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.     

Expectations and recall of texts: The more able–more difficult effect

Expectations about self-competence and difficulty of a task to be undertaken can foster motivation and hence affect engagement, giving rise to individual differences in performance. This effect was examined in a memory task. An increase in recall performance following instructions about high competence was hypothesised; in addition, a modulating effect of instructions about easiness or difficulty of the material was expected. Two experiments were performed, in which expectations were established by giving instructions of high or low competence and easiness or difficulty of two texts: objectively, one easy, one difficult. The results showed that being given instructions about high competence raises performance if presented alone and if difficult texts are expected when the actual text is easy: the more able–more difficult effect.     

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.     

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.     

Efficient sample preparation in immuno-matrix-assisted laser desorption/ionization mass spectrometry using acoustic trapping

Acoustic trapping of minute bead amounts against fluid flow allows for easy automation of multiple assay steps, using a convenient aspirate/dispense format. Here, a method based on acoustic trapping that allows sample preparation for immuno-matrix-assisted laser desorption/ionization mass spectrometry using only half a million 2.8 μm antibody covered beads is presented. The acoustic trapping is done in 200 × 2000 μm² glass capillaries and provides highly efficient binding and washing conditions, as shown by complete removal of detergents and sample processing times of 5-10 min. The versatility of the method is demonstrated using an antibody against Angiotensin I (Ang I), a peptide hormone involved in hypotension. Using this model system, the acoustic trapping was efficient in enriching Angiotensin at 400 pM spiked in plasma samples.     

On the determinants of employment-related organised education and informal learning

This paper analyses the distribution of employment-related organised education and informal learning in the Canadian workforce. The paper draws on a large-scale survey, the Changing Nature of Work and Lifelong Learning (WALL), which was based on structured and standardised telephone interviews with a representative sample of 5783 Canadian members of the employed labour force. In exploring the determinants facilitating employment-related informal learning, three analytical categories of factors derived from previous research on learning participation were used: individual-level factors, job characteristics and workplace environment. The analyses focus on differences in individuals, jobs and workplace characteristics among adult workers who acquired or improved their job-related skills through different training pathways. In addition, analyses were performed to compare the extent to which these factors differ in their influence on learning decisions among workers who combine both organised education and informal learning and those who receive only informal learning. The results indicate that important predictors of participation in employment-related organised education and informal learning are age, educational attainment, learning skills, occupational class, education-job relation, degree of autonomy, degree of labour intensity, principal area of production and organisation size.     

‘Thou shalt not plagiarise’: from self-reported views to recognition and avoidance of plagiarism

Throughout much of the literature on plagiarism in higher education, there is an implicit assumption that students who understand plagiarism, who have high ethical views and declare not to engage in plagiaristic behaviour are able to recognise it and avoid it in practice. Challenging this supposition, this paper contrasts students’ self-reported data with their ability to recognise and avoid plagiarism in a proposed case scenario. A questionnaire was adapted from previous literature and administered to a sample of undergraduate first- and second-year students in an Irish university. Results show that self-reported measures are not a powerful predictor of the students’ ability to recognise the practical case as an academic breach, nor to avoid the breach through referencing. This suggests that students’ understanding and awareness of academic breaches would benefit from experiential learning and that higher education institutions should not merely rely on providing statements and definitions of academic misconduct. Also, the results highlight the potential unsuitability of using self-reported measures to study plagiarism, despite their widespread use.