**3.1 Method**

A qualitative research design is best suited to answer the research question in order to ensure the subject-relatedness and subjective assessments of teachers on this issue. An expert survey was chosen as the research method, which was conducted in the form of guided interviews. A guideline enables a partial standardization and comparability of the individual interviews [33, 34]. The quality criteria of qualitative research, according to Mayring [34], were observed in the presented study.

The study was conducted in spring 2022, i.e., after the end of the distance learning phases. [11].

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

#### *3.1.1 Study participants*

To answer the research question, an attempt was made to select a representative sample. According to Hug and Poscheschnik [33], a sample is representative if it reflects the population in terms of essential characteristics. This resulted in several characteristics related to the sample.


Due to the limitations of the research field based on the aforementioned criteria, nine female teachers from four Austrian provinces finally participated in the study.

What is interesting about the sample is that one teacher manages a public school and leads a class at the same time. A second teacher does not teach herself but manages a school with a total of 12 classes. In this school, half of the classes are taught by teachers with Montessori training, while the other half of the teachers have not had Montessori training [11].

**Table 1** shows an overview of the participants and whether they were teaching an elementary class or managing a school and in which Austrian region they were working:

Due to the selection criteria, especially based on their training (elementary school teaching degree, Montessori training) of the teachers participating in the study, they can all be called experts. Thus, they can be recognized as having expert status in their field of activity [33, 35].


#### **Table 1.** *Overview of the participants.*

#### *3.1.2 Survey tool*

The interviews with the experts were conducted as guided interviews. This method restricted maximum openness, allowing for all possibilities and expressions. The guide was designed to still allow for openness, but still be as structured as possible [35]. The guide consists of exploratory questions, guiding questions relevant to answering the research question, and the opportunity to ask ad hoc questions if the course of the interview necessitates it [34].

The questions about the subject area of mathematics arose from the research area presented [4, 12, 14, 26, 27, 30]. Teachers were asked about what materials they used prior to the conversion of instruction to distance learning and what role action orientation played in their mathematics instruction. Another question was related to the implementation of mathematics instruction during the distance learning phase. Finally, teachers were asked how they experienced the development of their students' mathematical performance and what conclusions they could draw from it [11].

#### *3.1.3 Evaluation of the data*

The interviews were conducted as video conferences via Zoom, recorded, and subsequently transcribed. The transcripts were subjected to a comprehensive data analysis and evaluated in a rule-based and theory-based manner. The qualitative content analysis according to Mayring [34] was applied. In order to be able to compare the statements of the interviews with each other, categories were deductively formed, which resulted from the questions [11].

#### **3.2 Results of research**

In order to trace the development of teaching from face-to-face teaching before the school closures through the different phases of distance learning, the teachers described their teaching, specifically including their mathematics teaching [11].

Prior to the school closures, all teachers interviewed facilitated open instruction, although to varying degrees. In no class, frontal teaching was mentioned as the primary method of instruction. All students of the interviewed teachers had many opportunities during open lessons to work on, practice, repeat, and consolidate mathematical lesson contents in an activity-oriented way with Montessori materials, but also with other didactic materials. Although the teaching of the interviewed teachers was very heterogeneous, child-centered, action-oriented, open teaching was important to all teachers [11].
