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Institute
We use numbers and fractions every day, for example when we are doing our shopping or baking a cake. But mathematics is, of course, much more: it is the language of science, or, to use Galileo's words, “the book of Nature is written in mathematical language” (Galileo, 1623) and some mathematical competencies beyond basic arithmetic are required in most professions. Basic mathematics, i.e., elementary arithmetic, elementary geometry and some elements of calculus, is taught in school, not just for everyday life, but as a tool for many different professions. In school, however, mathematics is either “loved” or “hated”, as Hersh and John-Steiner masterfully describe in their book “Loving and Hating Mathematics” (Hersh and John-Steiner, 2010). Research in mathematics education has definitely contributed to reducing school students' hatred of mathematics and this reduction may be seen as one of its many goals.
In contrast with mathematics, the field of mathematics education is strongly interdisciplinary; the closest field to influence it directly is psychology. In fact, mathematics education is consistently shaped by both behavioral and cognitive perspectives, since so many factors—the power of visualizations, the effect of representation formats, but also factors like gender, self-efficacy, etc.—influence and sometimes determine students' performance.
Our aim for this Research Topic and for the collection of papers we are now publishing has thus been to illustrate the relevance of such various psychological perspectives for mathematics education using the contributions of colleagues from around the world. All the contributions we have collected address these interdisciplinary perspectives explicitly or implicitly.
Maturity models are increasingly used to advance the processes of organizations, including Higher Education Institutions. In this paper, we review existing maturity models to analyze and optimize the accessibility of organizations. Therefore, we conducted a systematic literature research in the databases Web of Science, IEEE Xplore, BASE, ACM, and Google Scholar, resulting in 13 different maturity models. An additional web search on maturity models for accessibility found another 12 maturity models that we added to the results. Finally, we analyzed the 25 maturity models in more detail, specifically the indicators that each maturity model uses to measure accessibility. The most frequent indicators were “responsibility”, “competences & training”, and “monitoring”, with differences in the frequencies when separated by target group. Out of the 25 maturity models found, only 6 focused on Higher Education Institutions. None of the existing maturity models focuses on teaching and learning of accessibility explicitly.
Introduction:
Results from experimental research in instructional psychology
imply that a deep menu structure of a e-learning website may provide useful segmentation. However, menu depth also increases the need for navigation and thus, might have impairing eects on learning. Furthermore, instructional support can be provided by including a checklist, to ensure that learners reflect on their
study progress. The study aimed at investigating which menu structure is beneficial for e-learning websites and whether a checklist could compensate the negative effects of an unfavorable menu structure.
Methods:
Therefore, in an online experiment, we let 101 students learn facts about rocks from an e-learning website with either a deep or a flat menu structure. We further manipulated whether metacognitive support through a checklist was provided or not. Learning outcomes, cognitive load, metacognitive factors as well
as learning time were measured.
Results:
Results show no main eects of the menu depth or the presence of
a checklist on retention and transfer performance. Learning achievements in percent for retention were 37.31 (deep menu/checklist), 31.10 (deep menu/no checklist), 36.07 (flat menu/checklist), 38.13 (flat menu, no checklist) and for transfer were 35.19 (deep menu/checklist), 34.40 (deep menu/no checklist), 37.78 (flat menu/checklist), 33.23 (flat menu, no checklist). Yet, there are hints that the deeper menu structure had a negative eect on learning processes: The deep menu structure led to an enhanced extraneous cognitive load (ECL) and reduced
learning efficiency. However, providing a checklist had beneficial eects mainly when learning with a deep menu structure but not overall. Unexpectedly, the presence of the checklist did not influence metacognitive measures.
Discussion:
Our study suggests that possible costs of a deep menu structure
should be considered when designing instructional checklists. However, the study also provides a way in which these costs can be compensated, which is by using a checklist. Implications for instructional research and e-learning are discussed.
Parental self-efficacy (PSE) is an essential predictor of parenting practices and child development. The content-specificity of PSE is not well understood: Previous studies are based on either measure of general parental self-efficacy or task-specific parental self-efficacy but not measures of both constructs. Thus, we do not know how both constructs are related. With data from the “AQuaFam” study, we compared four-factor models to investigate the structure of PSE. It was a priority whether (1) task-specific and general PSE could be assessed separately or (2) be mapped in a hierarchical model with task-specific PSE factors and a superordinate factor of general PSE. A Chi-square test shows no significant model improvement, which indicates general and task-specific PSE being separate dimensions. US studies suggest that low-income parents, migrants, or parents with a lower educational status experience lower PSE. To adequately support these parents, we need to know whether differences according to families’ background characteristics occur in task-specific and general PSE beliefs. We tested general PSE and PSE in four parenting tasks for differences according to families’ background characteristics. Parents with a university degree they were self-efficacious in communicating responsible media use than parents without a university degree. Parents with a non-German family language they were self-efficacious in communicating a responsible media use, caring for a sick child, and in their general PSE compared to parents with German as a family language. The results of the group differences are discussed in the context of how to support different parent groups.
Introduction
Interprofessional collaboration of physicians and midwives is essential for appropriate and safe care of pregnant and parturient women as well as their newborns. The complexity of woman-centered care settings requires the continuous exchange of information and the coordinated implementation of multi-and interprofessional care concepts. To analyze the midwives’ perspective on the multi-and interprofessional care process during pregnancy, birth and postpartum period, we aimed to adapt and psychometrically evaluate the Interprofessional Collaboration Scale (ICS).
Methods
The ICS (13 items) was answered by 299 midwives for (i) prenatal and postpartum care as well as (ii) perinatal care. Three items on equitable communication (EC) identified in qualitative interviews with N = 6 midwives were added as further aspects of quality in collaborative midwifery care. Confirmatory factor analysis was used to test competing theoretically hypothesized factorial model structures, including both care settings simultaneously, i.e., birth and prenatal/postpartum.
Results
A two-dimensional structure assuming the 13 original ICS items and the 3 items on EC as psychometric distinct item groups accounts for the data best. After deleting 5 ICS items with insufficient indicator reliability, a very good-fitting model structure was obtained for both prenatal/postpartum as well as perinatal care: χ2df = 192 = 226.35, p = 0.045, CFI = 0.991, RMSEA = 0.025 (90%CI: [0.004; 0.037]). Both the reduced ICS-R and the EC scale (standardized response mean = 0.579/1.401) indicate significantly higher interprofessional collaboration in the birth setting. Responsibility in consulting, attitudes toward obstetric care and frequency of collaboration with other professional groups proved to be associated with the ICS-R and EC scale as expected.
Discussion
For the adapted ICS-R and the EC scale a good construct validity could be confirmed. Thus, the scales can be recommended as a promising assessment for recording the collaboration of midwives with physicians working in obstetric care from the perspective of midwives. The instrument provides a validated assessment basis in midwifery and obstetric care to identify potentially divergent perspectives within interprofessional care teams in woman’s centered care.
Abstract
Mathematical word problem solving is influenced by various characteristics of the task and the person solving it. Yet, previous research has rarely related these characteristics to holistically answer which word problem requires which set of individual cognitive skills. In the present study, we conducted a secondary data analysis on a dataset of N = 1282 undergraduate students solving six mathematical word problems from the Programme for International Student Assessment (PISA). Previous results had indicated substantial variability in the contribution of individual cognitive skills to the correct solution of the different tasks. Here, we exploratively reanalyzed the data to investigate which task characteristics may account for this variability, considering verbal, arithmetic, spatial, and general reasoning skills simultaneously. Results indicate that verbal skills were the most consistent predictor of successful word problem solving in these tasks, arithmetic skills only predicted the correct solution of word problems containing calculations, spatial skills predicted solution rates in the presence of a visual representation, and general reasoning skills were more relevant in simpler problems that could be easily solved using heuristics. We discuss possible implications, emphasizing how word problems may differ with regard to the cognitive skills required to solve them correctly.
The results of three meta-analyses show that the effectiveness of learning from animations, when compared to learning from static pictures, is rather limited. A recent re-analysis of one of these meta-analyses, however, supports that learning from animations is considerably more effective than learning from static pictures if the specifics of the displayed changes need to be learned. In order to further validate this finding as well as to clarify the educational strengths and weaknesses of animations and static pictures, an experimental study with three groups was conducted. Overall, 88 university students participated in the study. One group of learners (n = 30) watched a single picture of a gear mechanism, one group of learners (n = 28) watched four pictures, and one group of learners (n = 30) watched an animation. All groups had to identify specific motions and spatial arrangements covered by the gear mechanism. While learners who watched the animation exhibited the best performance with respect to the identification of motions, learners who watched the pictures showed the best performance with respect to the identification of spatial arrangements. The effect sizes are large. The results of the study help to clarify when animations and when static pictures are most suitable for learning.
Prior research indicates that student teachers frequently have misconceptions about multimedia learning. Our experiment with N = 96 student teachers revealed that, in contrast to standard texts, refutation texts are effective to address misconceptions about multimedia learning. However, there seems to be no added benefit of making “concessions” to student teachers’ prior beliefs (i.e., two-sided argumentation) in refutation texts. Moreover, refutation texts did not promote the selection of appropriate multimedia material. This study suggests that refutation texts addressing multimedia-learning misconceptions should be applied in teacher education. Yet, further support seems needed to aid the application of the corrected knowledge.
Science competencies are considered an important 21st century skill. How this skill develops in childhood is, however, not well understood, and in particular little is known about how different aspects of science competencies are related. In this prospective study with 58 children aged 5–6 years, we investigate the development of two aspects of science competence: scientific thinking and science content knowledge. Scientific thinking was assessed with a comprehensive 30-item instrument; science content knowledge was measured with an 18-item instrument that assesses children’s knowledge with regard to melting and evaporation. The results revealed basic competencies in scientific thinking and science content knowledge at the end of kindergarten (46% and 49% correct, respectively, both different from chance). In mid-kindergarten, children performed better than chance on the assessment of science content knowledge (40% correct) but not on the assessment of scientific thinking (34% correct). Science content knowledge in mid-kindergarten predicted children’s science content knowledge at the end of kindergarten, as well as scientific thinking (both at 6 years). The opposite pattern did not hold: scientific thinking in mid-kindergarten did not predict science content knowledge at the end of kindergarten. Our findings show initial science competencies during kindergarten, and they suggest that children’s science content knowledge and scientific thinking are interrelated in a meaningful way. These results are discussed with respect to the different hypotheses that connect scientific thinking and science content knowledge as key features of science competencies. Implications for research and teaching are discussed.
The world is facing severe global challenges such as climate change, food security, rising migration, social justice, or the current corona crisis. In these times, citizenship education seems more important than ever. How can this citizenship education relate to mathematics and science learning? The research project MaSDiV (Supporting mathematics and science teachers in addressing diversity and promoting fundamental values) connected mathematics and science with citizenship education by modeling real-life problems relevant to society. In this paper, we present the foundational design features of the PD course as well the results from the accompanying evaluation of this PD course, which was implemented by partners in six countries to support teachers in connecting mathematics and science education with citizenship education. More specifically, we investigate how participating teachers experienced the PD program; how their self-efficacy beliefs, learning-related beliefs, as well as teaching practices change; and which factors contributed to that change. In order to investigate the outcome of the PD program, we surveyed N = 311 mathematics and science teachers’ pre- and post-participation of the PD in six different European countries. Among others, our results show that in general, most participating teachers reported a high overall satisfaction with the course across all six participating countries. They also indicate that teachers’ self-efficacy beliefs about using relevant contexts, their learning-related beliefs about the benefits of using contexts, as well as their own teaching practice changed significantly after participating in the MaSDiV PD course.
In the course of demographic change, the notion of age(ing) seen as something unavoidable has changed into something more adaptable. Through a healthy lifestyle, which aims at the self-responsible management of physical risks through fitness and discipline, individuals can expand their independence. However, the chances of doing so depend largely on one’s social position. In addition, the shift in health ideology towards the individual and the trend towards active ageing may lead to social pressure for some individuals. This qualitative interview study attempts to shed more light on this field of tension: What are the benefits and constraints of working on the body in the gym? Furthermore, what similarities and differences can be identified in identity constructions in the two samples with regard to the different underlying healthcare systems? The evaluation of the interviews was based on qualitative content analysis and was carried out with technical support (MAXQDA). It appears that for the respondents creating a fit body results primarily in self-empowerment gains. At the same time, submissions to Western body and fitness norms are also evident. Inequalities in health opportunities exist in both countries: While the respondents in the German sample (26 interviews) rely on public health services, the privileged American women (14 interviews) are covered by private insurance. They indicate that claiming government benefits appears as a stigmatisation of one’s own way of life. Consequently, a lack of resources in the form of cultural and economic capital prevents successful age(ing).
Objective
The aim of the current project was the development, implementation and evaluation of the programme, Motivational‐Volitional Intervention‐Movement After Breast Cancer (Mo‐Vo‐BnB), an intervention for the sustainable promotion of physical activity of breast cancer survivors.
Methods
In a multi‐stage interdisciplinary development process, the pedagogical‐didactic, psychological and physical evidence‐based programme was developed and implemented for women after breast cancer who were approved for medical rehabilitation and were minimally, physically active (<60 min/week). Train‐the‐trainer seminars were carried out for the implementation. Four sessions were implemented in two German clinics. The training quality, didactic methods and accompanying material were evaluated 6 weeks and 12 months after implementation by patients, trainers and project members (n = 127 evaluations).
Results
The standardised and published MoVo‐BnB programme can provide practical and quality training. Content and methods can be implemented according to the manual. Training quality, didactic methods, and accompanying materials were evaluated positively.
Conclusion
The results suggest that MoVo‐BnB is a useful standardised intervention for promoting the physical activity of breast cancer survivors. The demonstrated process is also suitable for other projects.
Clinical trial registration
German Clinical Trials Register (DRKS): DRKS00011122; Trial registration date: 2016 October 13.
Background
When parents want to make health-related decisions for their child, they need to be able to handle health information from a potentially endless range of sources. Early childhood allergy prevention (ECAP) is a good example: recommendations have shifted from allergen avoidance to early introduction of allergenic foods. We investigated how parents of children under 3 years old access, appraise and apply health information about ECAP, and their respective needs and preferences.
Methods
We conducted 23 focus groups and 24 interviews with 114 parents of children with varied risk for allergies. The recruitment strategy and a topic guide were co-designed with the target group and professionals from public health, education, and medicine. Data were mostly collected via video calls, recorded and then transcribed verbatim. Content analysis according to Kuckartz was performed using MAXQDA and findings are presented as a descriptive overview.
Results
Parents most frequently referred to family members, friends, and other parents as sources of ECAP information, as well as healthcare professionals (HCPs), particularly pediatricians. Parents said that they exchanged experiences and practices with their peers, while relying on HCPs for guidance on decision-making. When searching for information online, they infrequently recalled the sources used and were rarely aware of providers of “good” health information. While parents often reported trying to identify the authors of information to appraise its reliability, they said they did not undertake more comprehensive information quality checks. The choice and presentation of ECAP information was frequently criticized by all parent groups; in particular, parents of at-risk children or with a manifested allergy were often dissatisfied with HCP consultations, and hence did not straightforwardly apply advice. Though many trusted their HCPs, parents often reported taking preventive measures based on their own intuition.
Conclusion
One suggestion to react upon the many criticisms expressed by parents regarding who and how provides ECAP information is to integrate central ECAP recommendations into regular child care counseling by HCPs—provided that feasible ways for doing so are identified. This would assist disease prevention, as parents without specific concerns are often unaware of the ECAP dimension of issues such as nutrition.
Eye tracking is an increasingly popular method in mathematics education. While the technology has greatly evolved in recent years, there is a debate about the specific benefits that eye tracking offers and about the kinds of insights it may allow. The aim of this review is to contribute to this discussion by providing a comprehensive overview of the use of eye tracking in mathematics education research. We reviewed 161 eye-tracking studies published between 1921 and 2018 to assess what domains and topics were addressed, how the method was used, and how eye movements were related to mathematical thinking and learning. The results show that most studies were in the domain of numbers and arithmetic, but that a large variety of other areas of mathematics education research was investigated as well. We identify a need to report more methodological details in eye-tracking studies and to be more critical about how to gather, analyze, and interpret eye-tracking data. In conclusion, eye tracking seemed particularly beneficial for studying processes rather than outcomes, for revealing mental representations, and for assessing subconscious aspects of mathematical thinking.
Research on productive failure suggests that attempting to solve a problem prior to instruction facilitates conceptual understanding compared to receiving instruction prior to problem solving. The assumptions are that during the problem-solving phase, students activate their prior knowledge, become aware of their knowledge gaps, and discover deep features of the target content, which prepares them to better process the subsequent instruction. Unclear is whether this effect results from merely changing the order of the learning phases (i.e., instruction or problem solving first) or from additional features, such as presenting problem-solving material in the form of cases that differ in one feature at a time. Contrasting such cases may highlight the deep features and provide grounded feedback to students’ problem-solving attempts. In addition, the effect of the order of instruction and problem solving on procedural fluency is still unclear. The present experiment (N = 181, mean age = 14.53) investigated in a 2 × 2 design the effects of order (instruction or problem solving first) and of contrasting cases in the problem-solving material (yes/no) on conceptual understanding and procedural fluency. Additionally, the quality and quantity of students’ solution attempts from the problem-solving phase were coded. Regarding the learning outcomes, the ANOVA results suggest that for procedural fluency instruction prior to problem solving was more beneficial than problem solving prior to instruction. Merely delaying instruction did not increase conceptual understanding. The contrasting cases did not affect the quality of solution attempts, nor the posttest results. As expected, students who received instruction first generated fewer, but higher-quality solution attempts.
Although raised in the early days of research on teacher noticing, the question of context specificity has remained largely unanswered to this day. In this study, we build on our prior research on a specific aspect of noticing, namely teachers’ analysis of how representations are dealt with in mathematics classroom situations. For the purpose of such analysis, we examined the role of context on the levels of mathematical content area and classroom situation. Using a vignette-based test instrument with 12 classroom situations from the content areas of fractions and functions, we investigated how teachers’ analyses regarding the use of representations are related concerning these two mathematical content areas. Beyond content areas, we were interested in the question of whether an overarching unidimensional competence construct can be inferred from the participants’ analyses of the different individual classroom situations. The 12 vignettes were analysed by N = 175 secondary mathematics teachers with different degrees of teaching experience and their written answers provided the data for this study. Our findings show that the data fit the Rasch model and that all classroom situations contributed in a meaningful way to the competence under investigation. There was no significant effect of the mathematical content area on the participants’ analyses regarding the use of multiple representations. The results of the study indicate that explicitly considering questions of context can strengthen research into teacher noticing.
As an important component of teaching expertise, teacher noticing is gaining growing attention in our intercultural mathematics education community. However, it is likely that in many cases the researchers’ perspectives on what characterizes high instructional quality in mathematics classrooms shape what they expect teachers to notice. In particular, it is an open question how potentially different norms of instructional quality influence how teacher noticing is operationalized in East Asian and Western cultures. Consequently, in a first step, this bicultural research project on teacher noticing in Taiwan and Germany focuses on exploring the researchers’ frames of reference for investigating teacher noticing. In this paper, we thus propose a concurrent process for developing vignettes and eliciting corresponding expert norms as a prerequisite to investigating teacher noticing in a way that is sensitive to different cultural contexts. In this process, the research teams in both countries developed in parallel, text vignettes in which, from their perspective, a breach of a norm regarding a specific aspect of instructional quality was integrated. In an online expert survey, these vignettes were then presented to German and Taiwanese researchers in mathematics education (19 from each country) to investigate whether these experts recognize the integrated breach of a norm. This approach allows researchers to identify potentially different norms of instructional quality in mathematics classrooms. In particular, by means of a specific representation of practice, it became visible how expert norms of responding to students’ mathematical thinking can be different from a Taiwanese compared to a German perspective.
Diagnostic competences are an essential facet of teacher competence. Many studies have investigated the quality of teachers’ judgments of students’ competences. However, little is known about the processes that lead to these judgments and about the ways to promote these processes in the early phase of teacher training. The aim of the research project on which we report in this paper was to develop a simulated computer-based environment that allows assessing and promoting the diagnostic processes of prospective teachers. In the simulated environment, ‘virtual third-graders’ solve mathematical problems. Participants are asked to diagnose the students’ competence levels according to a theoretical model, which has been empirically validated. Participants can repeatedly select mathematical problems of varying difficulty levels, assign them to a virtual student, and then receive the student’s written solution. In this paper, we present the conceptualization of the simulated environment. We also report on the results of a pilot study with 91 prospective primary school mathematics teachers to analyze whether the environment allows an assessment of individual differences in diagnostic processes. The majority of participants rated the environment as authentic and as one in which they could become immersed. Overall, participants were fairly accurate in their diagnoses concerning the student’s competence level. However, log data and participants’ written notes indicated that there was large variability in their diagnostic processes. Participants varied greatly in the number of mathematical problems they assigned to a student during their diagnostic process, and in how strongly the difficulty of these problems deviated from the student’s true competence level. Overall, the data suggest that the simulated environment has the potential to assess diagnostic processes in a valid way. We discuss open questions and issues for further development.
Background
The SF-8 is a short form of the SF-36 Health Survey, which is used for generic assessment of physical and mental aspects of health-related quality of life (HRQoL). Each of the 8 dimensions of the SF-36 is covered by a single item in the SF-8. The aim of the study was to examine the latent model structure of the SF-8.
Method
One-, two- and three dimensional as well as bi-factor structural models were defined and estimated adopting the ML- as well as the WLSMV-algorithm for ordinal data. The data were collected in a German general population sample (N = 2545 persons).
Results
A two- (physical and mental health) and a three-dimensional CFA structure (in addition overall health) represent the empirical data information adequately [CFI = .987/.995; SRMR = .024/.014]. If a general factor is added, the resulting bi-factor models provide a further improvement in data fit [CFI = .999/.998; SRMR = .001]. The individual items are much more highly associated with the general HRQoL factor (loadings: .698 to .908) than with the factors physical, mental, and overall health (loadings: −.206 to .566).
Conclusions
In the SF-8, each item reflects mainly general HRQoL (general factor) as well as one of the three components physical, mental, and overall health. The findings suggest in particular that the evaluation of the information of the SF-8 items can be validly supplemented by a general value HRQoL.
Background
A markedly negative self-image and pervasive shame proneness have consistently been associated with borderline personality disorder (BPD). The present experimental study investigated the intensity of negative emotional responses with a focus on shame in BPD compared to healthy control persons (HCs) during an experimental paradigm promoting self-awareness, self-reflection, and self-evaluation. Furthermore, the relationship between levels of state shame during the experiment and shame proneness in BPD compared to HCs was examined.
Methods
A sample of 62 individuals with BPD and 47 HCs participated in the study. During the experimental paradigm, participants were presented with photos of (i) the own face, (ii) the face of a well-known person, and (iii) of an unknown person. They were asked to describe positive facets of these faces. Participants rated the intensity of negative emotions induced by the experimental task as well the pleasantness of the presented faces. Shame-proneness was assessed using the Test of the Self-Conscious Affect (TOSCA-3).
Results
Individuals with BPD experienced significantly higher levels of negative emotions than HCs both before and during the experimental task. While HC participants responded to their own face particularly with an increase in shame compared to the other-referential condition, the BPD patients responded above all with a strong increase of disgust. Furthermore, the confrontation with an unknown or well-known face resulted in a strong increase of envy in BPD compared to HC. Individuals with BPD reported higher levels of shame-proneness than HCs. Higher levels of shame-proneness were related to higher levels of state shame during the experiment across all participants.
Conclusion
Our study is the first experimental study on negative emotional responses and its relationship to shame proneness in BPD compared to HC using the own face as a cue promoting self-awareness, self-reflection, and self-evaluation. Our data confirm a prominent role of shame when describing positive features of the own face, but they emphasize also disgust and envy as distinct emotional experience characterizing individuals with BPD when being confronted with the self.