Open Access

Developing and validating a technology-based diagnostic assessment using the evidence-centered game design approach: an example of intrapreneurship competence

Empirical Research in Vocational Education and Training20179:6

https://doi.org/10.1186/s40461-017-0049-0

Received: 14 November 2016

Accepted: 17 February 2017

Published: 14 March 2017

Abstract

Background

Educational experts commonly agree that tailor-made guidance is the most efficient way to foster the learning and developmental process of learners. Diagnostic assessments using cognitive diagnostic models (CDMs) have the potential to provide individual profiles of learners’ strengths and weaknesses on a fine-grained level that can enable educators to assess the current position of learners. However, to obtain this necessary information a strong connection has to be made between cognition (the intended competence), observation (the observed learners’ responses while solving the tasks), and interpretation (the inferences made based on the observed responses of learners’ underlying competencies). To secure this stringent evidence-based reasoning, a principled framework for designing a technology-based diagnostic assessment is required—such as the evidence-centred game design (ECgD).

Aim

With regard to a diagnostic assessment, three aspects are of particular importance according to the ECgD approach: (I) the selection of a measurable set of competence facets (so-called skills) and their grain-size, (II) the constructed pool of skill-based tasks, and (III) the clear and valid specified task to skill assignments expressed within the so-called Q matrix. The Q matrix represents the a priori assumption for running the statistical CDM-procedure for identifying learners’ individual competence/skill profiles. These three prerequisites are not simply set by researchers’ definition nor by experts’ common sense. Rather, they require their own separate empirical studies. Hence, the focus of this paper is to evaluate the appropriateness and coherence of these three aspects (I: skill, II: tasks, and III: Q matrix). This study is a spin-off project based on the results of the governmental ASCOT research initiative on visualizing apprentices’ work-related competencies for a large-scale assessment—in particular, the intrapreneurship competence of industrial clerks. With the development of a CDM I go beyond the IRT-scaling offering the prerequisites for identifying individuals’ skill profiles as a point of departure for an informative individual feedback and guidance to enhance students’ learning processes.

Methods

Therefore, I shall use a triangulated approach to generate three empirically based Q matrix models from different sources (experts and target-group respondents), inquiry methods (expert ratings and think-aloud studies), and methods of analyses (frequency counts and a solver–non-solver comparison). Consequently, the four single Q matrix models (researchers’ Q matrix generated within the task construction process and the three empirically based Q matrix models) were additionally matched by different degrees of overlap for balancing the strengths and weaknesses of each source and method. By matching the patterns of the four single Q matrix models, the appropriateness of the set of intrapreneurship skills (I) and the pool of intrapreneurship tasks (II) were investigated. To identify and validate a reasonable proxy for the task to skill assignments for selecting the best fitting Q matrix model (III), the single as well as the matched Q matrix models where empirically contrasted against N = 919 apprentices’ responses won and scaled up within the ASCOT-project using psychometric procedures of cognitive diagnostic within the DINA (Haertel in J Educ Meas 26:301–323, 1989) model.

Results

The pattern matching resulted in a set of seven skills and 24 tasks. The appropriateness of these results was emphasized by model fit values of the different Q matrix models. They show acceptable up to good sizes (SRMSR between .053 and .055). The best fitting model is a matched Q matrix of which the match is not that strict or smooth with regard to the degree of overlap.

Conclusions

The study provides a principled design for a technology-based diagnostic assessment. The systematic and extensive validation process offers empirical evidence for (I) the relevance and importance of the specified intrapreneurship skills, (II) tasks prompting the intended skills, and (III) the sophisticated proxy of real cognitive processes (in terms of the Q matrix), but also give hints for revision. This—within a diagnostic assessment—preliminary work aims at identifying the best-fitting Q matrix to enable the next step of depicting learners’ individual strengths and weaknesses on a sound basis.

Keywords

Diagnostic assessmentCognitive diagnostic assessmentPrincipled assessment designEvidence-centered designTechnology-based assessmentVocational education and training intrapreneurship

Background

Arising from different research streams we know that informative feedback, guidance etc. is the most efficient method for fostering and supporting learners’ learning and development processes and outcomes (Hattie 2012). It has therefore become a decisive competence facet within teacher standards around the world: in Germany (KMK 2004), in Switzerland (Oser 1997) and internationally (Interstate Teacher Assessment and Support Consortium 2011). In the workplace learning literature, comparable concepts are discussed, for example, “guidance” by Billett (2002) or “learning support” by Tynjälä (2013). But how can one do this? In order to realize such fine-grained and informative feedback, the various authors suggest (a) addressing the learners where they currently are, (b) working out their strengths and weaknesses to support them individually, according to their particular needs, and (c) designing, adapting and delivering tailor-made instructions and opportunities to learn. But how can one discover such individual information? Currently, most educators rely on test scores to differentiate between high and low achievers within the group of learners. When the average percentage of low achievers has not reached the class or course goal more support is necessary. Therefore, the majority of educators continue with teaching and assessing the whole pool of tasks. Some other educators are applying item response theory (IRT) to obtain information about learners’ abilities corresponding to item difficulty. This information enables the educator to keep teaching and training on that particular task that has been identified as difficult. The educator can also work further with clearly identified groups on particular achievement levels and collections of tasks with the corresponding difficulty in order to strengthen the ability of the students on that particular achievement level and to guide them to the next performance level.

However, on the basis of assessments using the cognitive diagnostic model (CDM; e.g. Roussos et al. 2007) (hereafter referred to as “diagnostic assessments”), educators can obtain feedback on a much more informative and fine-grained level. This feedback includes information about (a) the percentage of the whole group of learners mastering a specific competence facet (skill), (b) the percentage of different groups of learners with equal profiles of strengths and weaknesses (skill classes), and (c) individual competence profiles for each learner, which entails information about particular competence facet(s) a learner is lacking or has weaknesses in, but also his/her particular strengths which were used to solve the tasks (individual skill profiles) (Helm et al. 2015). CDMs are able to fulfil the entitlement of a plurality of politicians, scientists, teachers, trainers, and other stakeholders of educational research that assessments can be used as a tool for instructional design and for directly supporting learning by evidence-based informative feedback (e.g. Helm et al. 2015; Nichols and Joldersma 2008). Therefore, this type of assessment analysis can be used to describe examinees’ capabilities, explain examinees’ level of performance, allow customized instruction tailored to examinees’ abilities, screen examinees for further advancement or for other selection purposes, and to classify learners into different groups (so-called skill classes) according to indicated skill states (Leighton and Gierl 2007).

However, independent from the intended assessment information (e.g. achievement levels on the basis of IRT or individual competence profiles on the basis of CDMs) assessment experts are generally in agreement that a principled assessment design is desperately needed to make valid interpretations on learners’ underlying competencies, on the basis of observable problem-solving activities (Pellegrino 2010; Shavelson 2012; Wilson 2005). The assessment triangle (Pellegrino et al. 2001), as a crucial assessment design concept, is based on the rational of evidence-based reasoning and links three corners in a coherent manner: (A) the cognition corner, (B) the observation corner, and (C) the interpretation corner. The cognition corner (A) provides claims about learners’ underlying latent competencies in the domain of interest which is defined within the curriculum. A coherent observation corner (B) provides a set of assumptions about the kind of situations and tasks that are needed to prompt learners to use the claimed latent competencies by showing the proposed evidences. The interpretation corner (C) represents the most suitable statistical model (mostly still imperfect) to translate examinees’ responses (observation) into helpful intended information on learners’ competence (cognition). A practical step by step approach to implement ideas of the assessment triangle is the evidence-centered design (ECD: Mislevy and Haertel 2006; Roussos et al. 2010), more specifically the evidence-centered game design (ECgD: Mislevy et al. 2014) for technology-based learning and assessment environments. Authors of the ECgD framework structure their process in three parts. Part 1 involves an extensive “domain analysis” and the “domain modelling” to identify “big ideas” of acting and learning in that particular domain. Part 2—the core of the framework—is focused on the assessment development by defining and evaluating the three components of the “conceptual assessment framework”: (A) the competence model (cognition corner), (B) the task model (observation corner), and (C) the statistical model (interpretation corner). As depicted by the added brackets, as well as in Fig. 1, the three components of part 2 of the ECgD correspond with the three corners in the assessment triangle. Finally, the sounded assessment can be implemented in practice to deliver the intended feedback information (part 3).
Fig. 1

Combining the assessment triangle and the evidence-centered (game) design for an application to cognitive diagnostic models

(adapted from Pellegrino et al. 2001, and de la Torre and Minchen 2014)

Applying the principled assessment design ideas of the ECgD to diagnostic assessments using statistical CDM procedures three crucial characteristics are important to consider (Roussos et al. 2007; Rupp et al. 2010): (I) their underlying deep level of grain-size expressed by domain-specific skills (Rupp et al. 2010), (II) their skill-based constructed tasks, which are able to prompt these intended skills (de la Torre and Minchen 2014), and (III) their need for a substantive assignment of skills to tasks expressed within a so-called Q matrix (Tatsuoka 1983). Skills (I) are fine-grained facets of a competence. Following the principles of the ECgD implies that an intended interpretive argument on a fine-grained skill level requires a sounded specification of a manageable set of skills on the basis of the competence model (A). On a coherent level of grain size, tasks (II) have to be able to prompt these intended skills, so that their construction has to be fundamentally diagnostic. Consequently, skills (I) connect the competence model (A: cognition corner) and the task model (B: observation corner) by being the target for the task (II) development. The Q matrix (III) is a specific need for psychometric models of the CDM family, wherein the task to skill assignments are specified. That means, for each task it has to be identified which skill(s) is/are intended to be measured by a particular task. Because it describes hypothesis about variations in task performances, the statistical model (C: interpretation corner) is linked to the task model (B: observation corner) of the assessment triangle (Fig. 1).

State of the art in diagnostic assessments

At present, there are only a rare number of diagnostic assessments fitting the assumptions of principled assessment design and the use of psychometric models of the CDM family (de la Torre and Minchen 2014). Existing diagnostic assessments that work effectively capture small and scientifically well-researched constructs of primary school curricula like “fraction subtraction ability” (e.g. (de la Torre 2008; de la Torre and Douglas 2004; Leighton et al. 2004; Tatsuoka 1983), “reading comprehension ability” or “listening comprehension ability” (Jang 2009; Li and Suen 2013; Sawaki et al. 2009). The alternative application of originally IRT-based assessments for diagnostic purposes (so-called retrofitting studies) yield continuously unacceptable diagnostic classification results (Gierl and Cui 2008; Leighton et al. 2004). These unsatisfactory consequences can mostly be justified by the unique nature of diagnostic assessments (I: fine-grained skills; II skill-based constructed tasks, and III sounded Q matrix) missing a principled assessments design (e.g. ECgD) for diagnostic purposes (Habermann et al. 2008; Rupp and Templin 2008). This is because a diagnostically measureable set of skills (I), a successfully working pool of tasks (II), and a correctly specified Q matrix (III) cannot easily be determined by using a certain source (e.g., researchers or experts), a certain method of inquiry (e.g., document analysis or expert rating), or a certain method of analysis (e.g., counted frequencies of expert ratings) (Kunina-Habenicht et al. 2012). For this reason, the process of development and validation of diagnostic assessments’ crucial aspects (I: skills, II: tasks, and III: Q matrix) requires special study.

Diagnostic assessment for intrapreneurship competence

In contrast to existing diagnostic assessments for well-defined domains, in this study I emphasise intrapreneurship (IP) as a professional competence that is much more complex and transferable for work and life (so-called twenty first century-skills: Pellegrino 2014; Pellegrino and Hilton 2012; Weber et al. 2014). With the exception of the work of Weber and colleagues (2014, 2015, 2016a, b) within the ASCOT1 research initiative, intrapreneurship has been subject to little research to date. Therefore, I refer to their work where IP competence has been conceptualized, operationalized, and scaled up by IRT procedures with the purpose of comparing groups within a large-scale assessment (LSA). Their assessment design also follows the steps of the ECD. At this point, all three ECD parts (1 domain analyses and modelling, 2 conceptual assessment framework, and 3 assessment implementation and delivery) have been completed. In particular, I refer to their domain analysis and modelling material, their competence model, their task model,2 and the data base of their main study.

The ASCOT project was run within the German apprenticeship program of industrial clerks. In Germany about half of all school graduates start an apprenticeship program each year (Federal Ministry of Education and Research 2014). More precisely, the target group of industrial clerk apprentices was chosen because (a) their program facilitates central job tasks in the area of business and commerce which were comparable across six European countries (Breuer et al. 2009),3 (b) a considerable amount of every-day work tasks is required for innovative behavior and project management abilities (Trost and Weber 2012; Weber et al. 2015), and (c) IP is a fixed learning goal of their official German curriculum and anchored within their oral examinations (KMK 2002).

By applying CDM procedures to intrapreneurship competence I go beyond the existing studies, because of the identification of groups with similar strengths and weaknesses and of learners’ individual skill-profiles enabling an informative feedback. As innovative behavior and IP are decisive twenty first century skills (Pellegrino and Hilton 2012) education and, in particular, vocational education and training in the field of business and commerce have to equip young people accordingly. Previous studies show that on average apprentices are already achieving IP on a medium to high proficiency levels as a result of their German apprenticeship program (Weber et al. 2015, 2016b). However, as innovative behaviour/IP competence is a decisive issue at current workplaces it should be supported by individual guidance and informative feedback to bring more apprentices up to a higher level of achievement.

Diagnostic assessment design, by using the ECgD, stresses the coherent and elaborately validated specification of several indicating factors for providing valid informative feedback information. Building on the existing materials (domain analyses and modelling) and results (competence model and task model) of Weber and colleagues, the focus of this study is to specify and evaluate the crucial aspects of a coherent diagnostic assessment design: (I) the description of a measurable set of fine-grained skills, (II) the evaluation of the pool of skill-based tasks, and building on this, (III) the identification of the best proxy of skill to task assignments (Q matrix).

Structure of the paper

After outlining the theoretical considerations of diagnostic assessments using CDM, I shall introduce the technology-based diagnostic assessment design for IP using the ECgD with particular regard to theoretical assumptions about the set of skills (I), the pool of tasks (II), and the Q matrix (III). The empirical part concerns the validation process of these aspects by capturing empirical evidence on apprentices’ underlying cognitive processes in a triangulated approach (different sources, inquiry, and analysis methods) and depicting them in three empirically based Q matrix models (instruments for pattern matching). By matching the patterns of these empirically based Q matrix models with those of researchers’ Q matrix, which were generated within the task construction process, an appropriate set of IP skills (I) and a coherent pool of tasks (II) can be identified. Because no source and no method is beyond limits it is expected that an overlap of all the theoretically and empirically constructed Q matrix models will fit apprentices’ underlying cognitive process best. By varying the degree of overlap four, so-called matched Q matrix models were constructed (as additional instruments for empirical Q matrix evaluation). Pattern matching and empirical evaluation procedure will be presented in the section analyses. Finally, the results will be summarized, discussed, and concluded.

Theoretical considerations on diagnostic assessments using cognitive diagnostic models (CDMs)

Psychometric models of the CDM family are probabilistic categorical-latent trait measurement models with the purpose of extracting multidimensional individual competence profiles (Rupp and Templin 2008). In the following, latent traits are labelled as competencies and their fine-grained operationalizations as skills. CDM characteristics share several features with traditional item-response theory models (e.g., latent trait model, probabilistic model, item-response-patterns), as well as with confirmatory factor analysis (CFA: e.g., complex loading structure, a priori defined skill to task assignments as depicted within the Q matrix). Two of the most important differences are that assessments based on IRT are mostly uni- or low-dimensional and that skills in CDMs mostly are conceptualized as dichotomous (instead of continuous) and, therefore, a person’s ability, is expressed in terms of skill-master versus skill-non-master (Kunina-Habenicht et al. 2012).

CDMs underlying idea is that the probability to be a task-solver depends on the combination of (a) the person’s skill-vector (=all skills that a person is able to master) and (b) the task’s skill-vector (=all skills that are needed to solve the task correctly).4 I am assuming here,5 that skills are non-compensable.6 That means if a person is master of all skills needed for a task, he/she has a high probability of solving this task correctly. But if he/she has a skill-deficit in at least one of the skills needed for a particular task, he/she has only a low probability of solving the task correctly. Consequently, a person with a certain skill-deficit (e.g., is not “able to work with domain specific tools”: TOOL) in its skill-vector will, for example, have a low probability of solving tasks which require the application of IP specific tools “TOOL”, irrespective of other needed skills. The other way around, a person who fails all tasks with “TOOL” in their skill-vector can be diagnosed with a high probability as a “TOOL”-non-master. Summarizing, the deterministic form of a CDM can be described as follows: if one knows a person’s state of mastery for all necessary skills for a task, then the correctness or incorrectness of the task solution for this examinee is clearly designated (Roussos et al. 2007, p. 20).

The correctness of this conclusion also depends on other factors (e.g., guessing or slipping; Roussos et al. 2007), mainly on a fundamentally diagnostic assessment model specified by the Q matrix. The importance of correctly specified Q matrices can be demonstrated by the following example of the “TOOL”-non-master: if a task’s skill-vector claims erroneously for “TOOL”, then obviously “TOOL” is not necessary for solving the task correctly; hence, the “TOOL”-non-master has—given he/she is a master of all the other skills of the task’s skill vector—a high probability of solving this task correctly. Under the assumption of a correctly specified Q matrix, the “TOOL”-non-master shows an ambivalent response pattern concerning the skill “TOOL”. That means, misspecified Q matrices have a strong impact on poor model-data-fit and, therefore, on the quality of a person’s diagnostic information.

But unfortunately this developmental step cannot easily be taken. There have been different methods used so far: (a) apply existing test specification, if a skill to task assignment already exists (Xu and von Davier 2008), (b) use eye-tracking technology which records individuals’ eye movement data during stimulus processing to understand underlying solving processes (Gorin 2007), (c) invite a group of subject matter experts to comprehend underlying cognitive processes of target groups’ task solution processes (Ravand 2015; Sawaki et al. 2009; Sorrel et al. 2016), and (d) extract skill to task assignments on the basis of target group think aloud protocols, when they solve the tasks (Gao and Rogers 2011; Jang 2009; Li and Suen 2013; Wang and Gierl 2011). Unfortunately, none of the mentioned methods are without limitations (Kunina-Habenicht et al. 2009; Li and Suen 2013). For this reason, I have used a triangulation of different sources, inquiry and analysis methods for balancing the advantages and disadvantages of each method. Because there is no existing skill to task assignment for IP tasks (a), and as eye-tracking technology is not useful for dynamic technology-based computer simulations, as is the case for the IP assessment (see also “III. Q matrix: theoretical assumptions of skill to task assignments” section) (b), the two last mentioned approaches will be applied in this study. However, how well the Q matrix will fit the data is basically dependent on (I) an appropriate specified set of skills, in combination with (II) a representative depict domain by tasks, because skills and tasks are the two elements of (III) the Q matrix. At this point, it should be noted, that due to the number of possible combinations of tasks (especially considering time restrictions), only a limited number of skills can be measured. CDM experts suggest not more than 7–10 skills, and a set of at least 15–20 tasks (de la Torre and Minchen 2014; Roussos et al. 2007).

Technology-based diagnostic assessment design for IP using the ECgD

I. Skills: theoretical assumptions of diagnosable IP skills

For specifying an initial set of skills, I refer to the competence model for IP competence developed by Weber et al. (2014, 2015, 2016a, b) on the basis of an extended domain analysis of IP in the German apprenticeship programs.7 The following “big picture” appeared for modelling IP competence, especially for diagnostic purposes. The term “IP” is defined in accordance with Perlman et al. (1988, p. 14). An IP person is an entrepreneur within a firm (Antončič and Hisrich 2001; Wunderer and Bruch 2000) who generates and initiates innovative projects and who tries to realize these ideas via project work (Korunka et al. 2009). Typical IP project themes in (apprenticeship) practice are, for example, to promote an event, to introduce a new product, to regular customers, or to run a fashion show. Representative challenges within these projects are to recognize opportunities, to generate a new project or idea, to search for and to structure information, and to plan and to work with domain-specific terms. Typical observable evidence of apprentices’ IP-specific behavior is: to select relevant information from given documents or to decide among different alternative solutions in view of disturbances (changes in markets). The underlying skills to solve tasks correctly are not compensable, meaning that a low ability (lack) of a specific skill (e.g., TOOL) of one’s person-skill-vector cannot be compensated by a high ability of another skill (e.g., INFO). Hence, persons without the skill TOOL in their person-skill-vector will fail to master this particular task, but also all other tasks which require this particular TOOL-skill. Most IP activities were computer-based by using tools for communication, calculation, word-processing, or presentation. Typical observable examples of apprentices’ intrapreneurship-specific behavior are: to create a GANTT chart on the basis of given information, to select relevant information from given documents, or to decide among different alternative solutions in view of disturbances (changes in markets). The competence model based on central assumptions for modelling professional competences as discussed in the international literature (for more details see Weber et al. 2016a, b). The model comprises three layers with an increasing depth of operationalization: six phases of IP (e.g., analyses IP situations or procure information and (IP) project planning) and the fine-grained set of fourteen multiple IP skills (e.g., arrange aspects in sequences or procure, assess, and structure information) which will be used in this study as an initial set of skills (see Table 1). An analysis of apprentices’ final exam reports (as one source of the domain analysis) delivers evidence that the listed skills are used in IP projects on apprentice level (Weber et al. 2015).
Table 1

Initial set of IP skills (in accordance with Weber et al. 2014, p. 303)

Skill number and abbreviation

Skill description

Examples for evidence

The apprentice…

1

REC

Recognize IP challenges and opportunities

…becomes aware and realizes an IP problem or chance

2

ANAL

Analyse IP situations

…analyzes the perceived IP problem or chance (explicating main and side effects, taking perspective etc.)

3

IDEA

Create an (IP-)idea

… generates a new innovative (at least an incremental) IP idea with regard to the perceived IP chance or problem

4

CREA

Use creativity techniques

…applies tools for supporting the idea-generating process

5

SEQU

Arrange aspects in sequences

…creates a GANTT-chart

6

INFO

Procure, assess and structure information

… searches for relevant information in documents or data files

7

TERM

Use of domain-specific terms and techniques

…applies, for example, a break-even-point by means of complex calculations

8

TOOL

Use of domain-specific tools

…calculates a break-even-point by means of spreadsheets

9

DEC

Reasoned decisions

…decides among alternative solutions in view of disturbances (e.g., changes in market) on the basis of concrete reasons and arguments

10

RISK

Identify and analyse risks

…assesses different risk scenarios

11

TEAM

Teamwork

…shows that he/she knows and understands central categories of team work

12

DIST

Identify and manage disturbances

…analyzes and chooses appropriate strategies when team work begins to break down or gets stuck

13

REF

Reflect on whether the project was effective

…reflects on phases, elements or the whole project and evaluates them with regard to goal achievement, appropriateness, or success (explaining things that went wrong or well etc.)

14

DEF

Distribute, defend, or introduce a project

…presents his/her IP project and persuades others to accept it

II. Tasks: diagnostic assessment tasks for the domain of IP

A valid assessment design for professional and complex competencies like IP implies an authentic modeling of the world of work where examinees can think and act as if at real workplaces (Darling-Hammond et al. 2013; Janesick 2006; Pellegrino et al. 2016; Shavelson 2012; Weber et al. 2014; Wiggins 1998; Winther and Achtenhagen 2009). Therefore, all 22 diagnostic tasks reflect typical IP situations as they were identified by domain analysis.8 Additionally, all of them were implemented into a technology-based platform (called ALUSIM Ltd.; see Achtenhagen and Winther 2014). The ALUSIM platform represents a computer-based simulated company for producing aluminum boxes and cans which is rebuilt according to an existing firm. Apprentices may have to play the role of an apprentice of ALUSIM Ltd. who works as part of IP project-teams in various situations (e.g., on time, cost or profit planning tasks) in two holistic projects: (authentic scenario 1) setting up an online shop as an additional distribution channel and (authentic scenario 2) attracting apprentices under the existing situation of shortage of skilled workers in Germany as a recruiting task (Antončič and Hisrich 2001). The simulation is equipped with realistic tools (such as a file system, client email, calculator, spreadsheet, and text processing program) and introduced and explained by video clips.

Screen shots of the technology-based implemented task 3 are presented in Fig. 2. The apprentice is sitting at his/her simulated workplace and receives, via email, the task to create a GANTT chart for setting up the new online shop-project. Attached to this email is an elaborated GANTT chart of a pre-project, the company’s internal GANTT-chart template, and the protocol of the last team meeting. The template of the GANTT chart consists of a table where the four main work packages, as well as the forthcoming months, are already registered. The apprentice has to fill out the right cells for each work package by using the spreadsheet marking function (Weber et al. 2014, p. 305). The apprentice masters the task if he/she fills out the right cells for three of the four work packages.
Fig. 2

Task example, “Creating a GANTT chart”

At an early stage of task development, the whole pool of 22 IP tasks were checked on their substantive validity (Bley et al. 2015). Construct-irrelevant cognitive load, such as confusing technology issues or wrong association provoking task formats and assignments, was revised.

III. Q matrix: theoretical assumptions of skill to task assignments

The Q matrix connects the skill-vectors of all 22 IP tasks. For specifying the skill-vectors the task constructors anticipated for each task, according to the results of the extended domain analysis and their expert knowledge on teaching and learning theories, the cognitive process an apprentice usually engages in when solving particular tasks. This first validity check was done within the ASCOT project (Bley et al. 2015). For example, to solve task 3 successfully the apprentice needs the following four skills (skill-vector 00001111000000: see Table 1). First of all, he/she has to understand and apply the economic term “GANTT-chart” (TERM: “use domain specific terms and routines”). Furthermore, he/she has to select relevant information about time issues for each work package from the team meeting protocol (INFO: “procure, assess, and structure information”) and sequence them in the right order by taking into account the required time (SEQU: “arrange aspects in sequence”). By using the marking function of the spreadsheet tool and filling out the right cells in the template (TOOL: “use domain-specific tools”), the apprentice creates finally the GANTT chart. This fine-grained construction process was done for each task and their skill-vectors were translated into the initial Q matrix (see Table 2).
Table 2

Initial Q matrix (Q-I) constructed by researchers

Task

REC

ANAL

IDEA

CREA

SEQU

INFO

TERM

TOOL

DEC

RSIK

TEAM

DIST

REF

DEF

1

0

0

0

0

1

0

0

0

0

0

1

0

0

0

2

1

0

0

0

1

0

0

0

0

0

1

0

0

0

3

0

0

0

0

1

1

1

1

0

0

0

0

0

0

4

0

0

0

0

1

1

1

0

0

0

0

0

0

0

5

0

0

0

0

1

1

1

0

0

0

0

0

0

0

6

0

0

0

0

0

0

1

1

0

0

0

0

0

0

7

0

0

0

0

0

1

1

0

0

0

0

0

0

0

8

1

1

0

0

0

0

0

0

1

1

0

0

0

1

9

0

1

0

0

0

1

1

0

0

1

0

0

0

0

10

0

0

0

0

0

1

1

1

0

0

0

0

0

0

11

0

0

0

0

0

1

1

0

1

0

0

0

1

1

12

1

1

0

0

0

1

1

0

0

0

0

1

0

0

13

0

1

0

0

0

0

1

0

0

0

0

1

0

0

14

0

1

0

0

0

0

1

0

0

0

0

1

0

0

15

0

0

0

0

0

0

1

0

1

0

0

1

1

1

16

1

1

0

0

0

1

1

0

0

0

0

0

0

0

17

1

1

0

0

0

0

1

0

0

0

0

0

0

0

18

1

1

0

0

0

0

1

0

0

0

0

0

0

0

19

0

1

0

0

0

1

1

0

1

0

0

0

0

0

20

0

1

0

0

0

1

1

0

1

0

0

0

0

0

21

0

1

1

1

0

0

0

0

0

0

0

0

0

0

22

1

1

1

0

0

0

0

0

0

0

0

0

0

0

Research questions

On the basis of theoretical considerations, an extensive domain analysis, and preliminary work in modeling the competence of IP (e.g., Weber et al. 2014; Weber et al. 2016a), a set of fourteen IP skills (I), a pool of 22 diagnostic IP assessment tasks (II), and an initial Q matrix model (III) exist. The question arises whether these specifications (skills, tasks, Q matrix) are adequate to fit the target groups’ cognitive processes and response patterns as a prerequisite for identifying learners’ individual fine-grained skill profiles for providing an informative feedback.
  1. I.

    Following the suggestions of CDM experts the set of fourteen IP skills exceeded the number of reliable measurable skills by using CDM procedures. Therefore, it needs to be evaluated which of the fourteen skills are relevant in a sufficient amount of tasks’ skill-vectors and in a unique manner. Skills which are only relevant in combination with other skills, or which are only necessary in a small amount of tasks, are statistically problematic (Roussos et al. 2007; Jang 2009). By triangulating different sources, inquiry and analysis methods, empirically based Q matrix models were constructed. These models serve, besides the theoretically based researchers’ Q matrix, as a basis for a pattern matching to specify the most important IP skills.

    RQ I: Skills: Which are the most important fine-grained IP skills?

     
  2. II.

    Taken from the other way around, it needs to be evaluated if the existing tasks are able to depict the skills of interest appropriately. Because skills and tasks are interdependent, the same Q matrix models used in RQ I serve as a basis for analysis.

    RQ II: Tasks: Are the constructed assessment tasks able to prompt the fine-grained specified IP skills?

     
  3. III.

    Research question III concerns the evaluation of the skill to task assignments. Although learners’ underlying cognitive process while solving the tasks are crucial to specify task to skill assignments (Q matrix), there is no opportunity to capture them directly. It could be assumed that a balanced match of different single Q matrix models constructed from different sources, using different inquiry methods, and applying different ways of analysis, are able to depict cognitive processes to the best available proxy of the Q matrix (García et al. 2014). Therefore, the single Q matrix models (the theoretically based researchers’ Q matrix and the three empirically based Q matrix models) will be matched by four different degrees of overlap (=matched Q matrix models). This means that the strictest match includes only skill to task assignments which were identified to be relevant in all four Q matrix models; the smoothest match includes all skill to task assignments which were identified in at least one of the four single Q matrix models. By an empirical evaluation all single and matched matrix models were contrasted.

    RQ III: Q matrix: Which Q matrix model best fits the response patterns of the target group?

     

Methods

Design

For evaluating the set of skills (RQ I) and the pool of tasks (RQ II), as well as for working out the sophisticated proxy of real cognitive processes (Q matrix) (RQ III) as the decisive prerequisite of running an effective CDM, besides the already given researchers’ Q matrix three additional empirically based Q matrix models have been constructed and subsequently matched (see also Fig. 3).
Fig. 3

Research design

Empirically based Q matrix models

The three empirically constructed Q matrix models are based on different sources [experts (E) in the field of VET and apprentices (A) at the end of their apprenticeship as target group respondents], inquiry methods [expert ratings (R) and apprentices’ think-aloud (TA) studies], and analysis methods [counting of frequencies (C) and solver-non-solver comparison (S)]. Out of this triangulation, three empirically based Q matrix models were created: (1) experts’ Q matrix on the basis of counted ratings (Q-ERC), (2) apprentices’ Q matrix on the basis of counted utterances from think-aloud studies (Q-ATAC), and (3) apprentices’ Q matrix on the basis of the significant relationship between task-solving and skill-mastering (Q-ATAS). These three empirically based Q matrix models are the basis for answering RQ I and II. Therefore, from these analyses the final set of skills and the final pool of tasks are specified.

Matched Q matrix models

RQ III is the most sophisticated endeavour. Because no source and no method (inquiry as well as analysis method) is without limitations, the four single Q matrix models (researchers’ initial Q matrix: Q-I and the empirically based Q matrix models: Q-ERC, Q-ATAC, Q-ATAS) will additionally be matched with regard to different degrees of overlap: Q-MATCH4 includes all skills which were identified to be relevant in at least one of the four Q matrix models, Q-MATCH3 includes skills which were identified to be relevant in at least two single matrix models, Q-MATCH2 includes skills which were identified to be relevant in at least three of the four matrix models, and Q-MATCH1 includes only skills which were identified to be relevant in all four single Q matrix models. Thus, these four matched Q matrix models balance the strengths and weaknesses of the single Q matrix models in different ways (triangulation process) and, furthermore, they provide, besides the single Q matrix models, additional models for specifying the best proxy for apprentices’ real cognitive processes while solving the tasks. This empirical evaluation process will be carried out by CDM procedure.

Sample

The expert sample consists of four vocational educational training (VET) school teachers and five trainers from small (<50 employees: n = 1), medium (51–250 employees: n = 1), large (251–1000 employees: n = 1), and very large (>1000 employees: n = 2) enterprises. All of the interview partners were experts with an average of more than 5 years of experience working with apprentices and more than two years of experience with IP activities. The think-aloud study was conducted with 26 voluntarily participating apprentices (12 males, 14 females). All of them were at the end of their apprenticeship in small (n = 1), medium (n = 4), large (n = 17) or very large enterprises (n = 4). Half of the participants had an intermediate level of education, while the other half had a university-level education, with an average age of 21 years (SD = 1.89). The sampling process of both groups (experts and apprentices) was facilitated by advertising and self-selection—all participants (experts and apprentices) received €40 for their cooperation.

The empirical Q matrix evaluation is based on data from the main study of the ASCOT project CoBALIT (Weber et al. 2016a). The national wide sample study was collected in 2014 in seven states (Baden-Wuerttemberg, Bavaria, Hesse, Lower Saxony, North Rhine, Westphalia, and Thuringia). Within a 4-h survey, besides the IP instrument, further business competence instruments, as well as individual and social context variables, were conducted by applying a booklet design. Out of the whole group of 2171 apprentices, a group of 919 apprentices solved the diagnostic assessment of IP. Apprentices were, on average, aged 21 (SD = 2.3). Thereof, 554 were female and 317 male; there were 48 missings. 578 apprentices have a certificate of university entrance qualification and 279 finished their secondary education (12 without completing secondary education, 50 missings). They had apprenticeship contracts with large (more than 501 employees: n = 282), medium (51–500 employees: n = 499), and small companies (1–50 employees: n = 105; 33 missings).

Analysis methods

In order to answer RQ I and II a pattern matching of the four single Q-matrix models (Q-I, Q-ERC, Q-ATAC, Q-ATAS) was carried out. On the basis of patterns’ commonalities and differences, the most important and statistically measurable skills (RQ I) will be identified, and the sufficiency and validity of the tasks (RQ II) will be evaluated.

Because of its parsimony in terms of model parameters and its non-compensatory assumption (which was basically hypothesized during the process of defining our Q matrix), the CDM DINA (deterministic input, noisy, and gate) model (Haertel 1989) was chosen for the empirical validation of the different versions of Q matrices (RQ III) in order to identify the best-fitting proxy (Q matrix). The DINA model expresses the statistical relationship between responses and skills as follows:

Deterministic model: \(\xi_{ij} = \prod\nolimits_{k = 1}^{K} {\upalpha}_{ik}^{{q_{jk} }}\)

Probabilistic model: \(P \left( {X_{ij} = 1 | \varvec{\alpha}_{i} } \right) = P\left( {X_{ij} = 1 | \xi_{ij} ,g_{j} ,s_{j} } \right) = (1 - s_{j} )^{{\xi_{ij} }} g_{j}^{{1 - \xi_{ij} }}\)

where \(\xi_{ij}\) is the response of apprentice j to task i (1 if correct; 0 if incorrect), \(\upalpha_{ik}\) specifies the existence of skill k in in the skill-profile of apprentice j (\(q_{jk} = 1\) if apprentice j is able to do skill k; \(q_{jk} = 0\) if otherwise), \(q_{jk}\) specifies the requirement for mastery of skill k for task i (\(\upalpha_{ik} = 1\) if task i requires s; \(\upalpha_{ik} = 0\) if otherwise), \(g_{j}\) is the probability to guess the task response, and \(s_{j}\) is the probability to make a mistake obviously person’s skill vector fits the task’s skill vector.

The DINA model was estimated and evaluated with the R (R Core Team 2015) package CDM (George et al. 2016). As suggested by de la Torre and Minchen (2014) most criteria that have been shown useful in the (traditional) IRT context can be adapted to CDMs. Therefore, the model fit was assessed using the following quality criteria—two indices for absolute model fit: (1) item/task pairwise χ 2 and the associated p value, as well as (2) the standardized root mean square residual (SRMSR); (3) three information criteria: AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion), and CAIC (Consistent AIC); and (4) the mean Item Discrimination Index (IDI j ). Benchmarks for evaluation were: (1) in a well-fitting model the maximal item pairwise χ 2 statistic should not be significant; (2) Maydeu-Olivares (2013) suggests that SRMSR should be smaller than .05 for well-fitting models; (3) the model with the smallest information criteria should be favored over the other models; and (4) item discrimination values close to one indicate a good separation between examinees with low and high abilities.

Instruments for pattern matching: constructing empirically based Q matrix models using different sources, inquiry and analysis methods

Information sources: experts (E) and apprentices (A)

Experts (E)

A panel of experts serves as a first source. In this case, teachers from vocational education training (VET) schools, as well as trainers from private enterprises, provide conceptual parameters for the learning domain IP in schools and on the job. Furthermore, these experts are able to determine whether the tasks reflect the underlying learning objects and required cognitive processes needed to solve them. However, a large concern is that experts’ abilities to solve the tasks is significantly higher than that of apprentices (Leighton and Gierl 2007). Additionally, there could be a high degree of variance in expert opinions, at least between the experts of two different learning settings (in school and on the job), which could be obstructive.

Apprentices (A)

A second resource is the target group of industrial clerk apprentices. The source advantage is the target level of the ability, while the disadvantage is that learners at the novice level are not usually able to assess and verbalize their used cognitive processes to solve tasks in detail. For this reason, Ericsson and Simon (1996) suggest holding think-aloud studies (TA) for extracting thinking strategies more indirectly.

Inquiry methods: expert ratings (R) and think-aloud studies (TA)

Expert ratings (R)

On the basis of their practical experience with the learning processes of apprentices in general and their IP-relevant tasks in particular, subject-matter experts are able to validate an identified set of diagnosable skills and to describe trainees’ task-solving processes and determine necessary skills per task interaction. A briefing session was held prior to the formal rating, wherein the previously skill-based task construction process was introduced. Afterwards, experts have to solve the tasks to perform the rating task. Discrepancies and related practical evidence have to be discussed.

Think-aloud studies with apprentices (TA)

Concurrent think-aloud studies have thus far enabled the best possible determination of cognitive processes while solving tasks (Ericsson and Simon 1996) and are therefore often suggested in Q matrix development (Jang 2009; Pressley and Afflerbach 1995; Taylor and Dionne 2000). Although think-aloud studies hypothetically increase the cognitive load, the initial result shows that this method does not hinder cognitive processes (Leow and Morgan-Short 2004). To achieve the best possible result, Ericsson and Simons (1996) and Pressley and Afflerbach (1995) suggest various rules (Ericsson and Simon 1996, pp. 80–83): use separate rooms for each session; use trained test administrators who are seated outside the apprentices’ field of vision and who interrupt the think-aloud process only after a silence of more than 5 s to remind the examinees to continue speaking; use standardized instruction; and hold preliminary practice sessions with participants. “To figure out what a learner knows (on the basis of what he says […]) and how that knowledge influences the way the learner reasons and solves problems, correctly or incorrectly” (Chi 1997, p. 274), the verbal data were analysed in accordance with the above suggested approach. A content analysis (according to Mayring 2010) was run. The process of quantifying verbal data of think-alouds is presented in Appendix 2.

Quantitative analysis methods: counting of frequencies (C) and solver-non-solver comparisons (S)

Counting experts’ ratings and apprentices’ utterances (C)

Skill necessity is defined by the counted frequencies on the basis of a prior defined cut-off point. To determine the cut-off point for expert ratings the strict suggestion of Shrout and Fleiss (1979), of a good interrater agreement rate of 80%, was followed. That means if 80% or more experts judged a certain skill as being necessary for a certain task, then the skill receives a “1” in the Q matrix; otherwise, it receives a “0” (unnecessary). The cut-off point for apprentices’ utterances was determined at the level of 50%. Thus, if there are utterances in more than 50% of the 26 apprentices’ verbal protocols, this skill will be included (“1”) in the Q matrix; otherwise a “0” has to be filled in. The severity of the cut-off point is due to the issue that some apprentices, with respect to their person-skill-vectors (and in accordance with CDM ideas, see “Theoretical considerations on diagnostic assessments using cognitive diagnostic models (CDMs)” section), are not able to solve certain tasks and therefore do not use (i.e., think-aloud) certain skills. This matter can become a problem if certain tasks require skills that are obviously harder than others and are therefore missed in many (more than 50%) apprentices’ skill-profiles. It can also become a concern if certain tasks require a large set of skills, as one might claim that the probability of solving a task decreases with an increasing number of necessary skills. Therefore, for obtaining the best proxy depicting the underlying cognitive solving processes, different Q matrices are created and matched.

Solver-versus-non-solver comparison (S)

To address the limitation of apprentice-solver versus apprentice-non-solver of the first method, a cross-table comparison between the two groups [apprentices who solve (1) versus those who do not solve (0) the task] regarding their skill-mastering [apprentices who use a certain skill correctly (1) as opposed to those who do not use a certain skill, or use the skill incorrectly (0)] were added. This approach is based on the deterministic CDM model [“Theoretical considerations on diagnostic assessments using cognitive diagnostic models (CDMs)” section], which stated that solvers are able to solve tasks correctly because they are disposed to apply all of the necessary skills in the correct way (=skill-master). However, non-solvers are not able to answer tasks correctly because they do not dispose of all necessary skills or they apply one or more of the skills in an incorrect fashion (=skill non-master). In other words, necessary skills were significantly more often applied (in the right way) with solvers than with non-solvers. Conversely, those skills that are significantly more often used by solvers than by non-solvers are necessary for the task solution process and have to be included in the Q matrix as necessary (“1”). Those skills that are applied in the case of a certain task and do not significantly differ between solvers and non-solvers are, by definition, not necessary. On the basis of the categorical variable characteristics, a phi-coefficient analysis (Bühner and Ziegler 2008, pp. 627–629) was run for each skill to task assignment. On the basis of a 5% significance level, skill level necessity was decided. It is critical to note that the solver-versus-non-solver procedure has only limited significance if the number of group sizes differs considerably. This is especially the case if tasks are quite easy (solver group is much bigger than non-solver group) or quite difficult (solver group is much smaller than non-solver group).

Finally, four single Q matrix models serve as the basis for the pattern-matching procedure. The theoretically based Q-I (researchers’ task construction and decisions) (see Table 2) and the three empirically based Q matrices: Q-ERC (experts’ counted ratings), Q-ATAC (apprentices’ counted arguments from the think-aloud studies), and Q-ATAS (apprentices’ skills used when solving the tasks correctly) (see Appendices 2, 3, 4).

Instruments for empirical Q matrix evaluation: matching single Q matrix models by different degrees of overlap

As CDM experts suggest, a set of seven to ten IP skills provides a reliable measurable basis. Therefore, the empirical evaluation is built on the results of the pattern-matching procedure. This means that all single Q matrix models will be revised according to the adapted (reduced) set of IP skills and the adapted pool of tasks.9 Furthermore, the four (revised) single Q matrix models will be matched with regard to different degrees of overlap for balancing the strengths and weaknesses of the single Q matrix models: Q-MATCH4 includes all skills which were identified to be relevant in at least one of the four Q matrices, Q-MATCH3 includes skills which were identified to be relevant in at least two single matrices, Q-MATCH2 includes skills which were identified to be relevant in at least three of the four matrices, and Q-MATCH1 includes only skills which were identified to be relevant in all four single Q matrices. These matches Q matrix models provide, besides the single Q matrix models, the basis for identifying the best proxy for apprentices’ real cognitive processes while solving the tasks.

Analysis: pattern matching and the empirical evaluation process

Pattern matching of single Q matrix models (concerning RQ I and RQ II)

In order to compare the patterns of the different single Q matrix models, I shall focus on cells which claim a skill necessity and, therefore, are filled by a “1”, because a consistency in “0” (skill is not needed) is, in many cases, of subordinate interest. A frequency based view on these cells, which were claimed as necessary in at least one of the four single Q matrix models (n = 82 cells), indicates that 35 cells (=43%) were defined consistently in all four models as necessary. However, for 57% of the cells at least one Q matrix model does not claim the skill as necessary. This result confirms the statement that each source and method (researchers’ Q matrix model included) provides different suggestions of necessary skill to task assignments for the same task. An evaluation of the number of cells filled by a “1” for each Q matrix model illustrates that researchers (Q-I: n = 76 cells), as well as VET experts (Q-ERC: n = 69 cells), defined overall considerably more skills as necessary than could be the result from using different analysis methods using data from think-aloud studies (Q-ATAC: n = 57 cells, Q-ATAS: n = 48 cells). Consequently, the overlap between Q-I and Q-ERC is the highest (84%) and between Q-I and Q-ATAS is the lowest (58%). The percentage of overlap between researchers’ expectations (Q-I) and counted utterances in apprentices’ verbal protocols (Q-ATAC) is in between these two comparisons (73%).

To decide on the importance and measurability of each IP skill the following aspects are considered in a balanced way: (i) how often a particular skill is represented by the tasks (empirical importance); (ii) how often a particular skill is needed in combination with another skill (skill pairs); and (iii) how important the particular skill is regarding content validity aspects (practical importance).

Aspect (i): Skill frequencies vary between the different IP skills (from 1 to 17) and within different Q matrix models (skill “TERM”: from 9 to 17, see Fig. 4). Skills with the highest mean frequencies are “REC,” “ANAL,” “SEQU,” “INFO,” “TERM,” and “DEC.”
Fig. 4

Frequencies, mean and standard deviation (sd) of IP skills in the four single Q matrix models

Aspect (ii): The overlap of all skill pairs for the four single Q matrix models is depicted in Appendix 5, Figs. 9, 10, 11, 12. The following is an example of how to read the table concerning the important skills “TERM” and “INFO”: in Q-I (Fig. 9) the skill “TERM” is needed in 100% of the tasks which also required the skill “INFO” (cell: row “TERM”—column: “INFO”); in reverse (cell: row “INFO”—column: “TERM”), the skill “INFO” is needed in 67% of the tasks which also required the skill “TERM”. For this skill pair other Q matrix models also deliver rather high connections (Q-ERC: 91 and 63%; QATAC: 100 and 79%; Q-ATAS: 50 and 44%). The results for this skill pair indicated that they should be merged into one skill. Aspect (iii): All skills were critically scrutinized concerning their content validity.

Because all three aspects are involved, and the connections of skill pairs can vary considerably over the different Q matrix models, there is no fixed rule regarding how to revise a certain skill. Finally, the following five different actions were used to compress the initial set of IP skills. (1) Empirically and/or practically important skills, with a low tendency to be part of a high overlapping skill pair, were maintained as initially introduced (e.g., “TOOL”). (2) Practically important, but hard to depict, skills needed for tasks from the individual assessment have to be eliminated (only “TEAM”). (3) Practically important, but less empirically represented, skills in existing tasks were enhanced by additionally constructed tasks (e.g., “IDEA”). (4) Empirically less important, but practically important, skills with a high tendency to need another important skill for a task solution were integrated into the more important skill (e.g., skill “RISK” were integrated into skill “ANAL”). And finally, (5) empirically as well as practically important skills, with a high tendency to be needed together, were merged into one new skill (e.g., “INFO” and “TERM” became “INFO + TERM”). In summary, the set of diagnosable skills could be reduced to a manageable number of seven skills (the revision process is documented in Table 3).
Table 3

Revision of the set of IP skills

Initial skill

Action

Explanation

Skill name (new)

Skill number (new)

REC

1

REC

1

ANAL

1

ANAL

2

RISK

4

Included in ANAL

ANAL

2

DIST

4

Included in ANAL

ANAL

2

IDEA

3

Additional task(s)

IDEA

3

CREA

4

Included in IDEA

IDEA

3

SEQU

1

SEQU

4

TOOL

1

TOOL

5

INFO

5

With TERM

INFO + TERM

6

TERM

5

With INFO

INFO + TERM

6

DEC

5

With DEF

DEC + DEF

7

REF

4

Included in DEC + SELL

DEC + DEF

7

DEF

5

With DEC

DEC + DEF

7

TEAM

2

The analyses of all four single Q matrix models (see Table 2 and Appendix Figs. 6, 7, 8) show that all IP tasks need at least one of the 14 IP skills (expectation: skill “DIST” in Q-ATAC and Q-ATAC). Using skill revision (see Table 3), less represented skills were integrated into another skills (e,g., “DIST”), eliminated (“TEAM”), or enhanced by additional tasks (“IDEA”). Therefore, the revised set of seven skills could be prompted by the extended pool of 24 tasks.

Empirical evaluation of single and matched Q matrix models (RQ III)

As a result of the pattern-matching procedure, the set of IP skills was reduced from fourteen to seven skills, and the pool of tasks was enhanced by two tasks, from 22 to 24. All single Q matrix models (Q-I, Q-ERC, Q-ATAC, Q-ATAS) were revised accordingly, so that each Q matrix model consisted of seven skills and 24 tasks.10 On this basis, the matched Q matrix models (Q-MATCH1, Q-MATCH2, Q-MATCH3, and Q-MATCH4) were constructed. Consequently, the four single, as well as the four matched, Q matrix models were evaluated by using the DINA model for selecting the best fitting model, by using a diverse set of fit indices (Table 4).
Table 4

Model fit indices

Models for Q matrices

Absolute model fit

Relative model fit

Item discrimination

Max (χ 2)

SRMSR

AIC

BIC

CAIC

Mean IDI

Q-I

84.348*

.054

24,112.19

24,483.58

24,560.58

.403

Q-ERC

100.660*

.054

24,135.98

24,507.37

24,584.37

.406

Q-TTAC

95.126*

.053

24,060.62

24,432.01

24,509.01

.416

Q-TTAS

81.762*

.053

24,121.11

24,492.50

24,569.50

.412

Q-MATCH4

86.257*

.055

24,125.97

24,497.36

24,574.36

.413

Q-MATCH3

84.334*

.053

24,100.02

24,471.42

24,548.42

.417

Q-MATCH2

93.328*

.053

24,096.61

24,468.00

24,545.00

.398

Q-MATCH1

94.414*

.054

24,114.37

24,485.76

24,562.76

.397

The three best values per column are marked in italics

* Significant on a 1% level

The two absolute fit criteria show ambivalent comparable results for all Q matrix models; while the SRMSR benchmark of .05 is only slightly exceeded, the very strict criterion of maximal item pairwise χ 2 statistic is always significant. Therefore, the best fitting model is selected by relatively compared values over all indices. There is no model that outperforms all other models, but all fit criterions of Q-MATCH3 are at least one of the third best compared to the others. Hence, a matched Q matrix, Q-MATCH3 (see Appendix 6), that balances the strengths and weaknesses of different resources and methods, with a match not as smooth as Q-MATCH4 (including all skills which were identified to be relevant in at least one of the four Q matrices) nor as strict as Q-MATCH1 (including only skills which were identified to be relevant in all four single Q matrices), provides the best data fit and has, therefore, been selected as the final Q matrix.

Results and comprehensive discussion

RQ I investigated the appropriateness of the initial set of skills on the basis of a pattern matching of empirically constructed Q matrix models (Q-ERC, Q-ATAC, Q-ATAC) with the theoretically derived initial researchers’ Q matrix (Q-I). The reduction of the initial set of fourteen skills to seven skills caused a balanced consideration of (i) how often a skill was represented by the tasks, (ii) how often a skill was part of a skill pair in tasks, and (iii) how important the skill was with regard to content validity aspects. The results prompted a revision of skills using five different actions: (1) maintaining a skill as initially introduced, (2) eliminating a skill that is hard to depict, (3) constructing additional tasks to enhance poorly represented skills, (4) integrating a skill with another if the particular skill is usually only needed with another skill, but not the other way around, or (5) merging skills which often require each other into one new skill. These revisions go in line with suggestions of CDM experts to specify not more than 7–10 skills to yield in best results (de la Torre and Minchen 2014; Roussos et al. 2007).

RQ II demonstrated that information from the different sources, inquiry methods, and analysis show that all the skill-based tasks need at least one of the seven IP skills and, therefore, are valuable for the diagnostic assessment. However, two more tasks had to be constructed in order to prompt the demonstration of the skill “IDEA.”

The appropriateness of a set of seven IP skills (RQ I) and a pool of 24 tasks (RQ II) is additionally underscored by the absolute model fit value SRMSR, which varies only between .053 and .055 over all eight different Q matrix models and, thus, only slightly exceeded (Maydey-Olivares 2013) suggested benchmark of .05 for well-fitting models.

RQ III: In order to obtain insights into the “real” cognitive processes—in other words, to get an appropriate proxy of these cognitive processes when solving tasks—it is worthwhile to extend the researchers’ first underlying construction assumptions (Q-I) by additional information resources arising from different sources, inquiry methods, and analysis, as well as to balance this information by a triangulation process. Finally, the best fitting Q matrix model was selected on a diverse set of fit indices. As expected, the best description of apprentices’ skill application when solving representative IP tasks was yielded by a matched Q matrix model (Q-MATCH3: including skills which were identified to be relevant in at least two single Q matrix models) that balanced the (dis)advantages of different information sources, in a moderate manner, and that fits the data best.

Conclusions

In order to provide valid informative feedback—as claimed for in professional teacher behaviour and corresponding teacher standards (Interstate Teacher Assessment and Support Consortium 2011; KMK 2004; Oser 1997)—the here introduced cognitive diagnostic assessment using fine-grained units of analysis seems to be promising. For securing quality of such diagnostic assessments using CDM, a principled assessment design like the ECgD has to be used. Thereby, a coherent system of competence model, set of skills, task model/pool of tasks, a Q matrix, and statistical model have to be specified. Whereby, the Q matrix specifying the skill task assignment is an indispensable prerequisite for running CDMs as they function as an à priori defined assumption about learners’ cognitive processes when solving the tasks. Hence, the specification of a good Q matrix is a study in its own right (e.g. Kunina-Habenicht et al. 2012). Because VET competence measurement for diagnostic purposes is still in its infancy, the study focus was on the theoretical specification and empirical evaluation of the three crucial aspects used for diagnostic assessments: (I) set of skills, (II) pool of tasks, and (III) Q matrix.

The extensive amount of various empirical evidence as a result of triangulated data from different sources, different inquiry methods, and different analysis methods provides a comprehensive basis for adapting the coherence of the skills’ set, task pool, and Q matrix. As expected each single Q matrix is unique. The empirical result that a matched Q matrix model is the best proxy for describing apprentices’ underlying cognitive processes while solving each IP task confirmed the expectation that no source and no method is without limitations and that every different source and method delivers a unique contribution within the process of specifying a sounded Q matrix. Results of the Q matrix pattern matching shows that researchers, as well as experts in the field, overall rated more skills as necessary, as this could be found within the coding process of think-aloud study transcripts. With regard to empirical evaluation of these four single Q matrix models (Q-I, Q-ERC, Q-ATAC, Q-ATAS), models based on apprentices’ think-aloud studies usually show better model fit values than researchers’/experts’ Q matrix models. This underlies the special emphasis of the think-aloud method of target group respondents to understand underlying cognitive processes while solving tasks.

Obviously qualitative data of think-aloud studies are very helpful their quantifying can lead to a loss of information. Furthermore, decisions about cut-off points, such as 80% of the experts have to be agreed in their rating of a skill to task assignment, or 50% of the apprentices have to mention a skill for that skill to be considered necessary and be assigned to a task, are usually accompanied by reductions.

Summing up, the results indicate that I have succeeded in developing a decisive prerequisite of a diagnostic assessment (the best fitting Q matrix model as best proxy representing apprentices’ cognitive processes when solving IP tasks) which can enable (in a subsequent step) the measurement of the complex construct of IP competence on a much more fine-grained level than has been the case up until now. This means that by using this assessment in combination with the cognitive processes—described within the Q matrix—it will be possible to diagnose apprentices’ strengths and weaknesses concerning the seven intrapreneurship skills: “REC”—recognize IP opportunities and problems, “ANAL”—analyse IP situations and problems, “IDEA”—create IP ideas, “SEQU”—sequence resources and aspects, “TOOL”—use economic tools, “INFO + TERM”—search for relevant information and use economic terms, and “DEF + REC”—introduce, defend and reflect an IP project. This improved quality of diagnostic information can help apprentices to reflect their own performance progress, teachers and trainers to prepare individualized instruction and coaching, instructional design scientists to understand learning in the domain of IP on a deeper level, and politicians to fund and monitor intra-/entrepreneurship activities in a more effective way. E.g. the validated knowledge on cognitive processes by solving the typical intrapreneurship activity of creating a GANTT-chart (see Fig. 2)—specified within the Q matrix—enables teachers to understand apprentices’ cognitions and therefore to develop differentiating instructional concepts on a more effective way.

In the next step of the research project, the outcomes of the CDM DINA on intrapreneurship competence are presented and interpreted in terms of their potential to promote individual learning and performance processes (Bley and George, in press).

Footnotes
1

The main purpose of the research initiative ASCOT was the development of valid and reliable instruments for measuring competencies in the field of vocational education and training. Thereby, the preferred models of traditional IRT (item response theory) were used to measure in a first step more overarching competence dimensions (Beck et al. 2016).

 
2

From the outset, the tasks for measuring Intrapreneurship (part of the CoBALIT project) were constructed for addressing two purposes (the monitoring perspective measurable by IRT as well as the diagnostic perspective measurable by CDM). Although the assessments of both perspectives include the same tasks, they differ in their formation.

 
3

More information on the German apprenticeship system and categories of comparison are given with Busemeyer and Trampush (2012), and Weber and Lehtinen (2014).

 
4

Thereby, the diagnostic-assessment-based CDM approach basically differs from traditional instructional assumption in VET, in that each challenge/task has to comprise a complete vocational action (from perceiving until reflection) and that, therefore, in each challenge/task all skills are necessary (e.g., Oser et al. 2009). However, VET researchers generally agree that on a fine-grained consideration, context-based vocational challenges vary enormously and that therefore—although all skills are basically needed—some specific skills play a more important role than others. For the diagnostic purpose of CDMs—to identify apprentices’ strengths and weaknesses—the focus on the most important skills per task is essential.

 
6

Skills are non-compensable if a lack of one skill cannot be compensated by another skill (e.g., George and Robitzsch 2015).

 
7

The study builds on the extensive preliminary work of Weber, Bley, and colleagues for understanding IP activities in the apprenticeship program of industrial clerks (Bley et al. 2015; Weber et al. 2014, 2015). The domain analysis entails curricular (training regulations for schools and for the workplace), instructional (school-books, N = 6), classroom observations with follow-up target group surveys, as well as teacher and trainer interviews and assessment analyses (final exam reports held by the Chamber of Commerce, N = 205). Additionally, job advertisements (N = 437) to ensure ecological validity and scientific literature about intra-/entrepreneurship and innovative behavior in the fields of business, psychology, and pedagogic (N = 147 studies) were processed.

 
9

If two skills are merged into one skill, the new skill is specified as necessary if one of the original two skills was specified as necessary.

 
10

Skill vectors of the two new tasks are equal in all Q matrix models because these tasks were not part of the validation process.

 

Declarations

Authors’ information

Sandra Bley studied Human Resource Education and Management at Georg-August University in Göttingen from 2001–2006. She holds a Master of Business Research (MBR 2008) and a doctoral degree (Dr. oec publ. 2010) from Ludwig-Maximilians-University in Munich. Since 2011 she has been a senior researcher at the Institute for Human Resource Education and Management, Ludwig-Maximilians-University in Munich.

Acknowledgements

Not applicable.

Competing interests

The author has no competing interests.

Availability of data and materials

The data supporting the authors´ findings are provided by the author on request.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
Munich School of Management, Institute for Human Resource Education and Management, Ludwig-Maximilians-University in Munich

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