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

Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions

Competences of Mathematics Teachers in Diagnosing Teaching Situations and Offering Feedback to Students:Specificity, Consistency and Reification of Pedagogical and Mathematical Discourses

In the study we report in this chapter, we investigate the competences of mathematics pre- and in-service teachers in diagnosing situations pertaining to mathematics teaching and in offering feedback to the students at the heart of said situations. To this aim we deploy a research design that involves engaging teachers with situation-specific tasks in which we invite participants to: solve a mathematical problem; examine a (fictional yet research-informed) solution proposed by a student in class and a (fictional yet research-informed) teacher response to the student; and, describe the approach they themselves would adopt in this classroom situation. Participants were 23 mathematics graduates enrolled in a post-graduate mathematics education programme, many already in-service teachers. They responded to a task that involved debating the identification of a tangent line at an inflection point of a cubic function through resorting to the formal definition of tangency or the function graph. Analysis of their written responses to the task revealed a great variation in the participants’ diagnosing and addressing of teaching issues – in this case involving the role of visualisation in mathematical reasoning. We describe this variation in terms of a typology of four interrelated characteristics that emerged from the data analysis: consistency between stated beliefs/knowledge and intended practice, specificity of the response to the given classroom situation, reification of pedagogical discourses, and reification of mathematical discourses. We propose that deploying the theoretical construct of these characteristics in tandem with our situation-specific task design can contribute towards the identification – as well as reflection upon and development – of mathematics teachers’ diagnostic competences in teacher education and professional development programmes

The tasks and place of controlling department in the company

W artykule zaprezentowane zostały zadania i miejsce komórki controllingu w strukturze organizacyjnej przedsiębiorstwa. Na jej czele stoi controller, który pełni funkcję doradcy ekonomicznego zarządu. Jej głównym zadaniem jest opracowywanie planów operacyjnych i strategicznych, budżetowanie kosztów, przychodów i wyników w krótkich okresach czasu, monitorowanie odchyleń od budżetów i planów oraz wyjaśnianie przyczyn tych odchyleń. Rozwiązania dotyczące roli i miejsca komórki controllingu w strukturze organizacyjnej przedsiębiorstw są zindywidualizowane i elastycznie dostosowywane do potrzeb zarządu. Potwierdzają to zaprezentowane w artykule przykłady empiryczne. W pierwszym okresie wdrażania controllingu komórka controllingu jest podporządkowana prezesowi zarządu. Po utrwaleniu jej pozycji w przedsiębiorstwie komórka ta podlega viceprezesowi do spraw finansowych. W krajowych grupach kapitałowych oprócz komórki controllingu operacyjnego wydzielane są działy controllingu finansowego lub działy nadzoru kapitałowego nad spółkami zależnymi. W korporacjach międzynarodowych komórki controllingu występują na kilku szczeblach struktury organizacyjnej i podporządkowane są controllerowi centralnemu.The paper presents the tasks and place of controlling department in the company. The controller, who is at its forefront, plays the role of economic advisor for the management board. The main tasks of the department are to prepare operational as well as strategic plans, budgeting of costs, revenues and results within short period of time, monitoring the deviations from the budgets and plans and investigating the source of these deviations. The solutions regarding to the role and the place of controlling department in organizational structure are very individual and flexibly adopted to the management board needs. This is proven by the empirical examples given in this paper. In the first stage of controlling introduction process, controlling department is subordinated to CEO. Later, when the position of the department is settled in the company, the CFO takes the control over it. In domestic capital groups financial controlling departments or capital supervision departments over subsidiary companies are additionally formed. In international corporations there are controlling departments on several levels of organizational structure, subordinated to the central controller