¿Qué pueden aportar a los enseñantes los diferentes enfoques de la didáctica de las matemáticas? (segunda parte)

In the first part of this paper we raised the question of whether a customized theory of the didactics of mathematics was legitimate and presented and overview of such a theory. This second part analyses the contribution from and constraints the classical approaches and social practices on which they rely, and discusses the relationship between mathematics and its didactic

¿Qué pueden aportar a los enseñantes los diferentes enfoques de la didáctica de las Matemáticas? (primera parte)

This paper offers a general view of the relationships between Education, Mathematics Education and Mathematics

Alien Registration- Brousseau, Lucian G. (Fairfield, Somerset County)

https://digitalmaine.com/alien_docs/9788/thumbnail.jp

Teachers developing assessment for learning: impact on student achievement

While it is generally acknowledged that increased use of formative assessment (or assessment for learning) leads to higher quality learning, it is often claimed that the pressure in schools to improve the results achieved by students in externally-set tests and examinations precludes its use. This paper reports on the achievement of secondary school students who worked in classrooms where teachers made time to develop formative assessment strategies. A total of 24 teachers (2 science and 2 mathematics teachers, in each of six schools in two LEAs) were supported over a six-month period in exploring and planning their approach to formative assessment, and then, beginning in September 1999, the teachers put these plans into action with selected classes. In order to compute effect sizes, a measure of prior attainment and at least one comparison group was established for each class (typically either an equivalent class taught in the previous year by the same teacher, or a parallel class taught by another teacher). The mean effect size was 0.32

Effect of machining parameters and cutting tool coating on hole quality in dry drilling of fibre metal laminates

Fibre metal laminates (FMLs) are a special type of hybrid materials, which consist of sheets of metallic alloys and prepregs of composite layers stacked together in an alternating sequence and bonded together either mechanically using micro hooks or thermally using adhesive epoxies. The present paper contributes to the current literature by studying the effects of three types of cutting tool coatings namely TiAlN, AlTiN/TiAlN and TiN on the surface roughness and burr formation of holes drilled in an FML commercially known as GLARE®. While the cutting tool geometry is fixed, the study is also conducted for a range of drilling conditions by varying the spindle speed and the feed rate. The obtained results indicate that the spindle speed and the type of cutting tool coating had the most significant influence on the achieved surface roughness metrics, while tool coating had the most significant effect on burr height and burr root thickness. The most important outcome for practitioners is that the best results in terms of minimum roughness and burr formation were obtained for the TiN coated drills. However, such drills outperform the other two types of tools, i.e. with TiAlN and AlTiN/TiAlN coatings, only when used for short series of hole drilling due to rapid tool deterioratio

Expression Properties of Two Promoters During Callus and Shoot Development in Transgenic Poplar

The Arabidopsis thaliana developmental promoters of WUSCHEL (WUS) and COLD SHOCK DOMAIN PROTEIN 3 (CSP3) were tested for their suitability as potential control elements for the Cre-Lox recombination system in poplar cells. To remove the integrated transgene after CRISPR machinery has modified the genome, timely control of Cre is required. Both promoters are expressed in A. thaliana meristematic tissue, a crucial location of cell division, and we tested if the same would hold true when in transgenic poplar tissue. Both promoters were cloned upstream of a green fluorescent protein (GFP) encoding gene to track promoter activity. Transformed poplar plantlets were grown in vitro, then imaged and scored weekly to record GFP brightness level and tissue types. CSP3 was found to be the more reliable and consistent promoter due to higher activity during early shoot stages, and more consistency between genetic insertion events. However, neither WUS or CSP3 showed meristem-dominant expression as desired; both showed strong expression in callus tissue well before meristem differentiation, and also showed high variation in expression patterns and intensity between gene insertion events. Thus, additional layers of expression control, or other means of controlling Cre activity, are needed to meet system design goals.Keywords: CRISPR, promoter, recombinase, gene editing, WUSCHEL, COLD SHOCK DOMAIN PROTEIN 3, Cre-Lox, transgene, poplar, biotechnolog

Research on classroom practice: A monograph for topic study group 24, ICME 11 - The introductory chapter

published_or_final_versionThe 11th International Congress on Mathematical Education (ICME 11), Monterrey, Mexico, 6-13 July 2008. In Quaderni di Ricerca in Didattica, 2009, n. S4, p. 1-

Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic

Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-on-demand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-term (in the moment), medium-term (over several tasks), and long-term (over a year). The main factors conditioning students´ attention and its movement are identified and some didactical consequences are proposed

‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation

In this paper, we propose an approach to analysing teacher arguments that takes into account field dependence—namely, in Toulmin’s sense, the dependence of warrants deployed in an argument on the field of activity to which the argument relates. Freeman, to circumvent issues that emerge when we attempt to determine the field(s) that an argument relates to, proposed a classification of warrants (a priori, empirical, institutional and evaluative). Our approach to analysing teacher arguments proposes an adaptation of Freeman’s classification that distinguishes between: epistemological and pedagogical a priori warrants, professional and personal empirical warrants, epistemological and curricular institutional warrants, and evaluative warrants. Our proposition emerged from analyses conducted in the course of a written response and interview study that engages secondary mathematics teachers with classroom scenarios from the mathematical areas of analysis and algebra. The scenarios are hypothetical, grounded on seminal learning and teaching issues, and likely to occur in actual practice. To illustrate our proposed approach to analysing teacher arguments here, we draw on the data we collected through the use of one such scenario, the Tangent Task. We demonstrate how teacher arguments, not analysed for their mathematical accuracy only, can be reconsidered, arguably more productively, in the light of other teacher considerations and priorities: pedagogical, curricular, professional and personal

Ways to teach modelling—a 50 year study

This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author’s observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was entirely focused on their learning standards models of a restricted range of phenomena, largely from Newtonian mechanics. This did not develop the numeracy/mathematical literacy that was so clearly important for future citizens. Early explorations started with modelling workshops with high school teachers and mathematics undergraduates, observed and analysed—in some case using video. The theoretical basis of this work has been essentially heuristic, though the Shell Centre studies included, for example, a detailed analysis of formulation processes that has not, as so often, been directly replicated. Recent work has focused on developing a formative assessment approach to teaching modelling that has proved both successful and popular. Finally, the system-level challenges in trying to establish modelling as an integral part of mathematics curricula are briefly discussed