The major purpose of this study was to investigate factors and challenges that hindered effective teaching of mathematics for understanding in senior secondary schools in the Omusati Education Region in Namibia. The study investigated how the participants dealt with identified challenges in the mathematics classrooms in selected senior secondary schools. Further, the study attempted to establish necessary support and / or training opportunities that mathematics teachers might need to ensure effective application of teaching mathematics for understanding in their regular classrooms. The sample was made up of eight senior secondary schools out of the population of 12 senior secondary schools in the Omusati Education Region. The schools were selected from the school circuits using maximum variation and random sampling techniques. Twenty out of 32 mathematics teachers from eight selected senior secondary schools in the Omusati Education Region responded to the interviews and two lessons per participant were observed. Interviews and observations were used to collect data from the 20 senior secondary school mathematics teachers with respect to teaching mathematics for understanding. Frequency tables, pie charts and bar graphs were used to analyze the data collected. The results indicated that teaching for understanding was little observed in mathematics classrooms. Part of the challenges identified were, overcrowded classrooms, lack of teaching and learning resources, lack of support from advisory teachers, and automatic promotions, among others. Mathematics teachers needed induction programmes, in-service training opportunities, and advisory services amongst others in order to be able to teach mathematics effectively. The study recommended that teaching for understanding should be researched in all subjects in Namibian classrooms and should be made clearly understood by all teachers in order to be able to use and apply it during their teaching. New teachers should be provided with induction programmes to give them support and tools at the beginning of their teaching careers. Further research on teaching for understanding should be conducted in other school subjects in Namibia in order to ensure teaching for understanding across the curriculum.

Key words: teaching, understanding.

In this part of our work about a comparison between Kelly’s personal construct theory and phenomenology, we enter the fields of psychotherapy and research. The topic of intersubjectivity, meant as original recognition of the other’s subjectivity, provides a backdrop for both phenomenological clinic and Kellyan psychotherapy. Though Kelly never used the term “intersubjectivity,” his theory and the corollary of sociality in particular, reveals a view of interpersonal relationships as intercorporeality, which is much closer to phenomenological ideas than to the cognitive ones. Depending on such commonality, in either cases clinical relationship is not viewed as an “aspecific factor” of psychotherapy, but as the essential tool for the care of other. Furthermore, the core role of intersubjectivity in scientific knowledge implies a radical revision of the criteria of research. Consistently with the intent of a science of experience, it is no more a matter of collecting data, as of accepting meanings. Psychological research has to refound itself in continuity with life and recognize the need for a real involvement and real interaction with the subjects, as far as to reverse the traditional relation between clinic and research. It is nonsense to conceive clinic as an applicative sector of a pure science because clinic, on the contrary, is the place where one can know, in first-person, those meaningful realities which take shape in the intersubjective exchange of ideas, in order to make them comprehensible and controllable. Relevance: The publication explores the dimension of intersubjectivity in phenomenology (starting from Husserl) and personal construct theory, and its relevance in psychotherapy and research.

Sensory substitution constitutes an interesting domain of study to consider the philosopher’s classical question of distal attribution: how we can distinguish between a sensation and the perception of an object that causes this sensation. We tested the hypothesis that distal attribution consists of three distinct components: an object, a perceptual space, and a coupling between subjects’ movements and stimulation. We equipped sixty participants with a visual-to-auditory substitution device, without any information about it. The device converts the video stream produced by a head-mounted camera into a sound stream. We investigated several experimental conditions: the existence or not of a correlation between movements and resulting stimulation, the direct or indirect manipulation of an object, and the presence of a background environment. Participants were asked to describe their impressions by rating their experiences in terms of seven possible “scenarios”. These scenarios were carefully chosen to distinguish the degree to which the participants attributed their sensations to a distal cause. Participants rated the scenarios both before and after they were given the possibility to interrupt the stimulation with an obstacle. We were interested in several questions. Did participants extract laws of co-variation between their movements and resulting stimulation? Did they deduce the existence of a perceptual space originating from this coupling? Did they individuate objects that caused the sensations? Whatever the experimental conditions, participants were able to establish that there was a link between their movements and the resulting auditory stimulation. Detection of the existence of a coupling was more frequent than the inferences of distal space and object.

Key words: sensory substitution, distal attribution, space, object, objecthood, sensorimotor theory, sensorimotor coupling.

This is the second paper of a pair of two, the first one of which looked at a sociological theory of a computer-based future society distinct from earlier language-based ‘primitive’ society, writing-based ancient society, and printing press-based modern society. If the form of the next society’s culture will be the Spencer-Brownian form as we suggest, then sociological theory will have to reformulate itself in terms of an analysis of network synthesis. We look at possible reasons to do so, stemming above all from demands to be able to describe and understand how social actors are able to frame indeterminacy, present a possible model of social action, and advance the idea that it may be useful to base social analysis neither on subjects nor on objects but on a hypokeimon which we here propose to christen ‘catjects’. Catjects describe how a network synthesis comes about.

The paper is a reading of Martin Heidegger’s Contributions to Philosophy (Of the Even) by means of Ranulph Glanville’s notions of black box, cybernetic control and objects as well as by George Spencer-Brown’s notion of form and Fritz Heider’s notion of medium. In fact, as Heidegger was among those who emphasized systems thinking as the epitome of modern thinking, did in his lecture on Schelling’s Treatise on the Essence of Human Freedom a most thorough reading of this thinking, and considered cybernetics the very fulfilment of modern science it is interesting to know whether second-order cybernetics, as it was not known to Heidegger and as it delves into an understanding of inevitable complexity and foundational ignorance, falls within that verdict mere modernity or goes beyond it. If modern science in its rational understanding considers its subjects to be objects sitting still while being observed, then indeed second-order cybernetics is different. It looks into the observer’s interactions with black boxes, radically uncertain of where to expect operations of a self, but certain that we cannot restrict it to human consciousness.

Context: The integration of data measured in first- and third-person frameworks is a challenge that becomes more prominent as we attempt to refine the ties between the dimensions we assume to be objective and our experience itself. As a result, cognitive science has been a target for criticism from the epistemological and methodological point of view, which has resulted in the emergence of new approaches. Neurophenomenology has been proposed as a means to address these limitations. The methodological application of this discipline, even in its mildest form, enriches the methodology typically used in cognitive sciences. Problem: Nowadays psychological studies are difficult to replicate. As a way to achieve replication of results published in a previous study in order to develop a methodological adaptation suitable for electroencephalographic (EEG) measurements in a subsequent experiment, first-person accounts from the participants in our pilot study were included in the experiment construction. This study’s objective is to show the benefit of including a mild-neurophenomenology-inspired approach in the adaptation from an original paradigm, which requires, foremost, the ability to replicate the original results. Method: Interviews with open and semi-structured questions were carried out at the end of an Approach-Avoidance Task (AAT. The first-person reports, together with the behavioral outcomes of each pilot, were taken into account for the development of the next piloting phase until replication of the original results was achieved, and the final experimental design was elaborated. Results: A sequence of four pilots, where the integration of third- and first-person information derived from subjects’ behavior and reported experiences while carrying them out rendered the behavioral replication we sought to achieve, providing support for a first-person enriched cognitive science paradigm. Implications: Including first-person accounts systematically during the development and performance of classic cognitive paradigms ensures that those paradigms are measuring what they claim to measure. This is the next logical step to improve replication rates, to refine the explanation of the results and avoid confounding third-person data interpretation. Constructivist content: Including first-person experiences and acknowledging the active role that participants’ experiences regarding the paradigm had in the modeling of its final version is in concordance with a constructivist standing.

Key words: Mild neurophenomenology-inspired approach, piloting, first-person enriched experimental paradigm, phenomenological validity, replication.

This paper analyzes Humberto Maturana’s understanding abour the objectivity of scientific knowledge through a critical dialogue with other contemporary epistemological constructivist theories. The two subjects discussed are the relations between knowledge-reality and knowledge-society, which are the most common senses that guide the philosophical discussion about objectivity. This paper also includes a systematization of the main theses of Matuana’s biology of cognition, and a brief evaluation of the role of the notion of “autopoiesis” for the understanding of objectivity.

Key words: autopoiesis, objectivity, constructivism, epistemology, humberto maturana.

Constructivism is a heterogeneous intellectual movement that spans across different fields of knowledge. Within constructivism there is a variety of discussions that deal with their own questions and particular references, and that appear clustered in the journals and publications of different scientific areas. Attempting to clarify this communication, the present paper explores scientific publications from Latin America that include the term “constructivism” among their descriptors, as listed on CLASE, PERIODICA and SCIELO databases. These publications have been segmented into 3 very general groups, according to the way in which constructivism is used: (1) those that seek to “apply” constructivism to the problems of their area; (2) those that take “constructivism” as their object of study or criticism; (3) those that adopt constructivism as a “framework” for notional or conceptual analysis. Some data about those publication groups is described and compared in an attempt to show how scientific communication about constructivism organizes in Latin America (publication area, subjects, keywords, main authors).

Key words: constructivism, scientific publications from latin america, psychology and education, epistemology, science metrics

The attempt to define living systems in terms of goal, purpose, function, etc. runs into serious conceptual difficulties. The theoretical biologists Humberto Maturana and Francisco Varela realized that any such attempt cannot capture what is distinctive about them: their autonomy and unity. Goal, purpose, etc. always define the system in terms of something extrinsic, whereas living systems are unique because they maintain their unitary continuity of pattern despite the ceaseless turnover of their components. So, system-closure is a prerequisite of their adequate conceptual comprehension. Maturana and Varela themselves found that system-closure pertains exclusively to their organization, i.e. the set of relations among system-components which unify them. For living systems this comprises the relation between the system-components and the processes which they undergo. This relation is self-referential because it is closed, i.e. it essentially (re)produces itself. \\While this model worked very well in the biological domain, attempts to extend it to the social domain met with serious conceptual obstacles. The reason for this is that Maturana did not make a consistent enough application of it. He understood the components of social systems biologically (individuals, persons, etc.) and the relations between them socially (language). This inconsistency ruptured the system’s organizational closure. Consequently organizational closure (autopoiesis) can be maintained only when both the components of social systems and their processes are of the same type: social. This interpretation can be found in the work of Niklas Luhmann who recognizes that the components of social systems are not persons, individuals, actors or subjects but communicative actions themselves. This preserves the organizational closure of the system and permits the concept of autopoiesis to be used as a powerful instrument of social analysis.

Key words: Autopoiesis, communication, meaning, organization, social systems, structure.

In der jüngeren Sozialisationstheorie wird vermehrt die Intention formuliert, die Eigenaktivität des Subjektes im Sozialisationsprozess stärker zu berücksichtigen. Zum einen wird dies mit der Formel des ‘produktiv realitätsverarbeitenden Subjektes’ auf den Begriff gebracht, zum anderen bemüht sich insbesondere die kompetenzorientierte ‘konstruktivistische Sozialisationsforschung’ dieses Programm zu verfolgen. Dabei wird jedoch ein handlungstheoretisches Subjektverständnis bemüht, das eine begriffliche Unschärfe produziert, die eine konsistente Subjekttheorie und damit eine trennscharfe Bestimmung der Eigenaktivität des Subjektes erschwert. Um dieses Problem zu lösen, wird in dem Beitrag der Vorschlag gemacht, das Subjekt erkennt-nistheoretisch bzw. -kritisch zu konzipieren. Dadurch wird ein Subjektverständnis instruiert, das die Subjekt-Objekt-Dichotomie überwindet und die Wirklichkeit als je subjektives Konstrukt begreift Der Vorteil dieses zunächst heuristischen Vorschlages liegt einerseits in der Möglichkeit einer konsistenten Subjektbestimmung und andererseits in einer forschungsanleitenden Programmatik, die einen breiteren Zugang zu individuellen Entwicklungsverläufen ermöglicht. – English: From the “individual as a productive processor of reality” to the “individual as a productive producer of reality”. A philosophical foundation of theory of socialization. In recent theory of socialisation there is an increasing awareness giving more attention to the agency of subjects itself in the process of socialization. Direct indications about that change into the focus of theory of socialization are the often used formula of the “ individual as a productive processor of reality” or the programme of the constructivist research of socialization. In both cases still many problems are produced first of all through the idea of an action-theory based subject. One of the main theses in this article is that this understanding aggravates a consistent theory of subject in theories of socialization and so an unequivocal definition of agency of subjects. To solve that problems 1 suggest to conceptualise the subject epistemologically. The consequence of this strategy will offer a comprehension of the subject that is able to overcome the subject-object-dichotomy and to recognize “reality” as a construct made by subjects in a strict sense. On the one hand the advantage of this firstly heuristic proposal is the possibility to ascertain consistently the subject. On the other hand further research may be fruitful instructed because of the broader understanding of individual development. ||