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In many countries, assessment and curriculum reforms came into being in recent decades. In Iran, an important educational assessment reform took place called Descriptive Assessment (DA). In this reform, the focus of student assessment was moved from a more summative approach of providing grades and deciding about promotion to the next grade to a more formative approach of providing descriptive feedback aimed at improving student learning. In this study, we evaluated how seven fourth-grade mathematics teachers used the principles of DA. Data were collected by a questionnaire on assessment practices and beliefs, lesson observations, and interviews. Although the teachers varied in how they assess their students, in general their assessment practice is by and large in line with the DA guidelines. Nevertheless, in some respects we found differences. When assessing their students, the teachers essentially do not check the students' strategies and when preparing the report cards, they still use final exams because they do not sufficiently trust the assessments methods suggested by DA. The guideline to use assessment results for adapting instruction is also not genuinely put into action. The article is concluded by discussing dilemmas the teachers may encounter when implementing DA.

Actively involving the network during treatment, as recommended in Autism Spectrum Condition (ASC) guidelines, can be facilitated with the Network in Action-Questionnaire (NiA-Q), which identifies the current and potential sources of social support. The aims of this study were to (1) examine the factor structure of the NiA-Q and (2) to explore the self- and proxy-report on the social network. Before the start of treatment in a mental health institution, 193 adults with an ASC diagnosis and 84 proxies completed the NiA-Q. Factor analysis showed two factors: positive social support and interpersonal distress. Self- and proxy-report on the NiA-Q did not differ for most variables, except for social network wishes. The NiA-Q provides a basis for network involvement and strengthening.

The balance model is often used for teaching linear equation solving. Little research has investigated the influence of various representations of this model on students' learning outcomes. In this quasi-experimental study, we examined the effects of two learning environments with balance models on primary school students' reasoning related to solving linear equations. The sample comprised 212 fifth-graders. Students' algebraic reasoning was measured four times over the school year; students received lessons in between two of these measurements. Students in Intervention Condition 1 were taught linear equation solving in a learning environment with only pictorial representations of the balance model, while students in Intervention Condition 2 were taught in a learning environment with both physical and pictorial representations of the balance model, which allowed students to manipulate the model. Multi-group latent variable growth curve modelling revealed a significant improvement in algebraic reasoning after students' participation in either of the two intervention conditions, but no significant differences were found between intervention conditions. The findings suggest that the representation of the balance model did not differentially affect students' reasoning. However, analyzing students' reasoning qualitatively revealed that students who worked with the physical balance model more often used representations of the model or advanced algebraic strategies, suggesting that different representations of the balance model might play a different role in individual learning processes.

In this study, we explored the insights that Chinese primary mathematics teachers gained into their students' mathematical understanding from using classroom assessment techniques (CATs). CATs are short teacher-initiated targeted assessment activities proximate to the textbook, which teachers can use in their daily practice to make informed instructional decisions. Twenty-five third-grade teachers participated in a two-week program of implementing eight CATs focusing on the multiplication of two-digit numbers, and filled in feedback forms after using the CATs. When their responses described specific information about their students, emphasized the novelty of the gained information, or referred to a fitting instructional adaptation, and these reactions went together with references to the mathematics content of the CATs, the teachers' responses were considered as evidence of gained insights into their students' mathematics understanding. This was the case for three-quarters of the teachers, but the number of gained insights differed. Five teachers gained insights from five or more CATs, while 14 teachers did so only from three or fewer CATs, and six teachers showed no clear evidence of new insights at all. Despite the differences in levels of gained insights, all the teachers paid more attention to descriptions of students' performance than to possible instructional adaptations.

This paper explores how to balance test security and accessibility on licensure, credentialing, and certification exams. It examines K-12 test security policies related to educational assessments across states to discover lessons learned about how to meet accessibility needs of individuals with disabilities while minimizing test security risks. It then discusses how licensure and certification programs can adapt those lessons and policies to ensure exam score validity for all candidates without jeopardizing exam security.

In a three-phase study, with a total of 40 third-grade teachers and their 830 students, teachers were supported to use classroom assessment techniques (CATs) to reveal their students' knowledge of number operations. In phase I, four teachers and 66 third-grade students participated in five monthly workshops in which CATs were co-designed and their use was discussed. In phase II, the first phase was replicated with four workshops with six different teachers and 148 third-grade students. In these two exploratory phases, we evaluated student achievement on a standardized national mathematics test in a pre-/posttest design and compared changes herein to changes in the national norm sample. In phase III, a control condition was added to the design to experimentally investigate the effect on student achievement with 30 teachers and 616 third-grade students. Teachers were randomly assigned to participate in 0, 1, 2, or 3 1-hour workshops. In all three phases, we found a significant increase in students' mathematics achievement scores on the standardized mathematics test. In phase III, the increase was significantly larger in the classes of teachers participating in three workshops than in classes with less workshops. Additionally, results from the analysis of classroom observations, feedback forms, and interviews indicate that teachers could easily integrate the CATs into their practice and could gather valuable information on their students. The results from the different phases of this study combined indicate that supporting teachers in their development and use of classroom assessment in mathematics may contribute to the improvement of students' mathematics achievement.

In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n = 304). A confirmatory factor analysis showed that the four-factor structure fitted the empirical data from the Netherlands. For the Cyprus data a one-factor structure was found to have a more adequate fit. Regarding the effect of country on performance, a comparison at item level showed that the kindergartners in the Netherlands outperformed those in Cyprus in the majority of quantitative competence items. Analyses of variance revealed for each country a significant effect of kindergarten year on performance, with children in K2 (second kindergarten year) outperforming those in K1 (first kindergarten year). A statistical implicative analysis at item level revealed that in both countries the relevant implicative chain, showing what successful solving of an item implies for correct solving of another item, reflects by and large the sequential steps mostly followed in teaching kindergartners early number. This sequence starts with counting and subitizing, then continues with additive reasoning and finally multiplicative reasoning. These implicative chains also clearly show that the development of early quantitative competence is not linear. There are many parallel processes and cross-connections between the components of quantitative competence.

This paper reports an overview of contemporary research on early childhood mathematics teaching and learning presented at recent mathematics education research conferences and papers included in the special issue (2020--4) of "ZDM Mathematics Education." The research covers the broad spectrum of educational research focusing on different content and methods in teaching and learning mathematics among the youngest children in the educational systems. Particular focus in this paper is directed to what lessons can be drawn from teaching interventions in early childhood, what facilitates children's mathematical learning and development, and what mathematical key concepts can be observed in children. Together, these themes offer a coherent view of the complexity of researching mathematical teaching and learning in early childhood, but the research also brings this field forward by adding new knowledge that extends our understanding of aspects of mathematics education and research in this area, in the dynamic context of early childhood. This knowledge is important for future research and for the development of educational practices.

This paper discusses the potential of the creation and analysis of historical networks as didactic strategies in science education. To this end, we first argue the importance of combining critical approaches of the history of science with historical network research. This will be followed by a report of an empirical experiment in which the history of science high school students created historical networks of human and non-human objects using the ePistolarium platform in combination with other network visualization tools (Available at http://ckcc.huygens.knaw.nl/epistolarium/. Accessed on November 20, 2018). Finally, following this empirical exploration, we will explain how the creation of historical networks are in line with academic recommendations in Brazil, encouraging the development of projects by students and also using historical collections and computational tools, interdisciplinary teaching methodologies and approaches that can support the formulation of reflective questions about science. Negotiations between small groups of students that shape their historical networks in combination with mediations by the teacher in plenary meetings are the main characteristics of this educational project. Networks were made from students' observations, their research and their presentations. In successive meetings, the whole process was evaluated and the contribution of these historical networks to the history of science was discussed. Although we argue that historical networks can be a powerful instrument of collaborative learning, it will be demonstrated that their creation requires the supervision of teachers to prevent manipulations of historical data and biased interpretations hereof.

Neuroanatomy education is a challenging field which could benefit from modern innovations, such as augmented reality (AR) applications. This study investigates the differences on test scores, cognitive load, and motivation after neuroanatomy learning using AR applications or using cross-sections of the brain. Prior to two practical assignments, a pretest (extended matching questions, double-choice questions and a test on cross-sectional anatomy) and a mental rotation test (MRT) were completed. Sex and MRT scores were used to stratify students over the two groups. The two practical assignments were designed to study (1) general brain anatomy and (2) subcortical structures. Subsequently, participants completed a posttest similar to the pretest and a motivational questionnaire. Finally, a focus group interview was conducted to appraise participants' perceptions. Medical and biomedical students (n = 31); 19 males (61.3%) and 12 females (38.7%), mean age 19.2 [plus or minus] 1.7 years participated in this experiment. Students who worked with cross-sections (n = 16) showed significantly more improvement on test scores than students who worked with GreyMapp-AR (P = 0.035) (n = 15). Further analysis showed that this difference was primarily caused by significant improvement on the cross-sectional questions. Students in the cross-section group, moreover, experienced a significantly higher germane (P = 0.009) and extraneous cognitive load (P = 0.016) than students in the GreyMapp-AR group. No significant differences were found in motivational scores. To conclude, this study suggests that AR applications can play a role in future anatomy education as an add-on educational tool, especially in learning three-dimensional relations of anatomical structures.

Reasoning about graphical representations representing dynamic data (e.g., distance changing over time), including interpreting, creating, changing, combining, and comparing graphs, can be considered a domain-specific operationalization of the general twenty-first century skills of creative, critical thinking and solving problems. This paper addresses the issue of how these 21st century skills of interpreting and creating graphs can be supported in a six-lesson teaching sequence about graphing motion. In this teaching sequence, we focused on the potential of an embodied learning environment to facilitate the development of primary school students' reasoning about motion graphs by having primary school students (9-11 years) 'walk' graphs in front of a motion sensor to generate distance-time graphs. We asked: "How does students' reasoning about graphing motion develop over a six-lesson teaching sequence within an embodied learning environment?" Based on the collected data, we examined changes in students' level of reasoning on graph interpretation and graph construction tasks using a repeated measurement design. Additionally, we present two teaching episodes showing instances of how perceptual-motor experiences during the lessons aided students' reasoning about graphical representations of motion. Results show that students went from iconic understanding towards understanding in which they reasoned based on one or two variables when interpreting and constructing graphical representations of motion events. At these higher levels of reasoning these students showed understanding of modelling motion in line with the intended 21st century skills of generating, refining, and evaluating graphs.

Embodied learning environments have a substantial share in teaching interventions and research for enhancing learning in science, technology, engineering, and mathematics (STEM) education. In these learning environments, students' bodily experiences are an essential part of the learning activities and hence, of the learning. In this systematic review, we focused on embodied learning environments supporting students' understanding of graphing change in the context of modeling motion. Our goal was to deepen the theoretical understanding of what aspects of these embodied learning environments are important for teaching and learning. We specified four embodied configurations by juxtaposing embodied learning environments on the degree of "bodily involvement" (own and others/objects' motion) and "immediacy" (immediate and non-immediate) resulting in four classes of embodied learning environments. Our review included 44 articles (comprising 62 learning environments) and uncovered eight mediating factors, as described by the authors of the reviewed articles: "real-world context," "multimodality," "linking motion to graph," "multiple representations," "semiotics," "student control," "attention capturing," and "cognitive conflict." Different combinations of mediating factors were identified in each class of embodied learning environments. Additionally, we found that learning environments making use of students' own motion immediately linked to its representation were most effective in terms of learning outcomes. Implications of this review for future research and the design of embodied learning environments are discussed.

This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report "why" such a model is used, "what" types of models are used, and "when" they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a comprehensive overview of described rationales for using the balance model, its appearances, situations in which it was used, and the gained learning outcomes. Some trends appeared about how rationales, appearances, situations, and learning outcomes are related. However, a clear pattern could not be identified. Our study shows that this seemingly simple model actually is a rather complex didactic tool of which in-depth knowledge is lacking. Further systematic research is needed for making informed instructional decisions on when and how balance models can be used effectively for teaching linear equation solving.

This study investigated Chinese primary school mathematics teachers' views on assessment in an effort to determine their assessment profiles. A large-scale questionnaire survey with 1101 teachers from 12 Chinese provinces and regions was carried out. The teachers reported to use assessment on a daily or weekly basis for different purposes. They recognized the importance of assessing different types of skills and knowledge and considered assessment useful for improving teaching and learning. To determine teachers' assessment profiles, we used several latent variable modeling techniques. With exploratory factor analyses, we identified eight factors in the teachers' responses: general instructional decision-making assessment purposes [1], specific instructional decision-making assessment purposes [2], assessment methods [3], diversity of assessment problem format [4], importance of assessing skills and knowledge [5], importance of assessing extra-curricular skills [6], Perceived usefulness [7], and acceptance of assessment [8]. When these factors were used to interpret the results of a latent class analysis, three distinct assessment profiles could be distinguished. One fifth of the teachers were in the "Enthusiastic assessors" profile. These teachers not only reported to use assessment frequently [3, 4] and purposefully [1, 2], but also highly endorsed its importance [5, 6] and usefulness [7, 8]. Around half of the teachers were in the "Mainstream assessors" profile; these teachers scored close to the mean on all factors. The remaining teachers held the relatively negative views on assessment and were therefore in the "Unenthusiastic assessors" profile. This profile characterization sheds light on Chinese primary school mathematics teachers' assessment culture.

In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we established to what degree current textbooks provide non-routine problem-solving tasks for which students do not immediately have a particular solution strategy at their disposal. We also analyzed to what degree textbooks provide 'gray-area' tasks, which are not really non-routine problems, but are also not straightforwardly solvable. In addition, we inventoried other ways in which present textbooks facilitate the opportunity to learn problem solving. Finally, we researched how inclusive these textbooks are with respect to offering opportunities to learn problem solving for students with varying mathematical abilities. The results of our study show that the opportunities that the currently most widely used Dutch textbooks offer to learn problem solving are very limited, and these opportunities are mainly offered in materials meant for more able students. In this regard, Dutch mainstream textbooks have not changed compared to the situation a decade ago. A textbook that is the Dutch edition of a Singapore mathematics textbook stands out in offering the highest number of problem-solving tasks, and in offering these in the materials meant for all students. However, in the ways this textbook facilitates the opportunity to learn problem solving, sometimes a tension occurs concerning the creative character of genuine problem solving.

This article discusses students' perceptions as a source for understanding education. It addresses what didactically experienced children, called "didactikids", taught us about the empty number line as a didactical model for teaching whole number calculations. The article mainly reports on a student consultancy study carried out in the Netherlands. The findings are similar to what was revealed in an Australian study. Both studies explain what can go wrong when the number line is applied rigidly and wrongly implemented. (Contains 3 footnotes and 14 figures.)

This study investigated three conversational subskills in children with 22q11.2 deletion syndrome (22q11.2DS, n = 8, ages 7-13) and Williams syndrome (WS, n = 8, ages 6-12). The researchers re-evaluated these subskills after 18 to 24 months and compared them to those of peers with idiopathic intellectual disability (IID) and IID and comorbid autism spectrum disorders (IID+ASD). Children with 22q11.2DS became less actively involved over time. Lower assertiveness than in children with IID was demonstrated. They seemed less impaired in terms of accounting for listener's knowledge than children with IID+ASD. Children with WS showed greater difficulties with discourse management compared to children with IID and 22q11.2DS. They had similar levels of conversational impairments to children with IID+ASD but these were caused by different shortcomings. Over time taking account of listener's knowledge became challenging for them. Findings suggest that children with 22q11.2DS and those with WS would benefit from conversational skills support and that regular re-evaluation is needed to anticipate conversational challenges.

Background: Children with 22q11.2 deletion syndrome (22q11.2DS) are reported to have socio-communicative impairments. Although many of these children are diagnosed with intellectual disability (ID) and/or autism spectrum disorder (ASD), these populations are seldom used as control groups. Hence, information regarding syndrome-specific socio-communicative challenges is lacking. Method: Parental concerns regarding everyday communication were investigated by means of the Children's Communication Checklist-2-NL (Geurts, 2007). Twenty children with 22q11.2DS (chronological age: 6 years-13 years 3 months) were compared to 21 children with idiopathic ID and 23 children with idiopathic ID and comorbid ASD. All groups were matched for fluid intelligence ("Gf"), chronological age, and core language scores. Results: Neglect or inadequate use of context information was more prevalent in children with 22q11.2DS than in children with idiopathic ID. Nonverbal communication seemed less impaired than in children with idiopathic ID + ASD. Conclusion: Pragmatic language skills and developmental trajectories in children with 22q11.2DS merit further investigation.

The importance of laying a foundation for algebraic reasoning at a young age is increasingly being emphasized. In this article, the authors report on an activity that elicits in a natural way algebraic strategies that in a later stage of learning algebra are crucial for solving equations. The activity brings about the students' spontaneous use of symbolic notations. It also makes students' reasoning visible both to themselves and to their teacher and helps build students' conceptual understanding and foster productive classroom discussion. This activity involves the work of students aged 11-12, using a hanging mobile as a balance model representing an equation with unknowns.

Background: This study aimed to compare developmental courses of structural and pragmatic language skills in school-aged children with Williams syndrome (WS) and children with idiopathic intellectual disability (IID). Comparison of these language trajectories could highlight syndrome-specific developmental features. Method: Twelve monolingual Dutch-speaking children with WS aged 5.10 to 13.3 years were assessed by means of standardised structural language tests measuring receptive and expressive vocabulary and sentence comprehension and production. Pragmatic language was evaluated by means of an expressive referential communication task and a retelling test. All of these language abilities were re-evaluated with the same measures after a period of 18 to 24 months. Performance was compared to 12 children with IID pairwise matched for chronological age (CA) and non-verbal fluid reasoning (Gf) at Time 1. Non-verbal mental age (NVMA) was taken into account when delineating developmental trajectories. Results: Children with WS outperformed children with IID on expressive vocabulary development. In contrast, sentence comprehension was significantly poorer than in children with IID at the second time point. Increased variability and rather poor performance on pragmatic language tasks were demonstrated in the WS group. Irrelevant and off-topic extraneous information transfer continued to be a syndrome-specific characteristic of children with WS. Conclusion: The data provide new insights into diverging developmental trajectories across language domains. Expressive structural language skills tend to progress more rapidly than receptive language skills in children with WS causing more distinctive language profiles over time. Some children with WS seem to benefit from the growth in expressive structural language abilities to enhance their expressive pragmatic language skills, while in some others these abilities remain challenging. This study highlights the need for continued follow-up of language challenges in WS and for a dynamic and individualised interventional approach.

This study examined the effects of a teacher-delivered intervention with online mathematics mini-games on special education students' multiplicative reasoning ability (multiplication and division). The games involved declarative, procedural, as well as conceptual knowledge of multiplicative relations, and were accompanied with teacher-led lessons and class discussions. A pretest-posttest control-group design was employed, with 81 students from five schools for special primary education (three experimental schools and two control schools). The intervention consisted of two 10-week game periods in which a total of 16 mini-games were offered as part of the regular educational program for multiplicative reasoning. The control group students played non-multiplicative mini-games; for multiplicative reasoning, they followed their regular educational program without mini-games. In both groups, students' multiplicative reasoning ability significantly increased. Regarding declarative knowledge of multiplication facts, learning outcomes were significantly higher in the experimental group as compared with the control group. This finding indicates the usefulness of mini-games for enhancing special education students' mathematics fact knowledge. Learning outcomes on a test measuring procedural and conceptual knowledge of multiplicative reasoning did not differ between experimental and control group. For these learning outcomes, then, the mini-games intervention did not have added value but can still be considered a "safe" alternative approach.

This article describes a field experiment with a pretest-posttest control group design which investigated the potential of reading picture books to children for supporting their mathematical understanding. The study involved 384 children from 18 kindergarten classes in 18 schools in the Netherlands. During three months, the children in the nine experimental classes were read picture books. Data analysis revealed that, when controlled for relevant covariates, the picture book reading programme had a positive effect (d = 0.13) on kindergartners' mathematics performance as measured by a project test containing items on number, measurement and geometry. Compared to the increase from pretest to posttest in the control group, the increase in the experimental group was 22% larger. No significant differential intervention effects were found between subgroups based on kindergarten year, age, home language, socio-economic status and mathematics and language ability, but a significant intervention effect was found for girls and not for boys.

Background: This paper reports on the use of classroom assessment techniques (CATs) by primary school mathematics teachers in China. CATs are short, focused assessment activities that can reveal students' understanding of specific mathematical subjects. The study involved six female third-grade mathematics teachers from Nanjing, China. The focus was on assessing division. Data were collected by teacher interviews, feedback forms and final reports, lesson observations, and student work. Results: The study revealed that the teachers could easily include CATs in their daily practice. By conducting the CATs, the teachers got new information about their students' learning. Most teachers liked using the CATs, especially those with the red/green cards, which is a whole-classroom immediate response format, providing quick information of the students' learning. The teachers also found the CATs feasible to conduct and helpful to engage their students during the lesson. However, no evidence was found that they used the information gained from the CATs for adapting their instruction to meet the students' needs in subsequent lessons. In fact, the teachers only used the teacher guide of the CATs to adapt their instruction beforehand. The CATs, instead of being implemented as assessment activities, were often included as extra exercises in the pre-arranged lesson plans of the teachers. If necessary, the teachers provided their students with instant help in order to assist them to get the correct answers. Conclusions: In general, the teachers were positive about the CATs as a way to reveal their students' understanding of division in an effective and efficient fashion. The teachers recognized that it can be very revealing to challenge their students with questions that are not completely prepared by the content of their textbooks. The results of this study suggest that on the one hand CATs can be helpful for Chinese mathematics teachers' formative assessment practice in primary education. On the other hand, our study also provides some evidence that using CATs, as an approach to formative assessment, to make informed and adequate decisions about further teaching, can be a real challenge for teachers.

In this study, we investigated teachers' teaching practices and their underlying beliefs regarding context-based tasks to find a possible explanation for students' difficulties with these tasks. The research started by surveying 27 Junior High School teachers from seven schools in Indonesia through a written questionnaire. Then, to further examine teachers' teaching practices related to context-based tasks, four teachers were observed and video recorded in two mathematics lessons in which they were asked to deal with context-based tasks. The questionnaire data revealed that the teachers had a tendency toward a view on teaching and learning mathematics which includes encouraging students to be actively involved in solving problems in various contexts. Although this finding suggests that the teachers may offer opportunities to learn context-based tasks to students, the questionnaire data also revealed that the teachers saw context-based tasks as plain word problems. Furthermore, the observations disclosed that their teaching was mainly teacher-centered and directive, which is not considered to be supportive for learning to solve context-based tasks. Combining the findings of this study with the results from our earlier study on Indonesian students' errors when solving context-based tasks, we found a relationship between how Indonesian teachers teach context-based tasks and the errors Indonesian students make in solving these tasks. These findings support the conclusion that insufficient opportunity-to-learn to solve context-based tasks offered by teachers is a possible explanation for students' difficulties in solving these tasks.

This paper describes a dataset consisting of longitudinal data gathered in the BRXXX project. The aim of the project was to investigate the effectiveness of online mathematics mini-games in enhancing primary school students' multiplicative reasoning ability (multiplication and division). The dataset includes data of 719 students from 35 primary schools in the Netherlands, who were followed from end Grade 1 to end Grade 3. Participating schools were randomly divided over three experimental conditions (playing at school, at home or at home with debriefing at school) and a control group. Tests of multiplicative reasoning ability were administered at the end of Grade 1 (pretest) and the end of Grade 2 and Grade 3 (posttests). In addition to the scores on these tests, the dataset includes measures of gameplay behavior, i.e., the time and effort students put in the games, and some student background variables.

This study aimed at gaining further understanding of kindergartners' performance in imaginary perspective-taking (IPT) by examining whether they can imagine "what" is visible from a particular point of view (IPT type 1: visibility) and "how" an object or scene will look from a particular point of view (IPT type 2: appearance). The sample consisted of 4- and 5-year-old kindergartners in the Netherlands (N = 334) and in Cyprus (N = 304). IPT abilities were assessed by a paper-and-pencil test of various perspective-taking pictorial tasks. The study showed that the Dutch children performed generally better than those in Cyprus. In both countries the IPT type 1 items were on average significantly easier than the IPT type 2 items. This was confirmed by a statistical implicative analysis by which the relationships between the individual items of both IPT types were investigated and which revealed that some items are less or more difficult than other items of a particular type. Regarding the influence of children's characteristics, in both countries it was found that mathematics ability was significantly related to IPT performance, whereas this was not the case for gender. Contrary to Cyprus, in the Netherlands the children in the second year of kindergarten had a significantly higher IPT performance than the children who were in their first year.

Based on the findings of an error analysis revealing that Indonesian ninth- and tenth-graders had difficulties in solving context-based tasks, we investigated the opportunity-to-learn offered by Indonesian textbooks for solving context-based mathematics tasks and the relation of this opportunity-to-learn to students' difficulties in solving these tasks. An analysis framework was developed to investigate the characteristics of tasks in textbooks from four perspectives: the type of context used in tasks, the purpose of context-based tasks, the type of information provided in tasks, and the type of cognitive demands of tasks. With this framework, three Indonesian mathematics textbooks were analyzed. Our analysis showed that only about 10% of the tasks in the textbooks are context-based tasks. Moreover, at least 85% of these tasks provide exactly the information needed to solve them and do not leave room for students to select relevant information by themselves. Furthermore, of the context-based tasks, 45% are reproduction tasks requiring performing routine mathematical procedures, 53% are connection tasks requiring linking different mathematical curriculum strands, and only 2% are reflection tasks, which are considered as tasks with the highest level of cognitive demand. A linkage between the findings of the error analysis and the textbook analysis suggests that the lacking opportunity-to-learn in Indonesian mathematics textbooks may cause Indonesian students' difficulties in solving context-based tasks. Based on the results of this study, recommendations are given for improving the opportunities-to-learn to solve context-based tasks as well as for doing further research on this topic.

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

In recent educational research, it is well acknowledged that gestures are an important source of developing abstract thinking in early childhood and can serve as an additional window to the mind of the developing child. The present paper reports on a case study which explores the function of gestures in a geometrical activity at kindergarten level. In the study, the spontaneous gestures of the child are investigated, as well as the influence of the teacher's gestures on the child's gestures. In the first part of the activity, the child under study transforms a spatial array of blocks she has constructed by herself into a verbal description, so that another person, i.e., the teacher, who cannot see what the child has built, makes the same construction. Next, the teacher builds a new construction and describes it so that the child can build it. Hereafter, it is again the turn of the child to build another construction and describe it to the teacher. The child was found to spontaneously use iconic and deictic gestures throughout the whole activity. These gestures, and primarily the iconic ones, helped her make apparent different space and shape aspects of the constructions. Along with her speech, gestures acted as semiotic means of objectification to successfully accomplish the task. The teacher's gestures were found to influence the child's gestures when describing aspects of shapes and spatial relationships between shapes. This influence results in either mimicking or extending the teacher's gestures. These findings are discussed and implications for further research are drawn.

Background: The school environment has shown itself to be an important factor in explaining adolescent behaviour. The relationships and experiences that pupils have at school have been found to influence their development, psychological well-being, self-esteem and social adjustment. Purpose: The aim of the study is to explore whether there is a relationship between pupil-peer and pupil-teacher relationships and psychological well-being and self-esteem, and whether this relationship varies according to pupils' experience of bullying or being bullied. Sample: Data consisted of a sample of 3694 students (mean age?±?SD 14.3?±?0.62 years; 51% girls) from elementary schools in Slovakia. Design and method: Questionnaires were administered to the students. In terms of data analysis, linear regression was firstly used in the whole sample to explore pupil-peer and pupil-teacher relationships and psychological well-being (the depression/anxiety and social dysfunction subscales of GHQ-12) and self-esteem (positive and negative self-esteem subscales of RSE). Next, the whole sample was divided into four groups in terms of involvement in bullying (normative contrasts, passive victims, aggressive non-victims and aggressive victims). Linear regression was used to explore the associations between pupil-peer and pupil-teacher relationships with the two factors of psychological well-being and two factors of self-esteem in these four groups. Results: As findings showed, better pupil-peer relationships and also pupil-teacher relationships were significantly related statistically to less depression/anxiety and social dysfunction, as well as to more positive and less negative self-esteem. All bullying categories were significantly related to pupil-peer relationships and the four dependent variables. However, in the categories of aggressive victims and aggressive non-victims, the pupil-teacher relationship was not significantly related to their psychological well-being and self-esteem. Also, in all subgroups, better pupil-peer relationships were significantly related to less depression/anxiety and social dysfunction, as well as with more positive and less negative self-esteem. Conclusion: Given the differences found in the connections between pupil-teacher relationships and well-being and self-esteem, between those who bullied and those who were bullied, it would seem that the school environment can play an important role in implementing anti-bullying prevention strategies.

In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the students' online working when solving the problems. Before and after the intervention a paper-and-pencil test on early algebra was administered. The data analysis revealed that the online working contributed to the students' early algebra performance. There was a significant gain in performance across all grades. The highest effect was found in grade 6. Out of the three strategy profile clusters that could be distinguished in the whole sample, the cluster dominated by using extreme values and the cluster characterized by the trial-and-error strategy were most influential on the gain in early algebra performance. The students' level of online working, which was defined as a combination of online involvement and strategy use, appeared to have a marginally significant effect on the gain score for the total sample. Per grade there was no significant effect, yet the levels of online working were significantly related to grade. Free playing was mostly performed in grade 4, looking for answers in grade 5, and exploring relations slightly more in grades 5 and 6. About 17 % of the effect of grade on the gain score was mediated by the level of online working.

The purpose of this 3-wave study is to examine the micro process of how employees adapt to change over time. We combined Conservation of Resources theory with insights from the organizational change literature to study employees in a Dutch police district undergoing reorganization. A model was tested where employee adaptability, operationalized by the presence of resources, predicts individual adaptive attitudes as well as adaptive behavior over time. Change information was included as a contextual change resource and meaning-making as a personal change resource. The research design allowed for examining longitudinal relationships by capturing data (1) "before" (Time 1), (2) "during" (Time 2), and (3) "after" change implementation (Time 3). We expected adaptability before and during change implementation to predict adaptive attitudes and adaptive behavior (both during and after change implementation). In addition, different indirect effects were tested. Structural equation modeling analyses supported most of the hypothesized relationships between resources and outcomes, although relationships differed from T1 to T2 and from T2 to T3. T1 change information triggered T2 meaning-making which translated into T3 adaptive behavior. The relevance of meaning-making and change information as important predictors of adaptive behavior is emphasized. Implications of these longitudinal findings are discussed. (Contains 2 figures and 2 tables.)

This study investigated whether an intervention including an online game contributed to 236 Grade 6 students' performance in early algebra, that is, solving problems with covarying quantities. An exploratory quasi-experimental study was conducted with a pretest-posttest-control-group design. Students in the experimental group were asked to solve at home a number of problems by playing an online game. Although boys outperformed girls in early algebra performance on the pretest as well as on the posttest, boys and girls profited equally from the intervention. Implications of these results for educational practice are discussed.

Assessment results collected under low-stakes testing situations are subject to effects of low examinee effort. The use of computer-based testing allows researchers to develop new ways of measuring examinee effort, particularly using response times. At the item level, responses can be classified as exhibiting either rapid-guessing behavior or solution behavior based on the item response time. Most previous research involving the study of response times has been conducted using locally developed instruments. The purpose of the current study was to examine the amount of rapid-guessing behavior within a commercially available, low-stakes instrument. Results indicate that smaller amounts of rapid-guessing behavior exist within the data compared to published results using other instruments. Additionally, rapid-guessing behavior varied by item and was significantly related to item length, item position, and presence of ancillary reading material. The amount of rapid-guessing behavior was consistently very low among various demographic subpopulations. On average, rapid-guessing behavior was observed on only 1% of item responses. Also found was that a small amount of rapid-guessing behavior can impact institutional rankings. (Contains 3 tables, 4 figures and 5 footnotes.)

In this study, we examined special education students' use of indirect addition (subtraction by adding on) for solving two-digit subtraction problems. Fifty-six students (8- to 12-year-olds), with a mathematical level of end grade 2, participated in the study. They were given a computer-based test on subtraction with different types of problems. Although most students had not been taught indirect addition for solving subtraction problems, they frequently applied this procedure spontaneously. The item characteristics were the main prompt for using indirect addition. Context problems that reflect an adding-on situation and problems that have a small difference between the minuend and subtrahend most strongly elicited the use of the indirect addition procedure. Moreover, indirect addition was identified as a highly successful procedure for special education students, and the best predictor of a correct answer was found in combination with a stringing strategy. (Contains 5 tables, 4 figures, and 2 footnotes.)

The purpose of this study was to investigate what experts in the use of picturebooks in mathematics education consider powerful characteristics of such books in the support of young children's learning of mathematics. The study started by investigating experts' views of such characteristics, as reflected in academic and professional publications on the use of picturebooks in mathematics education. This resulted in a first version of a framework of learning-supportive characteristics of picturebooks. In the second part of the study the framework was refined, and its tenability was tested through a four-round Delphi method, in which seven experts were asked to comment on, and work with, the framework when evaluating three picturebooks. The experts' evaluations of these books showed that a larger number of learning-supportive characteristics were identified when using the framework than when not using it.

Research has shown that high expectations of teachers about their students' academic development have a positive influence on how these students actually develop. Therefore, when aiming to improve students' learning results it is essential to know how teachers think about their students' abilities. The present study was meant to investigate what perceptions primary school teachers in special education have of their students' potential in mathematics and what possibilities they see to reveal this potential. Data were collected through an online questionnaire. Surprisingly, the responses showed that, although the teachers teach students with low achievement scores in mathematics, most of the teachers were positive about the mathematical potential of their students. The teachers often attributed unused potential to causes outside the student and they underpinned this view with observations from school practice. The article concludes with discussing the consequences of these findings for the professional development of teachers. (Contains 2 tables, 2 figures and 2 notes.)

This paper reports on a research project on information and communication technology (ICT)-based dynamic assessment. The project aims to reveal the mathematical potential of students in special education. The focus is on a topic that is generally recognised as rather difficult for weak students: subtraction up to 100 with crossing the ten. The students involved in the project were 8-12 years old. Their mathematical level was one to four years behind the level of their peer group in regular schools. In special education, teachers often use standardised written tests to assess their students' mathematical understanding and computational skills. These tests do not allow students to use auxiliary resources. In the research project, an assessment instrument was developed and used in which items taken from a standardised written test were placed in an ICT environment. The digitised items were enriched with an optional auxiliary tool that students could use for solving the problems. Currently, two sub-studies, investigating two different auxiliary tools for the same set of subtraction problems, have been completed. In the first study (n = 37), the tool provided students with digital manipulatives. In the second study (n = 43), an empty number line was included in the ICT environment. In both studies the students' scores in the ICT version of the test items were compared with the standardised written version of the test items. The results of both sub-studies show that the students could benefit from using an auxiliary tool. Consequently, the ICT-based dynamic assessment could help to reveal weak students' potential in subtraction. In addition, the studies disclosed that in the manipulatives study there was a clear preference for direct subtraction procedures (taking away), whereas in the number line study indirect addition or subtraction procedures (e.g. adding on) were frequently used as well. (Contains 2 figures, 8 tables and 3 notes.)

The present study examines the cognitive activity that is evoked in young children when they are read a picture book that is written for the purpose of teaching mathematics. The focus of this study is to explore the effects of pictures on children's spontaneous mathematical cognitive engagement. The study is based on the assumption that the pictures in a picture book that is aimed at supporting children's learning of mathematics can have story-related components and mathematics-related components. The story-related components of the pictures contribute to grasp the global story context of the text and the mathematics-related components help to understand the mathematical content of the story. All of the pictures of the book under investigation, "Six brave little monkeys in the jungle," have both story-related and mathematics-related components included. The pictures have a representational or an informational function. Four 5-year-old children were read individually the book by one of the authors without any probing. A detailed coding framework was used for analyzing the children's utterances that provided an in-depth picture of the children's cognitive activity. The results show that the picture book as a whole has the potential for cognitively engaging children. However, the pictures with a representational function were found to elicit mathematical thinking to a greater extent than the pictures with an informational function. Moreover, this was found for both types of components included in the pictures. Findings are discussed, practical implications for using picture books in kindergarten are drawn and suggestions for further research are made. (Contains 9 tables and 3 notes.)

Background: Little is known about the way people with aphasia perceive their social participation and its influencing factors. Aims: To explore how people with aphasia perceive participation in society and to investigate influencing factors. Methods & Procedures: In this qualitative study thirteen persons with aphasia and twelve central caregivers kept a pre-structured diary over two weeks, followed by a semi-structured interview. Diaries and interviews were transcribed verbatim and analysed by two researchers independently using codes, categories and central themes inductively. Plausibility of the analyses was discussed several times with a third independent senior-researcher. In a focus group interview, the results were discussed with the participants. Outcomes & Results: The number of social activities and the character of these activities are not as important as the perceived engagement in the social activities for the participants. People with aphasia feel isolated but want to feel engaged. They feel burdensome to others and wish to function in an ordinary way. Extracting information from conversations is difficult but they want to know what is going on. Often they are not able to work and they wish to contribute to the community in other ways. Although they often feel stigmatized, they wish to be respected. Often they do not reach that goal. Perceived factors influencing engagement in social participation can be divided into personal, social and environmental factors. The following personal factors are reported: motivation, physical and psychological condition and communication skills. The social factors are: the role of the central caregiver and the characteristics of the communication partner(s), namely willingness, skills and knowledge. The environmental factors refer to quietness and familiarity of the place in which the person with aphasia live. Conclusions: Social participation is a theoretical concept that people with aphasia do not use. Instead, people speak in terms of engagement, involvement, having a feeling of belonging. People with aphasia describe the degree of engagement in activities in social life domains (i.e. the quality of activities) as more important than the quantity of performing activities. (Contains 1 table, 2 boxes, and 1 note.)

In this article we describe our experiences using picture books to provide young children (five- to six-year-olds) with a learning environment where they can explore and extend preliminary notions of mathematics-related concepts, without being taught these concepts explicitly. We gained these experiences in the PICO-ma project, which aimed to generate more knowledge about the effect of picture books on young children's learning of mathematics. The project's goal is to investigate how picture books can contribute to the development of mathematical concepts in young children, and how the actions of the teacher can strengthen the characteristics of picture books that support learning. The reading sessions described in this article were not intended to be mathematics "lessons". Instead, the reading sessions were intended to tell the children a pleasant story and, at the same time, give them something to think about. Based on our research we provide reasons for using picture books to develop mathematical thinking, and include recommendations for practitioners interested in using picture books for mathematics learning. (Contains 7 figures.)

This article discusses large-scale assessment of change in student achievement and takes the study by Hickendorff, Heiser, Van Putten, and Verhelst (2009) as an example. This study compared the achievement of students in the Netherlands in 1997 and 2004 on written division problems. Based on this comparison, they claim that there is a performance decline in this subdomain of mathematics, and that there is a move from applying the digit-based long division algorithm to a less accurate way of working without writing down anything. In our discussion of this study, we address methodological challenges that come in when investigating long-term trends in student achievements, such as the need for adequate operationalizations, the influence of the time of measurement and the necessity of the comparability of assessments, the effect of the assessment format, and the importance of inclusion relevant covariates in item response models. All these issues matter when assessing change in student achievement.

This paper reports a study aimed at revealing special-educational-needs pupils' learning potential by means of an ICT-based assessment including a dynamic visual tool that might help pupils when solving mathematics problems. The study focused on subtraction problems up to 100, which require "borrowing". These problems, in which the value of the ones-digit of the subtrahend is larger than the ones-digit of the minuend, are known as a serious difficulty for weak pupils in mathematics. Seven of such problems from a standardised test were placed in the ICT environment. Data were collected from two test conditions: the standardised written test format and the ICT version of the test items including the tool that provided pupils with a set of virtual manipulatives. The 37 pupils involved in the study were 8-12 years old and from two special-education schools in the Netherlands. Comparison of the performance scores in the two formats showed that an ICT-based assessment format, including a dynamic visual tool, can reveal weak pupils' learning potential and strategy use. The study also pointed out that "partial-tool use", i.e., not carrying out the complete subtraction operation with the tool, can provide sufficient support to find the correct answer.

The aim of this study was to examine the responsiveness of the Test of Basic Motor Skills for Children with Down Syndrome (BMS). Forty-one children with Down Syndrome, 3 to 36 months of age, participated in the study. Gross motor skills were assessed three times using the BMS and the Gross Motor Function Measure (GMFM) before and after a baseline period of 2 weeks (T1-T2) and after a period of 16 weeks (T2-T3). Internal and external responsiveness of the BMS was analyzed using Guyatt's Responsiveness Index (GRI) and 2 x 2 repeated measures. Change in BMS scores was compared to change in GMFM scores and parent and physiotherapist ratings of change. The responsiveness of the BMS was large (GRI = 2.55). A significant Time x Age interaction [F(1,37) = 8.87, p less than 0.01] indicated that BMS scores increased more for children [less than or equal] 2 years compared with children 2 to 3 years of age. The difference in GRI between the BMS and GMFM was 0.75 (95% CI -0.25-1.75), indicating that the BMS and GMFM did not significantly differ in responsiveness. The Time x Measure interaction was not significant, indicating that the increase in mean BMS and GMFM scores did not differ. Change in BMS scores were correlated with parent ratings of change (r = 0.65, p less than 0.001) but not physiotherapist ratings (r = 0.36, p = 0.23). The results provide evidence that the BMS is responsive to change in gross motor development in children with Down Syndrome from 3 to 36 months of age. (Contains 5 tables and 2 figures.)