Drawing-to-Learn: Active and Culturally Relevant Pedagogy for Biology

Students enter biology classrooms with ideas about the natural world already formed. Teachers can help students construct new knowledge by using active, culturally relevant pedagogy and by making space in their lesson for students to reveal, challenge, and/or reconcile their preconceptions with new knowledge. Drawing meets all of these needs. Drawing-to-learn (DTL) allows students to be metacognitive and creative as they generate concrete representations of their abstract conceptions. In this case study of biology classes for Tibetan Buddhist monastic students through the Emory-Tibet Science Initiative, we find that DTL engages students in active learning, allows multi-modal visualization and discourse about mental models, and beyond this, solicits cultural references from both students and teachers.

Assessing Preoperative Hope and Expectations Related to Functional Neurosurgery: A New Questionnaire

Background: Despite successful functional neurosurgery, patients suffering from epilepsy or Parkinson’s disease may experience postoperative psychological distress and social maladjustments. Difficulties in coping with postoperative changes, even positive ones, have shown to be related to patients’ presurgery cognitive representations (i.e., expectations, hope, abstract vs. concrete representations). The aim of this study was to develop an instrument assessing various key features of surgery outcomes’ representations, namely the Preoperative Hope and Expectations Questionnaire, PHEQ. Methods: Participants were patients (n = 50) diagnosed with Parkinson’s disease (n = 25) or epilepsy (n = 25), candidates for functional neurosurgery (i.e., Deep brain stimulation, anterior temporal lobectomy). At 2-3 weeks before the planned surgery, they were administrated items assessing their actual state, preoperative expectations, and hope regarding surgery outcomes. They also completed measures assessing optimism, quality of life and mood. Results: Exploratory analysis resulted in a 16-item version of the PHEQ composed of two factors (abstract representations, including psychological well-being and concrete representations, such as functional aspects of everyday functioning). The PHEQ demonstrated high internal consistency and good convergent validity. Patients were more prone to express postoperative improvements in terms of hope rather than expectations. They generally focused on concrete rather than abstract features, although patients with Parkinson’s disease had higher abstract future-oriented representations. Conclusions: The PHEQ presents satisfactory psychometric properties and may be considered as a reliable instrument for research and clinical practice.

ANALYSIS OF J. KEYNES'S CONTRIBUTION IN THE DEVELOPMENT OF ECONOMIC THEORY

The article describes the educational and scientific university environment in which Keynes's talent was formed, as well as the Bloomsbury Circle of Intellectuals, in which Keynes occupied a prominent place. The formation of Keynes's specific approach to economic problems, which combine the analysis of real problems, theory and formulation of the practical proposals, is considered on the example of the early work of Keynes in the 1910s. The article argues that Keynesianism is the real engine of the modern economy. Keynes developed methods and apparatus by which the conceptual vision of economics is transformed into concrete representations of the economic theory. After a long journey, shown in his works ("General Theory of Employment, Interest and Money"), Keynes developed his vision of economic and social phenomena as an analytically functional analysis, and finally destroyed the logical capacity of people's faith in the ability of a free market economy to automatically maintain full employment, identified the possibility of influencing the regulation of money circulation on prices, exports, imports, production process and employment. Despite criticism of his theoretical evidence, even his opponents agreed that Keynes's ideas had been confirmed in practice. At the end of the article are the assessments of Keynes' research by authors and scientists with different views.

Dynamical C*-algebras and Kinetic Perturbations

The framework of dynamical C*-algebras for scalar fields in Minkowski space, based on local scattering operators, is extended to theories with locally perturbed kinetic terms. These terms encode information about the underlying spacetime metric, so the causality relations between the scattering operators have to be adjusted accordingly. It is shown that the extended algebra describes scalar quantum fields, propagating in locally deformed Minkowski spaces. Concrete representations of the abstract scattering operators, inducing this motion, are known to exist on Fock space. The proof that these representers also satisfy the generalized causality relations requires, however, novel arguments of a cohomological nature. They imply that Fock space representations of the extended dynamical C*-algebra exist, involving linear as well as kinetic and pointlike quadratic perturbations of the field.

Gestures, Embodiment, and Learning the Rate of Change

Many researchers have stressed the embodied nature of mathematical understanding. Here we explore how embodied knowledge may evolve as students learn a basic calculus concept: the rate of change. We examined undergraduate students with different levels of calculus knowledge working in pairs to model the rate of change in an everyday phenomenon. Our findings revealed substantial differences between advanced and introductory students in how they represented the rate of change with their speech and gestures. In particular, the advanced students’ embodied representations showed alignment with the formal symbolic process of integration and reflected more advanced ways to coordinate the relation between multiple changing variables. For example, advanced students often made gestures that represented a “disk” when explaining how the rate at which water rose in a bottle was related to the change in height. Thus, both introductory and advanced students demonstrated embodied knowledge through speech and gestures, but the advanced students constructed different concrete representations that reflected an advancement in their embodied knowledge. Our findings are relevant to calculus education and to the study of gestures in mathematics learning.

One Instructional Sequence Fits all? A Conceptual Analysis of the Applicability of Concreteness Fading in Mathematics, Physics, Chemistry, and Biology Education

To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with concrete representations and progress stepwise to representations that are more idealized. Various researchers have suggested that concreteness fading is a broadly applicable instructional approach. In this theoretical paper, we conceptually analyze examples of concreteness fading in the domains of mathematics, physics, chemistry, and biology and discuss its generalizability. We frame the analysis by defining and describing MERs and their use in educational settings. Then, we draw from theories of analogical and relational reasoning to scrutinize the possible cognitive processes related to learning with MERs. Our analysis suggests that concreteness fading may not be as generalizable as has been suggested. Two main reasons for this are discussed: (1) the types of representations and the relations between them differ across different domains, and (2) the instructional goals between domains and subsequent roles of the representations vary.

Uwagi o abstrakcji, ufundowaniu i hipostazie

The article deals with philosophical issues concerning abstraction and concreteness, focusing on selected ontological and logical-ontological threads of this dif ficult and intricate problem. Thus, it will concern first of all abstract and concrete objects, and only then abstract representations and judgments and concrete representations and judgments. The subject of interest will also be the process of abstraction and the relations that take place between abstract objects such as features or relations, pure qualities, and ideal objects.

Uwagi o abstrakcji, ufundowaniu i hipostazie

The article deals with philosophical issues concerning abstraction and concreteness, focusing on selected ontological and logical-ontological threads of this dif ficult and intricate problem. Thus, it will concern first of all abstract and concrete objects, and only then abstract representations and judgments and concrete representations and judgments. The subject of interest will also be the process of abstraction and the relations that take place between abstract objects such as features or relations, pure qualities, and ideal objects.

The Shock of the New

In this chapter, we show how the newest developments in quantum mechanics of the late 1920s were very quickly compared with general relativity, with attempts made to demonstrate their mutual coherence. This involved focusing on the basic mathematical structures that formed the first concrete representations of quantum mechanical systems. The aim was structural harmonisation, rather than quantization. Likewise, we will find that conceptual debates, especially having to do with measurement and the uncertainty relations, as well as new cosmological discoveries (based on applications of general relativity) were also quickly compared, often with surprising results such as explanations of discreteness and predictions of particle production in curved spaces. We see two primary motivations pushing this research forward: coherence (into which the more formal approaches also fit) and utility (that is attempting to gain a better grip on the quantum theory).