten is represented as a bar with ten individual beads joined together. The number 100 is represented by ten tens bars joined together. The thousand is represented by a cube consisting of ten plates of hundreds. The beads can also be replaced by small cubes, as shown in the following **Figure 1**.

In the active confrontation, the students place quantities and numbers with this bead material and thereby recognize the decadic structure of the number system under the guidance of the teacher (see **Figure 2**).

However, not only numbers and quantities but also arithmetic operations can be placed and understood with this material. **Figure 3** shows how students use the bead material to place a division. Here, the total quantity of 642 is divided into two figures. The simultaneous notation provides insights into the algorithm of written division.

Due to the freedom of methods that the legal framework in Austria allows, teachers who have completed Montessori training can incorporate elements of Montessori education into their teaching. Studies show that in public elementary schools, the concept of Montessori education is not implemented in its entirety, but individual elements are used. The materials in mathematics are often used by Montessori teachers to enable the children to actively engage with the materials. Comparing the findings of current research in the field of mathematics didactics, it can be seen that the methodological approach of Montessori education is consistently confirmed [4, 15].

**Figure 1.** *Material for building the decadic number system.*

**Figure 2.** *Number sets with the decadic material.*

Of course, digital media do not yet play a role in Montessori's writings. Nevertheless, it must be questioned whether the use of digital media can also be justified in Montessori classes in the 21st century. Thus, Burow [16] also pleads to supplement the prepared learning environment, which in Montessori classes consists of analog materials, with digital offerings and virtual learning spaces, but not to replace them. The importance of action orientation, active doing, and acting engagement with the environment is thereby maintained, but expanded.

*The Importance of Activity-Based Learning for Mastering Mathematical Tasks during Distance… DOI: http://dx.doi.org/10.5772/intechopen.113303*

**Figure 3.** *Written division with the decadic material.*

#### **2.2 Distance learning in Austria**

As in many other European countries, schools in Austria were closed in March 2020 due to the COVID-19 pandemic. Teachers only had the weekend to change lessons to distance learning. The Ministry of Education gave instructions not to develop any new subject matter during the first weeks of the school closures but only to practice, repeat and consolidate already known content [17]. This situation, unique in Austrian history [18], was an attempt to fulfill the educational mission of schools even during the pandemic [19]. In the course of the next almost 3 years, schools were permanently confronted with new demands and framework conditions and were challenged to always adapt to the circumstances in a new and flexible way.

Schools were repeatedly closed for several weeks in 2020 and 2021, and students were cared for at home by parents. Teachers in the elementary schools primarily prepared workbooks in print format, which parents picked up from school, worked on with the children at home, and brought back to school at the end of the week. Teachers corrected students' work over the weekend and prepared the papers for the next week. Especially in elementary school, few digital offerings were used [17, 20].

Teachers played a special role in the design of distance learning. As has been confirmed in studies on face-to-face learning [21], teachers also had the most effective influence on student learning in distance learning [22]. Teachers were particularly challenged by the ever-changing environment. They had to completely change how they had been teaching, which meant significantly more time spent on school-related work [17, 23]. Despite the high workload, which resulted mainly from the lack of experience with distance learning, elementary school teachers showed a high level of commitment [24]. In addition to the high workload, teachers perceived the feeling of permanent accessibility and the dissociation of professional and private life as stressful. How teachers coped with the transition to distance learning was a function of their digital competencies and previous teaching styles. A large proportion of teachers tried to take their face-to-face teaching styles and map them digitally during distance learning. This was especially difficult for those teachers who typically work in a reform pedagogical, holistic, and student-centered manner [23].

The impact of school closures on children and young people has been enormous, but the long-term effects are not yet even foreseeable [25]. In addition to social and psychological symptoms among the children and adolescents, negative effects on learning development were evident early on. Particularly, educationally disadvantaged children achieved hardly any learning gains during distance learning. In the

Netherlands, for example, which has a high standard of schools compared to Austria, "The findings imply that students made little or no progress while learning from home, and suggest losses even greater in countries with weaker infrastructure or longer school closures" [26]. There are currently few studies for Austria, but they show that there are scissor effects in the development of basic cognitive skills and that many children have large gaps [27]. Unfortunately, the results of the IKM Plus study, which will be conducted nationwide in spring 2022, are not yet available.
