## 5 Discussion
### Discussion Research Objective One: Design of Open-Text Items for Assessing \"Selecting dLMs\"
Given the economics of pre-service teacher assessments, a decision must be made regarding the assessment type and the time required. We suggest that our approach using four items offers a more time-efficient method and may not be as comprehensive as other, more time-intensive approaches, like the evaluation of lesson plans. To summarize, concerning research question 1.1 and the overall research aim one, it can be concluded that (1) the four-item instrument satisfies the necessary criteria for objectivity, reliability, and validity in evaluating \"selecting dLM\". It can also be concluded (2) that the instrument provides an economical way to assess a \"competence facet\", namely \"selecting dLM,\" and TPACK reasoning. Hence, we position \"selecting dLMs\" within the TPACK component (see Figure 1). Discussion Research Objective Two: Empirical Investigation of Pre-Service Mathematics Teachers Using the New Instrument to Assess \"Selecting dLMs\"  
Regarding research question 2.1, the results show that the instrument can distinguish between levels of teacher preparation based on academic progression. Pre-service teachers with fewer semesters of study score lowest and have less ability to describe the learning content a dLM intends to deliver, place the learning content in the curriculum, and justify their selection of dLM--they have a lesser level of \"selecting dLM\". These results are consistent with the literature [9; 60]. However, the results of the ANOVA showed a small effect size (\(f=0.26\)) regarding academic progression. This may be due to other factors being at play, such as the university curriculum and coursework [14; 74], participants' previous experiences [9; 75], motivation, and attitude toward technology [42; 76]. In addition, other studies assessing digital competence using the TPACK framework, such as evaluating lesson plans, also do not consistently find or report different levels of TPACK [19; 77; 78]. In addition, comparing the effect size of assessing \"selecting dLMs\" objectively and the effect size of self-reported TPACK [32], concerning academic progression, showed differences. However, the differences were minor (\(f=0.26\) versus \(f=0.23\)), indicating that the objectively evaluated \"selecting dLMs\" performance parallels the self-reported TPACK [32] performance regarding academic progression. This aligns with the goals of educational institutions to equip pre-service teachers with competence and confidence in their abilities [12; 33]. Further regarding research question 2.1, the objective results for pre-service teachers at both universities indicate room for improvement in \"selecting dLMs\". Even the median scores of the subpopulations with the highest performance are less than half of the maximum. The low results for pre-service teachers at the beginning of their teacher education could be attributed to their entry dispositions [33]. Nevertheless, the overall low results for pre-service teachers in higher semesters could stem from the learning opportunities and outcomes of teacher education regarding \"selecting dLMs.\" In addition, some of the low results could also be explained by participants' beliefs about teaching with technology [76], or their voluntary participation in the online tests [21; 79]. Regarding research question 2.2, the results show that the statistical dependence of content knowledge (items 1-3) and sound reasoning (item 4), as revealed by the Spearman correlation, is consistent with the widely accepted notion that competence depends on (content) knowledge [11; 36; 41]. However, given the small effect size (\(r_{s}=0.17\)), this relationship may not be as strong as the literature assumes concerning \"selecting dLMs\" and the four-item instrument. For research question 2.3, the type of reasoning when \"selecting dLM\" for dLM1 revealed that only a few participants (6.3% in Study 2, see Figure 3) argued at the TPACK level or used multiple TCK or TPK reasoning.