THE EFFECT OF PURPOSEFUL MATHEMATICS DISCOURSE IN THE CLASSROOM ON STUDENTS’ MATHEMATICS LANGUAGE IN THE CONTEXT OF PROBLEM SOLVING

This study examines how one secondary school teacher’s use of purposeful oral mathematics language impacted her students’ language use and overall communication in written solutions while working with word problems in a grade nine academic mathematics class. Mathematics is often described as a distinct language. As with all languages, students must develop a sense for oral language before developing social practices such as listening, respecting others ideas, and writing. Effective writing is often seen by students that have strong oral language skills. Classroom observations, teacher and student interviews, and collected student work served as evidence to demonstrate the nature of both the teacher’s and the students’ use of oral mathematical language in the classroom, as well as the effect the discourse and language use had on students’ individual written solutions while working on word problems. Inductive coding for themes revealed that the teacher’s purposeful use of oral mathematical language had a positive impact on students’ written solutions. The teacher’s development of a mathematical discourse community created a space for the students to explore mathematical language and concepts that facilitated a deeper level of conceptual understanding of the learned material. The teacher’s oral language appeared to transfer into students written work albeit not with the same complexity of use of the teacher’s oral expression of the mathematical register. Students that learn mathematical language and concepts better appear to have a growth mindset, feel they have ownership over their learning, use reorganizational strategies, and help develop a discourse community.

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

Oral language competence in incarcerated young offenders : links with offending severity

Previous research in Australia and overseas has shown that young offenders serving community-based orders are at high-risk for undetected but clinically significant oral language difficulties. However, this phenomenon has received little attention in incarcerated samples, and links with offending severity, mental health, and other markers of early risk have not previously been systemically examined. A cross-sectional examination of 100 young offenders (mean age 19.03 years) completing custodial sentences in Victoria, Australia was conducted. A range of standardized oral language, IQ, mental health, and offending severity measures was employed. Forty-six per cent of participants were classified as language impaired (LI), and these were compared with the non-LI sub-group on background and offending variables. When the sub-group with high scores on a measure of offending severity was compared with those with (relatively) lower offending scores, significant differences on a range of language measures were identified. A range of early risk indicators (such as placement in Out of Home Care) was also examined with respect to language impairment in this high-risk group. Results are discussed with respect to policy and practice pertaining to early intervention for vulnerable children, and implications for service delivery within the justice system. In particular, emphasis is placed on the need to closely examine the oral language skills of children who struggle with the transition to literacy and then display behavioural difficulties in the classroom. Once a young person is engaged with youth justice services, a high index of suspicion should be maintained with respect to their oral language skills; for example, in relation to forensic interviewing and the ability to benefit from verbally mediated interventions.

Youth (in)justice : oral language competence in early life and risk for engagement in antisocial behaviour in adolescence

Youth offenders are complex and challenging for policymakers and practitioners alike and face high risks for long-term disadvantage and social marginalisation. In many cases, this marginalisation from the mainstream begins in early life, particularly in the classroom, where they have difficulty both with language/literacy tasks and with the interpersonal demands of the classroom. Underlying both sets of skills is oral language competence—the ability to use and understand spoken language in a range of situations and social exchanges, in order to successfully negotiate the business of everyday life. This paper highlights an emerging field of research that focuses specifically on the oral language skills of high-risk young people. It presents evidence from Australia and overseas that demonstrates that high proportions (some 50% in Australian studies) of young offenders have a clinically significant, but previously undetected, oral language disorder. The evidence presented in this paper raises important questions about how young offenders engage in forensic interviews, whether as suspects, victims or witnesses. The delivery of highly verbally mediated interventions such as counselling and restorative justice conferencing is also considered in the light of emerging international evidence on this topic.

Motivational Strategies to Increase Completion of Assignments in Mathematics Classes

The purpose of this paper is to share the results of an 8-week study that focused on the effects of incorporating real-life applications and rewards to measure their impact on student motivation. The goal was to reduce the number of students unmotivated to complete their mathematics assignments satisfactorily.

Pressure-induced charge transfer in lanthanum nickel ferrate (LaNi0.5Fe0.5O3) and analogies to composition-driven charge transfer in dilanthanum cuprate (La2CuO4): an infrared study

A reversible pressure-induced phase transition in lanthanum nickel ferrate (LaNi0.5Fe0.5O3) manifests itself in the infrared spectrum of the transition metal-oxygen stretching (nu(TM-O)) modes by the emergence of new peaks at pressures greater than similar to 1.4 x 10(9) Pa. Analogies to this transition are made by considering charge transfer in dilanthanum cuprate (La2CuO4) and its modification by partial substitution of copper ions by chromium ions.

A comparative approach to somatic cell nuclear transfer in the rhesus monkey

BACKGROUND: Despite the potential utility of primate somatic cell nuclear transfer (SCNT) to biomedical research and to the production of autologous embryonic stem (ES) cells for cell- or tissue-based therapy, a reliable method for SCNT is not yet availab

International on-line reciprocal peer tutoring to promote modern language development in primary schools

The paper reports data from an on-line peer tutoring project. In the project 78, 9–12-year-old students from Scotland and Catalonia peer tutored each other in English and Spanish via a managed on-line envi- ronment. Significant gains in first language (Catalonian pupils) modern language (Scottish pupils) and attitudes towards modern languages (both Catalonian and Scottish pupils) were reported for the exper- imental group as compared to the control group. Results indicated that pupils tutored each other in using Piagetian techniques of error correction during the project. Error correction provided by tutors to tutees focussed on morph syntaxys, more specifically the correction of verbs. Peer support provided via the on- line environment was predominantly based on the tutor giving the right answer to the tutee. High rates of impact on tutee corrected messages were observed. The implications for peer tutoring initiative taking place via on-line environments are discussed. Implications for policy and practice are explored

Periapical tissue healing after post space preparation with or without use of a protection plug and root canal exposure to the oral environment. Study in dogs

The purpose of this study was to evaluate the influence of coronal leakage on the healing of dogs' periapical tissues after root canal filling, post space preparation and protection or not with a temporary sealer plug. Forty root canals of dogs' teeth were instrumented and filled by the lateral condensation technique with gutta-percha points and Endomethasone or CRCS sealers. After post space preparation, the remaining filling material was protected or not with a plug of temporary Coltosol sealer and exposed to the oral environment for 90 days. Thereafter, the animals were sacrificed and the specimens were removed and prepared for histomorphological and histobacteriological analysis. The findings revealed 35% of microbial leakage in the groups without plugs and 15% of leakage in the groups with plugs. Statistical analysis showed that the use of a Coltosol plug improved significantly the histomorphological results regardless of the type of root canal sealer (p=0.05) and that CRCS and Endomethasone sealers showed similar results (p>0.05).

Multidimensional modelling to investigate interspecies hydrogen transfer in anaerobic biofilms

Anaerobic digestion is a multistep process, mediated by a functionally and phylogenetically diverse microbial population. One of the crucial steps is oxidation of organic acids, with electron transfer via hydrogen or formate from acetogenic bacteria to methanogens. This syntrophic microbiological process is strongly restricted by a thermodynamic limitation on the allowable hydrogen or formate concentration. In order to study this process in more detail, we developed an individual-based biofilm model which enables to describe the processes at a microbial resolution. The biochemical model is the ADM1, implemented in a multidimensional domain. With this model, we evaluated three important issues for the syntrophic relationship: (i) is there a fundamental difference in using hydrogen or formate as electron carrier? (ii) Does a thermodynamic-based inhibition function produced substantially different results from an empirical function? and; (iii) Does the physical colocation of acetogens and methanogens follow directly from a general model. Hydrogen or formate as electron carrier had no substantial impact on model results. Standard inhibition functions or thermodynamic inhibition function gave similar results at larger substrate field grid sizes (> 10 mu m), but at smaller grid sizes, the thermodynamic-based function reduced the number of cells with long interspecies distances (> 2.5 mu m). Therefore, a very fine grid resolution is needed to reflect differences between the thermodynamic function, and a more generic inhibition form. The co-location of syntrophic bacteria was well predicted without a need to assume a microbiological based mechanism (e.g., through chemotaxis) of biofilm formation.

Die Sprache der Auricher Juden. Zur Rekonstruktion westjiddischer Sprachreste in Ostfriesland:to reconstruct westjiddischer language residues in Ostfriesland

Western Yiddish, the spoken language of the traditional Jewish society in the German- and Dutch-speaking countries, was abandoned by its speakers at the end of the 18th in favour of the emerging standard varieties: Dutch and German, respectively. Remnants of Western Yiddish varieties, however, remained a medium of discourse in remote provinces and could be found well into the 19th and sometimes the 20th century in some South-western areas of Germany and Switzerland, the Alsace, some areas of the Netherlands and in parts of the German province of Westphalia. It appears that rural Jewish communities sometimes preserved in-group vernaculars, which were based on Western Yiddish. Sources discovered in 2004 in the town of Aurich prove that Jews living in East Frisia, a Low-German speaking peninsula in the North-west of Germany, used a variety based on Western Yiddish until the Second World War. It appears that until the Holocaust a number of small, close-knit Jewish communities East Frisia, which depended economically mainly on cattle-trading and butchery, kept certain specific cultural features, among them the vernacular which they spoke alongside Low German and Standard German. The sources consist of two amateur theatre plays, a memoir and two word lists written in 1902, 1928 and the 1980s, respectively. In the monograph these sources are documented and annotated as well as analyzed linguistically against the background of rural Jewish life in Northern Germany. The study focuses on traces of language contact with Low German, processes of language change and on the question of the function of the variety in day-to-day life in a rural Jewish community.

An iterative-style approach to constructing intelligent tutoring systems in mathematics

Mathematics is highly structured and also underpins most of science and engineering. For this reason, it has proved a very suitable domain for Intelligent Tutoring System (ITS) research, with the result that probably more tutoring systems have been constructed for the domain than any other. However, the literature reveals that there still exists no consensus on a credible approach or approaches for the design of such systems, despite numerous documented efforts. Current approaches to the construction of ITSs leave much to be desired. Consequently, existing ITSs in the domain suffer from a considerable number of shortcomings which render them 'unintelligent'. The thesis examines some of the reasons why this is the case. Following a critical review of existing ITSs in the domain, and some pilot studies, an alternative approach to their construction is proposed (the 'iterative-style' approach); this supports an iterative style, and also improves on at least some of the shortcomings of existing approaches. The thesis also presents an ITS for fractions which has been developed using this approach, and which has been evaluated in various ways. It has, demonstrably, improved on many of the limitations of existing ITSs; furthermore, it has been shown to be largely 'intelligent', at least more so than current tutors for the domain. Perhaps more significantly, the tutor has also been evaluated against real students with, so far, very encouraging results. The thesis thus concludes that the novel iterative-style approach is a more credible approach to the construction of ITSs in mathematics than existing techniques.