Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course

We present results from a classroom-based intervention designed to help a class of grade 10 students (14–15 years old) learn proof while studying trigonometry in a dynamic geometry software environment. We analysed some students’ solutions to conjecture-and-proof problems that let them gain experience in stating conjectures and developing proofs. Grounded on a conception of proof that includes both empirical and deductive mathematical argumentations, we show the trajectories of some students progressing from developing basic empirical proofs towards developing deductive proofs and understanding the role of conjectures and proofs in mathematics. Our analysis of students’ solutions is based on networking Boero et al.’s construct of cognitive unity of theorems, Pedemonte’s structural and referential analysis of conjectures and proofs, and Balacheff and Margolinas’ cK¢ model, while using Toulmin schemes to represent students’ productions. This combination has allowed us to identify several emerging types of cognitive unity/rupture, corresponding to different ways of solving conjecture-and-proof problems. We also show that some types of cognitive unity/rupture seem to induce students to produce deductive proofs, whereas other types seem to induce them to produce empirical proofs.     

Spanish savings banks: a view on intangibles

We study Spanish savings banks from the point of view of their efficiency, transparency in the disclosure of financial information through the net, and the provision of electronic banking services. Performance indicators are developed using data envelopment analysis and the tools of multivariate statistical analysis. The choice of indicators is framed within the theory of intangible assets. An attempt is made rank savings banks according to their level of achievement in each indicator. Savings banks are shown to be classified into four groups according to the level of achievement in the indicators of transparency and e-service. The relationship between efficiency and profitability is also discussed.     

The role of "genetics" in popular understandings of race in the United States

The increase in public representation of the science-based concept "genetics" in the mass media might be expected to have a major impact on public understanding of the concept of "race." A model of lay understandings of the role of genetics in the contemporary United States is offered based on focus group research, random digit dial surveys, and community based surveys. That model indicates that lay people identify are primarily by physical features, but these identifications are categorized into a variety of groupings that may be regional, national, or linguistic. Although they believe that physical appearance is caused largely by genetics, and therefore that race has a genetic basis, they do not uniformly conclude, however, that all perceived racial characteristics are genetically based. Instead, they vary in the extent to which they attribute differences to cultural, personal, and genetic factors.     

Visual Attention Preference for Intermediate Predictability in Young Children

How do children allocate their attention? There is too much information in the world to encode it all, so children must pick and choose. How do they organize their sampling to make the most of the learning opportunities that surround them? Previous work shows infants actively seek intermediately predictable information. Here we employ eye-tracking and computational modeling to examine the impact of stimulus predictability across early childhood (ages 3–6 years, n = 72, predominantly Non-Hispanic White, middle- to upper-middle-income), by chronological age and cognitive ability. Results indicated that children prefer attending to stimuli of intermediate predictability, with no differences in this pattern based on age or cognitive ability. The consistency may suggest a robust general information-processing mechanism that operates across the lifespan.     

Advancing opportunities for children’s informal STEM learning transfer through parent–child narrative reflection

This study examined whether families’ conversational reflections after a STEM (science, technology, engineering, and mathematics)-related experience in a museum promoted learning transfer. 63 children (M = 6.93 years; 30 girls; 57% White, 17.5% Latinx, 8% Asian, 5% African American, 9.5% mixed, 3% missing race/ethnicity) and their parents received an engineering demonstration, engaged in a building activity, and either recorded a photo-narrative reflection about their building experience or not at the museum. Thirty-six of these families completed a building activity with different materials weeks later at home, and the majority (77%) evidenced learning transfer of the building principle demonstrated at the museum. Those who participated in the photo-narrative reflection at the museum also showed learning transfer by talking more about STEM during the home building activity.     

Performance,Citizenship and the Knowledge Society: A new mandate for European education policy

In this paper we map out the debate concerning a new mandate for European education policy based on recent socio-economic, political and educational developments, seen from the perspective of educational researchers located on the European (semi)periphery. The first part of the paper looks at the category 'preparation for the labour market', while the second part concerns itself with the category 'citizenship'. With regard to the former, it is argued that a new mandate for European education policy finds itself inextricably linked to the new education mandate of the new middle class, in a setting of globalisation and, closer to home, European construction. The latter attempts to conceptualise the emergence of new forms of citizenship at a time when the modern social contract suffers a process of transformation (or, what we term, reconfiguration). Based on the distinction between 'attributed citizenship' and 'demanded citizenship', we analyse changes taking place in state regulation as well as explore some of their implications for schooling.     

Customer’s role in knowledge management and in the innovation process: effects on innovation capacity and marketing results

Scholars have acknowledged customer knowledge management (CKM) as a key strategic resource for improving innovation and supporting long-term customer relationship management. This study provides a deeper understanding of the internal antecedents of business innovation capacity overcoming previous approaches. A model that had not previously been tested was used to analyse the role of customer collaboration and CKM – measured as a second-order construct – in innovation processes and marketing results. To test the model, structural equation modelling (partial least squares) was applied to a random sample of 210 Spanish companies. Results confirm that CKM and customer collaboration are antecedents of innovation capacity and marketing results. Furthermore, the effect of CKM is greater than the effect of customer collaboration. This paper provides a basis for managers to encourage innovation in their companies and explains how managers can improve marketing results.     

The initial development of spelling in Spanish: From global to analytical

During a school year, samples of words written by three groups of children of successive ages were collected. Two groups of children were in first and second year of Kindergarten (4 and 5 years of age), when alphabetic rules were not taught in a systematic way. The third group was in first year of Primary School (6 years of age), and was being taught to read and spell in a systematic way. After classifying the words written by the children, seven categories of spelling were obtained, which may represent different stages in their learning process. Their analysis showed that they are related to different types of knowledge and processes, mainly phonological ones. The results show that the development of spelling in Spanish does not qualitatively differ from that of children who learn to spell in opaque writing systems. The differences mainly involve the time it takes to learn, and the rate of acquisition.     

SciJourn is magic: construction of a science journalism community of practice

This article is the first to describe the discoursal construction of an adolescent community of practice (CoP) in a non-school setting. CoPs can provide optimal learning environments. The adolescent community centered around science journalism and positioned itself dichotomously in relationship to school literacy practices. The analysis focuses on recordings from a panel-style research interview from an early implementation of the Science Literacy Through Science Journalism (SciJourn) project. Researchers trained high school students participating in a youth development program to write science news articles. Students engaged in the authentic practices of professional science journalists, received feedback from a professional editor, and submitted articles for publication. I used a fine-grained critical discourse analysis of genre, discourse, and style to analyze student responses about differences between writing in SciJourn and in school. Students described themselves as agentic in SciJourn and passive in school, using an academic writing discourse of deficit to describe schooling experiences. They affiliated with and defined a SciJourn CoP, constructing positive journalistic identities therein. Educators are encouraged to develop similar CoPs. The discursive features presented may be used to monitor the development of communities of practice in a variety of settings.     

Effect of Dental Course Cycle on Anatomical Knowledge and Dental Carving Ability of Dental Students

This study assessed the effect of the course cycle on theoretical knowledge of dental morphology and the dental carving ability of dental students. Thirty-two dental students from the third semester (initial cycle) and 30 students from the eighth and tenth semesters of the dental course (end cycle) had their theoretical knowledge on dental morphology assessed using a questionnaire with ten closed questions. Their dental carving ability was also assessed using wax carvings in macro models of plaster (for the third [S3] and eight [S8] semesters) and natural-sized artificial teeth (for the tenth [S10] semester). The teeth chosen for the dental carving activity were #16 and #47. The scores were statistically analyzed using the t-test, Kruskal–Wallis test, and Mann–Whitney test (α = 0.05). Students from the initial cycle presented better theoretical knowledge than the other groups did (P < 0.007). No significant differences in carving score were found between the initial and end cycles (P > 0.05), although S10 students obtained a higher score for teeth #16 and #47 (P < 0.05). Natural-sized artificial teeth received a higher evaluation score in dental carvings than the macro models (P < 0.001). Within the limits of this study, it was possible to conclude that students from the initial cycle (S3) presented higher theoretical knowledge, whereas no difference in carving ability was observed between the initial and end cycles. The tenth semester (S10) students performed dental carvings with better quality. Furthermore, carvings in natural-sized artificial teeth presented better quality compared with the macro models.