## 2 Theoretical Background
### TPACK Framework
#### 2.2.2 TPK-Reasoning  
TPK refers to the integration of technology in teaching and learning processes, and is subject-specific, as is TPK reasoning. Learner engagement and motivation may be why a teacher selects dLMs (TPK-1) [27; 45; 46; 54; 55; 56; 57]. In addition, learner motivation is also linked to improved student learning outcomes [6; 37; 41; 48; 51]. Moreover, dLMs can potentially support students' self-regulated learning processes (TPK-2) [41; 44; 54; 55; 57; 58; 59]. In addition, dLMs can enhance discovery learning (TPK-3) [14; 41; 44; 45] or be customized for learners, thus promoting differentiation and inclusion (TPK-4) [3; 14; 37; 41; 44; 45; 46], which could be reasons for their selection.  
Also, applying dLMs in assessments may positively impact teachers' efficiency (TPK-5) and can be a consideration in their selection [1; 9; 26; 45; 55]. On the other hand, dLMs may distract learners from the learning objective (TPK-6), which could be a reason for not selecting them [9; 38; 45; 57].  
Considering the multifaceted reasoning involved in \"selecting dLMs\" and the significance of this facet of digital competence for pre-service teachers, single- and multiple-choice items appear methodologically inadequate for assessing it. The evaluation of teaching approximations [11; 45], which necessitate \"selecting dLMs\" but do not allow for assessing the underlying reasoning, is similarly insufficient. In addition, their instrumentation is also time-consuming. Evaluating (fictitious) lesson plans requires \"selecting dLMs\" and can uncover the rationale, but it is also time-intensive for evaluators [11].  
We argue that open-text items for assessing \"selecting dLMs\" can capture the reasoning, are more time-efficient for evaluators, and are better suited than the frequently used TPACK self-assessments [11; 18].  
A literature review, focusing on the selection of digital resources, and particularly \"selecting dLMs\", further supports this approach and identified a methodological and empirical research gap regarding objective, reliable, and valid open-text items for its assessment [11]. Consequently, we focused on the following research objectives and questions:  
**Research objective one:** Design of open-text items for assessing \"selecting dLMs\".  
**RQ 1.1:** Are the designed items and scoring for assessing \"selecting dLMs\" objective, reliable, and valid?  
In addition, we are interested in how the measurement results of the present instrument for \"selecting dLMs\" compare to the results of the frequently used TPACK self-assessments [32]. We also want to see if the open-text items are sensitive to educational characteristics [60; 61] and what the relationship is between the instruments' items (see Table 2). Based on this objective, we pose the following:  
**Research objective two:** Empirical investigation of pre-service mathematics teachers using the new instrument to assess \"selecting dLMs\".  
**RQ 2.1:** Can the designed instrument for \"selecting dLMs\" assess different levels regarding the number of semesters of study, and are the results distinguishable from TPACK self-report results?  
**RQ 2.2:** What is the relationship between the designed items?  
**RQ 2.3:** What specific reasoning is considered when \"selecting dLMs\"?