Experience with using counterexamples in an introductory calculus class

The paper describes a personal experience with using counterexamples as a pedagogical strategy in the teaching and learning of an introductory calculus course at a university of technology

The school-tertiary interface in mathematics: teaching style and assessment practice

Issues arising in the transition from secondary school to tertiary mathematics study are increasingly coming under scrutiny. In this paper, we analyse two practical aspects of the school–tertiary interface: teaching style; and assessment. We present some of the findings arising from a 2-year national project in New Zealand titled “Analysing the Transition from Secondary to Tertiary Education in Mathematics” supported by the New Zealand Ministry of Education. The results provide evidence of similarities and differences between teachers and lecturers in their preferred teaching approaches and assessment strategies that contribute to a transitional gap between the school and tertiary sectors. The results also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a need for improved communication between the two sectors

The influence of attention on mathematical knowledge of teachers and lecturers: a comparison

This paper reports on some findings from the project ‘Analysing the Transition from Secondary to Tertiary Education in Mathematics’. One of key variables in the school to university transition is the teacher/lecturer, and here we deal with data analysing secondary teachers’ and tertiary lecturers’ responses to four mathematics questions. Elsewhere we consider knowledge, preparedness and teaching style etc, but this paper tracks the ability to use mathematical procedures. We hypothesise that this is a function of what we pay attention to, as described in Mason’s discipline of noticing. The results reveal that many teachers and lecturers fail to notice the necessary conditions for problems that imply that procedures are not always applicable. Possible reasons for this along with implications for student learning are discussed

Paradoxes and counterexamples in teaching and learning of probability at university

This article is devoted to practical aspects of teaching and learning of probability at university. It presents the difficulties and attitudes of first-year university science and engineering students towards using paradoxes and counterexamples as a pedagogical strategy in teaching and learning of probability. It also presents a student's point of view on the effectiveness of this pedagogical strategy

Overview of V.A. Plotnikov’s research on averaging of differential inclusions

In this review, we will first look in detail at Plotnikov’s results on the substantiation of full and partial schemes of averaging of differential inclusions of the standard form on finite and infinite intervals. Then we will consider the algorithms where it is not possible to find the average, but there is a possibility to find its estimation from below and from above. Such an approach is also used when the average can be found only approximately. This situation is common for differential inclusions with fast and slow variables. In the end, we will present the results on the substantiation of the full and partial averaging methods for impulsive differential inclusions on finite and infinite intervals

Діагностика внутрішнього середовища як етап формування стратегій розвитку підприємства

The study is structured and proposed approach to economic diagnostics of the internal environment of the enterprise of alternative energy, which is implemented and presented in the form II-x staged method of providing including the identification of potential and identify the strengths and weaknesses of the companies, to further the formation of their development strategies.  As a result of analysis of enterprises VRIO-shaped map of alternative energy strategy selection "resources-ability" and the coordinates of the vectors of development of industrial and economic systems.У процесі дослідження структуровано та запропоновано підхід до проведення економічної діагностики внутрішнього середовища підприємств  альтернативної енергетики, який реалізований та представлений у вигляді  II-ох етапного методу, що передбачає зокрема визначення потенціалу та виявлення сильних і слабких сторін підприємств, з метою подальшого формування їх стратегій розвитку. За результатами VRIO-аналізу підприємств альтернативної енергетики сформовано карту вибору стратегії «ресурси-здатності» та визначено координати векторів розвитку виробничо-економічних систем

The Architectonics of Facilitation-Reflective Methodology of Motivation in the System of Energy Management of Enterprise

The article is aimed at formation of architectonics of facilitation-reflective methodology of motivation in the system of energy management of enterprise, which will take attention to modern organizational-managerial technologies and is built on the basis of ISO 50001 standard. In the current formations of enterprises development, there is a problem of ensuring their energy efficiency, energy independence and energy security, that it is possible to have solved through introduction of energy management on the basis of ISO 50001. As one of the important structural components of the enterprise’s energy management system we have determined the motivation of staff to energy saving. A content analysis of existing practices of energy saving management on the basis of motivation mechanisms has provided an opportunity to develop a new facilitation-reflective methodology of staff motivation to energy saving. The authors present architectonics of the facilitation-reflective methodology of staff motivation in the system of energy management of enterprise that will allow to introduce measures of energy saving by means of the production-economic system with clear regulation in accordance with ISO 50001

A comparison of teacher and lecturer perspectives on the transition from secondary to tertiary mathematics education

The transition from school to tertiary study of mathematics comes under increasing scrutiny in research. This article reports on some findings from a project analysing the transition from secondary to tertiary education in mathematics. One key variable in this transition is the teacher or lecturer. This article deals with a small part of the data from the project – analysing secondary teachers’ and lecturers’ responses to questions on the differences they perceive between school and university and the importance of calculus, a bridging content. The results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great need for improved communication between the two sectors

Weak exponential stability for time-periodic differential inclusions via first approximation averaging

Published online: 20 June 2012In this work we propose a method to study a weak exponential stability for time-varying differential inclusions applying an averaging procedure to a first approximation. Namely, we show that a weak exponential stability of the averaged first approximation to the differential inclusion implies the weak exponential stability of the original time-varying inclusion. The result is illustrated by an example.FC

The effect of soil and climatic conditions on the distribution of nutrients in Actinidia arguta leaves

The patterns of the distribution of nutrients in kiwiberry (Actinidia arguta (Siebold & Zucc.) Planch. ex Miq.), family Actinidiaceae (Gilg & Werderm), leaves growing under different soil and climatic conditions (Ukraine and China) were studied. Using scanning electron microscopy, significant differences were shown in the distribution of assimilates and mineral nutrients in the leaves of kiwiberry cultivated under different climate and soil conditions (Kyiv city, Ukraine and Jiamusi, China). The leaves of plants grown in China have higher concentration of all of the studied nutrients exception for silicon. The differences found in the content of macro- and microelements in plant tissues are consistent with their total content in the soil, and depend on the synthesis of low molecular weight organic compounds, namely, hydroxybenzoic, benzoic and triterpene acids. An increase in the silicon content in the leaves of kiwiberry plants grown in Ukraine indicates the moisture deficit in the soil. This conclusion is confirmed by the anatomical differences viz. the presence of additional integumentary formations and fewer stomata number per 1 mm2 of leaf surface. The specific feature of ‘Perlyna sadu’ cultivar was high concentrations of sodium and aluminum in the foliar tissues, regardless of the place of growth. The analysis of the distribution of nutrients in the leaves located along the stem showed remobilization of the former within the three layers: the lower one nourishes the roots, the upper one nourishes the leaves in the active growth phase and the middle one allocates the assimilates in both directions. A significant positive relationship was found between the biosynthesis of photosynthetic pigments and electrophysiological activity, especially for the leaves of the lower zone. The revealed differentiation into layers differing in polarity of bioelectric potentials and the distribution of assimilates suggests functional differentiation of the kiwiberry leaves. In particular, the leaves of the lower layer perform a storage function. The middle part is less conservative and characterized by higher sensitivity to environmental factors performs a mainly synthetic function. The upper layer performs an active growth function. The results of the comparative analysis of the indicators of the number of chloroplasts in the mesophyll cells proved that the obtained dependence can be used as a diagnostic criterion in assessing the predicted plant productivity at the early stages of their development