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The study reported in this article investigated the appropriateness of Mathematical Knowledge in Teaching of three pre-service primary school teachers (PSTs), teaching an informal statistical inference (ISI) lesson to primary school students. Using an ISI framework and the Knowledge Quartet framework, the presence and appropriateness of the PSTs' teaching actions were coded and categorized. The results showed that PSTs were consciously engaged in making inferences based on sample data. The PSTs struggled to correctly interpret students' conceptual input and to explain ISI, in particular, how generalizing from a sample is possible. Teacher education should focus on how PSTs can foster students' understanding of the logic of drawing conclusions about a population based on a sample.

Non-routine word problem solving is an essential feature of the mathematical development of elementary school students worldwide. Many students experience difficulties in solving these problems due to erroneous problem comprehension. These difficulties could be alleviated by instructing students how to use visual representations that clarify the problem structure and the relations between solution-relevant elements (so-called visual-schematic representations). Research shows that instructional effectiveness depends largely on teachers' mathematical knowledge for teaching. Teachers' knowledge of visual representations is therefore essential to instructing word problem comprehension in this way. As there is little to no literature investigating teachers' practices in this area, the goal of the present study is to examine teachers' use of visual representations to support non-routine word problem solving. Eight mainstream elementary school teachers implemented an innovative approach focused on the use of visual-schematic representations. After a short training, teachers were able to produce these representations during instruction. However, some teachers seemed unclear about what these representations comprise and what function they serve within the word problem solving context. Teachers seemed to base their use of representations on personal preferences rather than on an optimal fit with the word problem characteristics. These aspects need to be addressed in teacher training and professional development programs. This study makes an unique contribution to research in the important and problematic area of word problem solving in regular classrooms. The results of this study are relevant for educational researcher, teachers, and teacher educators who deal with difficulties in instructing mathematical word problems.

The ability to reason inferentially is increasingly important in today's society. It is hypothesized here that engaging primary school students in informal statistical reasoning (ISI), defined as making generalizations without the use of formal statistical tests, will help them acquire the foundations for inferential and statistical thinking. Teachers who engage students in ISI need to have good content knowledge of ISI (ISI-CK). However, little is known about the ISI-CK of primary education pre-service teachers. Therefore, the aim of this paper is to describe this knowledge by surveying 722 first-year pre-service teachers from seven teacher colleges across the Netherlands. The survey consisted of five tasks using open-ended questions and true/false statements. The descriptive analysis showed that most respondents understood that descriptive statistics that take the global shape of the distribution into account can be used as arguments within ISI. Although a majority agreed that random sampling is a valid sampling method, distributed sampling was the preferred strategy for selecting a sample. Moreover, when asked to make a generalization beyond the data, most pre-service teachers only described the data and did not appear to understand that a representative sample can be used to make inferences about a population. These findings suggest that it may be useful if statistics education for pre-service teachers places more emphasis on sampling and inference, thereby prompting pre-service teachers to engage in ISI.

Aim: This study examines the effects of an intervention aimed at making the primary school pupils aware of their core qualities and promoting their use of these qualities. Method/Rationale: This article reports on a quasi-experimental study among 1346 pupils from 17 primary schools, based on insights from positive psychology. Findings: By using a questionnaire several effects on the pupils' well-being were found, both in the short-term (immediately after the intervention), and in the longer-term (three months after the intervention). Limitations: The data collection is about subjective self-reports of pupils and not about objective observations. A further limitation of the study might be that the pupils could only work with one core quality for four weeks. It is also somewhat unnatural when pupils discover various core qualities in themselves and yet are only allowed to specifically use one core quality and describe examples of its use. Conclusions: We can conclude that working with core qualities had a positive impact on the primary school pupil's wellbeing. The study yields interesting directions for further research. In particular, future research may study the effect of long-term interventions that involve several core qualities.

Fetters et al.'s (2013) mixed methods integration framework uses construction metaphors: building, connecting, merging, and embedding. In a similar vein, this article uses an architectural metaphor and introduces design patterns as building blocks for mixed methods research design. A design pattern embeds one specific design decision into its preceding design decisions. As an example, I will describe a design pattern for mixed methods matched comparisons sampling. Using one exemplar study, I will demonstrate the pattern's three design phases. Embedding matched comparisons sampling into its preceding design decisions shows that, to optimize the comparison of subpopulations in the qualitative research strand, the quantitative sample of this design pattern should aim to include almost all members of one small target population. [ABSTRACT FROM AUTHOR]

Teachers who engage primary school students in informal statistical inference (ISI) must themselves have good content knowledge of ISI (ISI-CK). However, little is known about how college education for pre-service teachers can contribute to the development of their ISI-CK. To address this shortcoming, we used a case study to investigate ISI-CK development in a class of 21 pre-service primary school teachers who participated in a short intervention (180 min). Based on qualitative and quantitative analyses of the pretest, posttest and intervention data, the results suggest that most participants acknowledged it is possible to make uncertain inferences. An assignment to search the media for inferential claims seemed to create awareness regarding inference and the need to distinguish between a sample and a population. A simulation involving random sampling and varied sample size probably increased the participants' knowledge of sampling variability and random sampling. No development was seen in the participants' knowledge about sufficient sample sizes. The statistical investigation conducted by the participants during a model lesson may have strengthened their awareness of ISI, but it also revealed that many participants continued to favour distributed sampling over random sampling. Further research on belief formation with regard to data as evidence, sampling methods and the expression of uncertainty in the context of ISI is needed.

The central purpose of this article is to provide an overview of the many ways in which special educators can generate and think about causal inference to inform policy and practice. Consideration of causality across different lenses can be carried out by engaging in multiple method and mixed methods ways of thinking about inference. This article differentiates between idiographic and nomothetic causality (as well as molecular and molar causality) and describes how both quantitative and qualitative information can inform understanding of causal mechanisms by reviewing different design applications. An overview of how these different lenses can be applied to special education inquiry is offered.

This article is predicated on the idea that, by interacting with differences of various kinds, researchers in special education can obtain conclusions that are more nuanced, sophisticated, richer, and, hence, better than when they would have ignored such differences. Based on the application of existing research guidelines to 6 recent exemplars of special education intervention research, 6 revised mixed methods guidelines are formulated and discussed. These involve including differences and diversity in research design, including differential views of different stakeholders, investigating differential effects of different elements of interventions, further exploration of differences and exceptions encountered during research, and incorporation of any differences encountered in the conclusions. We conclude by noting that without such diversification, the resulting conclusions will not be as helpful as they might otherwise be with respect to supporting practice.

It is often assumed that students with a higher potential for excellence are less motivated to collaborate. So far, the question remains whether this is actually the case. This survey study investigated the influence of business students' (N = 389) potential for excellence on their motivation to collaborate on a business-related task. Different aspects of potential for excellence were taken into account, including intelligence, creativity, first-year grade point average (GPA), and personality. A structural equation modeling analysis was applied. The findings demonstrated that only GPA had a negative influence on students' collaborative values, indicating that the assumption that students with a higher potential for excellence are less motivated to collaborate receives limited support. In addition, the findings showed that different aspects of potential for excellence were related to different aspects of motivation to collaborate. This indicates that the relationship between potential for excellence and motivation is more complex than often considered.

This literature review summarises the growing body of literature discussing teacher identities of university teachers. The aim was to understand what strengthens or constrains the development of a teacher identity. A qualitative synthesis of 59 studies was carried out. The review showed that several factors contribute to the development of teacher identity. While contact with students and staff development programmes were experienced as strengthening teacher identity, the wider context of higher education was experienced as having a constraining effect. Furthermore, the impact of the direct work environment was experienced as either strengthening or constraining, depending on whether or not teaching is valued in the department. Five psychological processes were found to be involved in the development of a teacher identity: a sense of appreciation, a sense of connectedness, a sense of competence, a sense of commitment, and imagining a future career trajectory. The findings suggest that developing a teacher identity in the higher education context is not a smooth process. In order to empower university teachers, it is important to reward teaching excellence and build community. Staff development activities can play a role in helping teachers to develop strategies for gaining confidence and taking active control of their work situation, both individually and collectively. The authors argue that more attention should be paid to the implicit messages that departments convey to their teaching faculty.

Educational innovations often involve intact subgroups, such as school classes or university departments. In small-scale educational evaluation research, typically involving 1 to 20 subgroups, differences among these subgroups are often neglected. This article presents a mixed method from a qualitative perspective, in which differences among intact subgroups regarding one construct or effect are first quantitatively identified and subsequently qualitatively described and explained by differences among the contexts of the separate intact subgroups. Its focus on the contexts of intact subgroups, where organizational factors can be modified, makes this method interesting from a management perspective. In evaluations, repeated application of the method deserves a place beside other analytical methods.

Students training to become primary school teachers appear to have little awareness of the core concepts of geography (teaching). To ensure that future primary school teachers are able to develop their pupils' geographical awareness, a six weeks programme was developed. The characteristics of this programme -- named Consciously Teaching Geography (CTG) -- are: principles of good geography teaching, conjunction and a recurrent structure during training, modelling and reflection. In a quasi-experimental research design the question is answered what the effects are of CTG on the development of pedagogical content knowledge (PCK) for the subject of geography of first year primary student teachers. The results indicated that the programme has a positive effect on the domain-specific PCK development in the short term.

For many instructors in higher education, use of a learning management system (LMS) is de facto mandatory. Nevertheless, instructors often have much freedom in deciding which functionalities of the LMS they use; that is, whether they perform each individual instructor task using the LMS. Alternatively, they may perform one specific instructor task using alternative means, or, quite often, not perform it at all. The current Technology Acceptance model (TAM) fails to describe this decision process accurately, as TAM (1) does not focus on the level of the individual task; (2) does not make a distinction between not performing a task and performing a task using alternative means; and (3) does not recognize one important factor that affects the performance of a specific task--task importance. A test of three different models shows that the decision process is best represented as a two-step process. First, influenced by task importance, a choice is made to either perform a specific task or not. Second, after the decision has been made to perform the task, and influenced by the usefulness and ease of use of the LMS, a choice is made between performing the task using the LMS and using alternative means. (Contains 4 figures and 2 tables.)

The best method for determining the size of learning objects (LOs) so as to optimise their reusability has been a topic of debate for years now. Although there appears to be agreement on basic assumptions, developed guidelines and principles are often in conflict. This study shows that this confusion stems from the fact that in the literature, hardly any attention is paid to different types of reusability. This study not only shows that there are different types of reusability, but also that different types of reusability go together with different principles for developing LOs and for determining LO size. A grounded theory analysis was performed on separate statements on LO development in 71 selected publications from LO literature. This resulted in the development of four scenarios for LO development, each with their own definition of reusability and their own principle for determining the size of LOs. A field test with 11 experts showed that the scenarios are recognisable. In higher education, educational technologists often assist amateur LO developers. Educational technologists can use the scenarios to determine which definition of reusability is applicable to their situation and which principle for determining the size of LOs should be applied. (Contains 2 tables and 1 figure.)

The literature on the re-use of learning materials has largely focused on the development of materials. This paper explores how re-use can be stimulated after learning materials have been developed and made available. We searched for and developed guidelines that support staff and/or management most frequently adopt in cases of (un)successful re-use of existing digital teaching and learning materials and methods by teachers in higher education. In a grounded theory approach, we collected existing guidelines from 11 literature studies, and developed new guidelines from 19 (mainly Dutch) case studies. Through constant comparison, we developed 'low-level' guidelines, which were classified into high-level guidelines. Five high-level guidelines turned out to be robust when subjected to repeated comparison with the case studies. Further, this paper elaborates existing guidelines by showing specific elaborations of them in our case studies. (Contains 2 figures.)

This paper describes a pilot study centred on the technology-enhanced self-development of competences in lifelong learning education carried out in the challenging context of the Association of Participants Agora. The pilot study shows that the use of the TENCompetence infrastructure, i.e. in this case the Personal Development Planner tool, provides various kinds of benefits for adult participants with low educational profiles and who are traditionally excluded from the use of innovative learning technologies and the knowledge society. The self-organized training supported by the PDP tool aims at allowing the learners to create and control their own learning plans based on their interests and educational background including informal and non-formal experiences. In this sense, the pilot participants had the opportunity to develop and improve their competences in English language (basic and advanced levels) and ICT competence profiles which are mostly related to functional and communicative skills. Besides, the use of the PDP functionalities, such as the self-assessment, the planning and the self-regulating elements allowed the participants to develop reflective skills. Pilot results also provide indications for future developments in the field of technology support for self-organized learners. The paper introduces the context and the pilot scenario, indicates the evaluation methodology applied and discusses the most significant findings derived from the pilot study. (Contains 2 figures and 2 tables.)

This study focuses on how to support students who have to work together in small groups, and who do not know each other, in performing grounding discussion. It compares two different implementations of a script, one using a structured interface, one using a textual instruction, on students' discussion behavior. The experiment involved two grounding discussions that were performed by 42 students from several countries, working together at a distance in small international groups of four to six students. Our main hypothesis was that the script would lead to better grounding discussions, and that the structured interface would strengthen the effect of the script. Several qualitative and quantitative analyses showed that (1) the script led to more and longer input to the discussion, more discussions, and the structured interface led to even longer inputs; (2) the script led to more effort on the grounding discussions, compared to other course components; and (3) the script led to better adherence to the order of course components, with the structured interface having an additional effect.

Describes an experimental Web site that was developed to facilitate the discussion of large texts. Explains the template which enables discussion participants to enter comments at the paragraph level and to view all relevant information while commenting, and considers potential applications for higher education. (LRW)