An assessment-based model for exploring the solving of mathematical problems: Utilizing revised bloom’s taxonomy and facets of metacognition

This paper provides a method that can be used to review the teaching, learning, and/or assessment of mathematics at either (or both of) the senior secondary and undergraduate levels. In this paper, how this method could be enacted is exemplified by considering the case of integral calculus. The method uses Revised Bloom’s Taxonomy (RBT) (Anderson et al., 2001) in conjunction with Efklides’s metacognition framework (Efklides, 2006, 2008) to design questions to address the different RBT cognitive processes and knowledge types. Using these two frameworks can help develop questions that target broader student thinking and a range of cognitive processes, including constructive ones, than traditional questions reach. In doing so, this method can be a starting point for Faculties seeking to reform their delivery and assessment of mathematics.     

Dutch sixth graders’ use of shortcut strategies in solving multidigit arithmetic problems

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth graders (12-year-olds) use shortcut strategies in solving multidigit addition, subtraction, multiplication, and division problems, to what extent student factors and task instructions affected this frequency of shortcut strategy use, and to what extent the strategies differed in performance. A sample of 648 sixth graders from 23 Dutch primary schools completed a paper-and-pencil task of 12 multidigit arithmetic problems, designed to elicit specific shortcut strategies such as compensation. Based on the students’ written work, strategies were classified into whether a shortcut strategy was used or not. Results showed that the frequency of shortcut strategies ranged between 6 and 21% across problem types, and that boys and high mathematics achievers were more inclined to use shortcut strategies. An explicit instruction to look for a shortcut strategy increased the frequency of these strategies in the addition and multiplication problems, but not in the subtraction and division problems. Finally, the use of shortcut strategies did not yield higher performance than using standard strategies. All in all, spontaneous as well as stimulated use of shortcut strategies by Dutch sixth graders was not very common.     

Fourth graders’ adaptive strategy use in solving multidigit subtraction problems

Using the choice/no-choice methodology we investigated Dutch fourth graders’ (N = 124) adaptive use of the indirect addition strategy to solve subtraction problems. Children solved multidigit subtraction problems in one choice condition, in which they were free to choose between direct subtraction and indirect addition, and in two no-choice conditions, in which they had to use either direct subtraction or indirect addition. Furthermore, children were randomly assigned to mental computation, written computation, or free choice between mental and written computation. One third of the children adaptively switched their strategy according to the number characteristics of the problems, whereas the remaining children consistently used the same strategy. The likelihood to adaptively switch strategies decreased when written computation was allowed or required, compared to mandatory mental computation. On average, children were adaptive to their own speed differences but not to the accuracy differences between the strategies.     

Analysing cognitive or non‐cognitive factors involved in the process of physics problem‐solving in an everyday context

Recently, the importance of an everyday context in physics learning, teaching, and problem‐solving has been emphasized. However, do students or physics educators really want to learn or teach physics problem‐solving in an everyday context? Are there not any obstructive factors to be considered in solving the everyday context physics problems? To obtain the answer to these questions, 93 high school students, 36 physics teachers, and nine university physics educators participated in this study. Using two types of physics problems—everyday contextual problems (E‐problems) and decontextualized problems (D‐problems)—it was found that even though there was no difference in the actual performance between E‐problems and D‐problems, subjects predicted that E‐problems were more difficult to solve. Subjects preferred E‐problems on a school physics test because they thought E‐problems were better problems. Based on the observations of students' problem‐solving processes and interviews with them, six factors were identified that could impede the successful solution of E‐problems. We also found that many physics teachers agreed that students should be able to cope with those factors; however, teachers' perceptions regarding the need for teaching those factors were low. Therefore, we suggested teacher reform through in‐service training courses to enhance skills for teaching problem‐solving in an everyday context.     

Children’s informal learning in the context of schools of the knowledge society

This paper builds on a key finding of a 5-year Danish research project con-cerning children in the 7 to 15 age group: children’s principal use of computers and the internet takes place in their spare time, and it is during their spare time that the majority of children really learn how to use interactive media. The project shows that in children’s spare-time use of ICT they employ informal forms of learning based to a large extent on their social interaction both in physical and virtual spaces. These informal learning forms can be identified as learning hierarchies, learning communities and learning networks; they are important contributions to the school of the knowledge society. The ICT in New Learning Environments project based on anthropologically inspired methods and social learning theories shows that students bring their informal forms of learning into the school context. This happens particularly when the school has undergone physical alterations and when its organisation of learning and teaching are also restructured, with project-based learning becoming an important part of the school work and with the media available in the learning environment. Using organisation theory, the school working with ICT and project-based learning is shown to simultaneously constitute a mixed mode between the school of the industrial and the knowledge society. The research shows that it is possible to tip the balance in the direction of the school of the knowledge society, and thus of the future, by comprehensively using ICT and project work in the day-to-day activities of the school, alongside and integrated with the traditional forms of learning, and not least by employing the informal learning processes children develop outside school. For teachers this will mean an extension of their function: no longer merely communicators of knowledge, they will have to become knowledge managers and overall leaders of projects, and this entails much more dialogue with the pupils.

Children’s sexual behavior problems: An ecological model using the LONGSCAN data

BackgroundAlthough prior research has indicated that sexual behavior problems (SBPs) are present among maltreated and non-maltreated children, risk factors for SBPs remain understudied. Further, few studies have examined multiple forms of trauma such as exposure to community violence and several likely important familial and environmental factors have yet to be investigated in the context of SBPs. The use of a more comprehensive ecological model of child, trauma-related, family, and environmental risk factors may help to further delineate the factors that contribute to the development of SBPs.ObjectiveThe aim of the current study was to build upon previous research by utilizing an ecological model that includes child, trauma-related, caregiver and familial, and environmental factors as potential predictors of SBPs.Participants and SettingThe present study was conducted with 1,112 8-year-old children (51.6% female; 48.9% Black) and their primary caregivers from the Longitudinal Studies in Child Abuse and Neglect (LONGSCAN) study.ResultsSeveral child, caregiver, and familial factors, as well as sexual and physical abuse demonstrated bivariate associations with SBPs. A number of these factors remained significant in a regression model, such as child’s living arrangement, child’s aggressive behaviors and posttraumatic stress symptoms (PTSS), sexual and physical abuse, caregiver’s psychological difficulties, and children’s perceptions of family health.ConclusionsThe findings highlight the role of select child, trauma-related, caregiver and familial, and environmental factors in the context of SBPs and also demonstrate the need to examine multiple levels of children’s environments when investigating SBPs.     

Children’s use of number line estimation strategies

This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint condition included an additional benchmark at the midpoint and children in the quartile condition were provided with a benchmark at every quartile. First, the inclusion of a midpoint resulted in more accurate estimates around the middle of the number line in the midpoint condition compared to the bounded and, surprisingly, also the quartile condition. Furthermore, the two additional benchmarks in the quartile condition did not yield better estimations around the first and third quartile, because children frequently relied on an erroneous representation of these benchmarks, leading to systematic estimation errors. Second, verbal strategy reports revealed that children in the midpoint condition relied more frequently on the benchmark at the midpoint of the number line compared to the bounded condition, confirming the accuracy data. Finally, the frequency of use of benchmark-based strategies correlated positively with mathematics achievement and tended to correlate positively also with estimation accuracy. In sum, this study is one of the first to provide systematic evidence for children’s use of benchmark-based estimation strategies in NLE with natural numbers and its relationship with children’s NLE performance.     

Value orientations and action conflicts in students’ everyday life: An interview study

The assumption that today’s German students are able to successfully combine synthesis achievement values and well-being values appears to be overly optimistic when regarded from the perspective of motivational psychology. The results of a qualitative-quantitative interview study with 25 students indicate that achievement and well-being values may come into conflict in everyday life. Incentives for achievement and well-being rarely co-occur in the same action domains. Whereas the school context is dominated by achievement incentives, leisure time is dominated by well-being incentives. Since both achievement and well-being are appreciated by most students, they should be prone to experience frequent everyday action conflicts. The motivational characteristics of postdecisional action conflicts are described on the phenomenal level and their possible impairing effects for learning processes are pointed out. Finally, alternative forms of value synthesis, which might be realized more successfully, are discussed.     

Participants’ views of the use of video in lesson study in higher education in Spain: An exploratory multiple case study

Abstract

Lesson study (LS) is a process through which teachers design, teach and discuss a lesson collaborating with colleagues. Sometimes, it includes video recording the lesson so teachers can use videos to later discuss the lesson and its improvement, however, there is little research addressing the consequences of doing it. This article investigates participants’ perceptions and use of video within LS. Results show that participants perceived video in LS as viable and with potential to stimulate reflection and to improve lessons, but also evince that video affects the outcomes, management and sustainability of LS. We analyze and discuss its potential and the challenges it poses, suggesting ideas for its implementation.     

A Multilevel Analysis of Asian Immigrant Children’s Reading Achievement in the Early Years: Evidence from the ECLS-K Data

This study investigates 1.5 generation¹ Asian immigrant children’s (n = 264) early literacy achievement patterns, treating them as a heterogeneous group. Specifically, the within-group variances in reading achievement from kindergarten to third grade are examined, drawing on four waves of data from the ECLS-K class of 1998–1999. Our analysis shows that ethnicity plays a role in shaping the children’s initial reading readiness and later growth, but the effects of languages spoken at home are not significant. Our analysis also demonstrates a persistent achievement gap between low- and high-socioeconomic status (SES) Asian groups. However, gender difference in terms of children’s reading development is not found to be significant. There is also no interaction between SES and the other factors such as gender, ethnicity and language backgrounds.     

Student teachers’ engagement in Facebook-assisted peer assessment in an initial teacher education context: speaking 2.0

Although peer assessment (PA) has been explored and implemented in higher education, little is known about how it is carried out through such a virtual platform as Facebook in an initial teacher education (ITE) context. To fill this practical void, this article showcases the brief portrait of Facebook-assisted PA in an English as a foreign language (EFL) classroom. This in-practice article shows how Facebook as an online platform serves as virtual engagement in PA among English student teachers in the EFL speaking classroom. This virtual engagement not only created an interactive virtual speaking classroom, but also it encouraged students to become critical reflective language learners.     

Language and Identity Construction of China’s Rural-Urban Migrant Children: An Ethnographic Study in an Urban Public School

This article investigates the identity construction process of China’s rural-urban migrant children through analyses of their discourses and of their use of language. Rural children have relocated to the urban centers with their parents on a massive scale over the past decades as China has undergone rapid economic changes. Many migrant children are able to attend urban public schools, and their identity construction emerges as an important issue that attracts increasing public and scholarly attention. This study draws on ethnographic data and presents four examples to illustrate the complex process of migrant identity construction. The results show that the migrant children deploy a range of linguistic features and claim multiple identities; in order for their identities to be established in social reality, they have to go through negotiation processes in which their identities are evaluated, ratified, challenged, or denied. Language is at the center of such processes.     

Exploring high school students' use of theory and evidence in an everyday context: the role of scientific thinking in environmental science decision‐making

This study examined 10th‐grade students' use of theory and evidence in evaluating a socio‐scientific issue: the use of underground water, after students had received a Science, Technology and Society‐oriented instruction. Forty‐five male and 45 female students from two intact, single‐sex, classes participated in this study. A flow‐map method was used to assess the participants' conceptual knowledge. The reasoning mode was assessed using a questionnaire with open‐ended questions. Results showed that, although some weak to moderate associations were found between conceptual organization in memory and reasoning modes, the students' ability to incorporate theory and evidence was in general inadequate. It was also found that students' reasoning modes were consistent with their epistemological perspectives. Moreover, male and female students appear to have different reasoning approaches.     

The ‘automatic’ use of context in children's reading

The present investigation examined developmental changes in the automatic use of context in single word recognition. A modified Stroop procedure was used in which children were asked to name the color of the ink of target words. The target was preceded either by a semantically related or by an unrelated word. Results suggested that, in contrast to attentional context effects (Pring and Snowling 1986), the older readers showed significantly more influence from the semantic context than the younger, less-proficient readers. The results are discussed with reference to the connections between a novice reading system and a child's rapidly growing semantic memory system.     

Children’s rights in education research: from aims to outcomes

One approach to children’s rights in research is to adopt a methodology that focuses on eliciting children’s perspectives. Ensuring representative participation from all children allows a diversity of contexts to be reflected in the results, and points to ways in which improvements can be made in specific settings. In cultural contexts where participation in decision-making is not a traditional role for children, their viewpoints are likely to provide results that highlight differences between cultural norms and children’s rights, and can offer an important focus of dialogue among stakeholders. It is proposed that children’s rights can therefore become integral to the whole process of a quantitative research project. This paper describes such an approach used in a Pacific Islands study, which investigated the quality of schooling through a probability-based sample survey of 1560 children in the first three years of formal education in 55 schools in Vanuatu, the Solomon Islands and Kiribati.     

Enablers and barriers to Educational Psychologists’ use of therapeutic interventions in an Irish context

Recent years have seen a revived interest in therapeutic educational psychology practice. The aim of this research is to identify the range of therapeutic approaches being delivered by Educational Psychologists (EPs) in an Irish context and to elicit the views of practitioners on the facilitators and barriers to therapeutic provision. Twelve participants were recruited from a total of 22 EPs working within one region of the National Educational Psychological Service (NEPS). Individual semi-structured interviews were held, and thematic analysis was used to examine the data gathered. Therapeutic approaches most commonly used by participants were Cognitive Behavioural Therapy (CBT) and Solution Focused Brief Therapy (SFBT). Barriers perceived by EPs as impacting therapeutic practice related to time, government policy, school factors, EP role, and training. Facilitators included service support, intervention outcomes and media interest. Findings suggest that many EPs are applying therapeutic approaches and are keen to provide more within their professional role.     

Children’s solving of ‘Tower of Hanoi’ tasks: dynamic testing with the help of a robot

Abstract

The present study investigated the usefulness of a pre-programmed, teleoperated, socially assistive peer robot in dynamic testing of complex problem solving utilising the Tower of Hanoi. The robot, in a ‘Wizard of Oz’ setting, provided instructions and prompts during dynamic testing to children when they had to solve 3?D Tower of Hanoi puzzles. Participants were 37?second grade 8-year-old children, of whom half received graduated prompts training between pre-test and post-test, delivered by the robot, and half did not. It was found that children’s progression in task accuracy varied considerably, depending on whether or not children were trained in solving Tower puzzles. Trained children showed greater progression in the number of Tower problems that they could solve accurately, made considerably fewer steps, although the Tower puzzles increased quickly in difficulty level. The mean completion time of trained children decreased at a slower rate than that of the untrained children, but both groups of children took considerably more time to think and plan ahead before they started the solving process. Only moderate relations with planning behaviour were found. In general, the study revealed that computerised dynamic testing with a robot as assistant has much potential in unveiling children’s potential for learning and their ways of tackling complex problems. The advantages and challenges of using a robot in educational assessment were discussed.     

An Interpretation of Ben’s Function in Intensifying Willy’s Tragedy from Aristotle’s Poetics

The play Death of a Salesman is undoubtedly the most influential play of Arthur Miller which depicts a tragic life of Willy Loman, a travelling salesman, induced by his false American Dream of making a fortune out of business. Unlike many other essays focusing on the hero Willy, this one tries to explore Willy’s dead brother Ben’s function in this play so as to demonstrate that Ben plays an important role in Willy’s life by making Willy’s life more tragic in terms of Aristotle’s tragic theory. The first part of the essay illustrates Ben’s importance to Willy and the second part centers on the way Ben pushes Willy to a more tragic situation.