A new approach to the assessment of children's mathematical competence

The report is a translation of part of a Swedish paper entitled “On Students' Achievement in Mathematics after Finishing Comprehensive School”. The intention of the investigation was to

- diagnose the retention of some basic skills in some topics in algebra and geometry,

- reveal difficult steps in the learning processes in these topics.

Starting with a complicated question, e.g. the equation \(\frac{{3x - 2}}{2} = \frac{x}{3}\) a sequence consisting of 5–15 problems were constructed. Each new problem followed by the preceding one by taking away one or two details. \(\begin{gathered} 3(3x - 2) = 2x \\ {\text{ 9}}x - 6 = 2x \\ {\text{ 7}}x - 6 = 0 \\ {\text{ 7}}x = 6 \\ \end{gathered} \) is an example of a sequence belonging to the equation above. From about 10 complicated problems (“top-items”) and their sequences, in all 130 items, 10 sub-tests were put together in such a way that the pupils who took the test were not aware of the sequences but found no connection between the problems. Many surprising results were found, e.g., that the students scored higher on 14/(x+2)=2 than on 4/x=3, that the difficulty in finding the area of a triangle depended on the position of the triangle and that the problems “Simplify a/a ², a²/a, a/a” were of quite unequal difficulty. A discussion about the students' thinking in patterns and mechanically learning ends the report.     

Making Sense of Number Words and Arabic Digits: Does Order Count More?

The ability to choose the larger between two numbers reflects a mature understanding of the magnitude associated with numerical symbols. The present study explores how the knowledge of the number sequence and memory capacity (verbal and visuospatial) relate to number comparison skills while controlling for cardinal knowledge. Preschool children’s (N = 140, M_{age-in-months} = 58.9, range = 41–75) knowledge of the directional property of the counting list as well as the spatial mapping of digits on the visual line were assessed. The ability to order digits on the visual line mediated the relation between memory capacity and number comparison skills while controlling for cardinal knowledge. Beyond cardinality, the knowledge of the (spatial) order of numbers marks the understanding of the magnitude associated with numbers.     

The school as a learning organisation: The concept and its measurement

A growing body of scholars, educators and policy makers has argued for reconceptualising schools as “learning organisations” in the last 25 years as. However, a lack of clarity on the concept has hindered its advance in theory and practice. This study responds to this problem by developing a schools as learning organisations scale that expands and clarifies the concept on several points. Drawing on survey data (nschool staff = 1,703) from Wales (UK), it examines the key characteristics of a school as a learning organisation through a principal component analysis and reliability analysis. The results showed that such a school is associated with eight dimensions: (a) a shared vision centred on the learning of all students, (b) partners contributing to school vision, (c) continuous learning opportunities, (d) team learning and collaboration, (e) a culture of enquiry, innovation and exploration, (f) systems for collecting and exchanging knowledge and learning, (g) learning with and from the external environment, and (h) modelling learning leadership. The resulting 65-item scale demonstrated good psychometric qualities. A reliable and valid schools as learning organisations scale can help enhance our understanding of the concept. The scale can also be used by school leaders, teachers and all others wanting to develop a thriving learning culture in their schools.     

Exploring features for the automatic identification of user goals in web search

Queries submitted to search engines can be classified according to the user goals into three distinct categories: navigational, informational, and transactional. Such classification may be useful, for instance, as additional information for advertisement selection algorithms and for search engine ranking functions, among other possible applications. This paper presents a study about the impact of using several features extracted from the document collection and query logs on the task of automatically identifying the users’ goals behind their queries. We propose the use of new features not previously reported in literature and study their impact on the quality of the query classification task. Further, we study the impact of each feature on different web collections, showing that the choice of the best set of features may change according to the target collection.     

Focal event,contextualization, and effective communication in the mathematics classroom

The aim of this article is to develop analytical tools for studying mathematical communication in collaborative activities. The theoretical construct of contextualization is elaborated methodologically in order to study diversity in individual thinking in relation to effective communication. The construct of contextualization highlights issues of diversity in collaborative activities as it emphasizes how students may struggle differently with a learning activity. The interaction of students (12 to 13 years old), playing a specifically designed dice game, is used as an example for illustration. The article shows how accounting for the focal events of the interlocutors, and the contexts in which they contextualize these events, help in organizing our thinking about mathematically effective communication in collaborative activities.     

Teaching together and learning together – Primary science student teachers’ and their mentors’ joint teaching and learning in the primary classroom

This paper focuses on what and how primary science student teachers and their mentors learn from planning and reflecting together on each other’s science lessons for pupils aged 7–9. The student teachers had had training in scientific knowledge, but only brief experience of teaching. The mentors were well experienced in the pedagogy of teaching and mentoring, but did not feel confident about their science content knowledge and the teaching of science. Throughout the process of teaching and reflecting together the student teachers and the mentors expressed several specific examples of their joint learning.     

Accuracy and precision of loadsol® insole force-sensors for the quantification of ground reaction force-based biomechanical running parameters

Force plates represent the “gold standard” in measuring running kinetics to predict performance or to identify the sources of running-related injuries. As these measurements are generally limited to laboratory analyses, wireless high-quality sensors for measuring in the field are needed. This work analysed the accuracy and precision of a new wireless insole forcesensor for quantifying running-related kinetic parameters. Vertical ground reaction force (GRF) was simultaneously measured with pit-mounted force plates (1?kHz) and loadsol^® sensors (100?Hz) under unshod forefoot and rearfoot running-step conditions. GRF data collections were repeated four times, each separated by 30 min treadmill running, to test influence of extended use. A repeated-measures ANOVA was used to identify differences between measurement devices. Additionally, mean bias and Bland–Altman limits of agreement (LoA) were calculated. We found a significant difference (p?® devices for these parameters. For these same parameters, the LoA analysis showed that 95% of all measurement differences between insole and force plate measurements were less than 12%, demonstrating high precision of the sensors. However, highly dynamic behaviour of GRF, such as force rate, is not yet sufficiently resolved by the insole devices, which is likely explained by the low sampling rate.     

Backstage accounting in preschool: analysing dealing with complaints as ‘rehearsing away’ professional knowledge

Citizens of modern societies must trust a broad range of systems and professionals. When distrust arises, professionals are expected to be accountable. This paper draws on conversational material from a preschool team meeting. When a preschool work team prepares to meet a parent who has complained about their recurring neglect to change her child’s nappies ‘in time’, they are found: (1) to carefully review the encounter with the client, (2) in a team-building fashion, to select suitable accounts to offer ‘front stage’ and (3) to internally justify their selection of accounts. Our results indicate that work team members who engaged in backstage rehearsal author the organisation for building trust and, simultaneously ‘rehearse away’ what should remain the organisations’ secrets. Communicating the intent to satisfy was deemed more important than was using evidence from their professional knowledge base.     

A comparative evaluation of regional subsidies for collaborative and individual R&D in small and medium-sized enterprises

We analyse whether public subsidies supporting collaborative research and development (R&D) projects in small and medium-sized enterprises (SMEs) are able to encourage persistent R&D investment and interorganisational networking more than subsidies supporting individual R&D projects. Adopting a counterfactual approach to policy evaluation, we compare subsidies for collaborative R&D and for individual R&D implemented in the same Italian region in the same period. Our findings suggest that, once public support is no longer available, the two subsidies have different effects on different types of SMEs. If the policymakers’ objective is to increase the number of R&D-performing SMEs over time, they should provide subsidies for collaborative R&D to firms with modest R&D experience. If their objective is to increase the amount of spontaneous R&D investment over time, they should target SMEs with some prior R&D experience, using either subsidy. Finally, if their objective is to induce SMEs to network with external organisations, subsidies for collaborative R&D projects should be preferred to subsidies for individual R&D projects.