No practical reasons exist to avoid in teaching Ptolemy's planetary model by suggesting the possibility of «seeing and speaking the way Ptolemy did» though we think as Copernicus.

Many researches document difficulties by learners of different ages and preparation in understanding basic astronomical concepts. Traditional instructional strategies and communication media seem not effective in producing meaningful understanding or even induce some misconceptions and misinterpretations. In line with recent proposals of pedagogical sequences and learning progressions about core concepts and basic procedures in physics and astronomy education, in this paper we suggest an intermediate, essential, step in the teaching path from the local geocentric view of the Earth-Sun system to the heliocentric one. At this aim we present data collected along a day and a year through an instrument we call "Parallel Globe", a globe positioned locally homothetic to the Earth we live on. Some analyses are suggested, in particular about the phenomenon of illumination of the Earth and its variations, consistent with the proposed instructional objectives.

Looking at human and natural reality, based on experience and awareness of its complexity, the western style of knowledge was divided into disciplines. These developed their own language and methods in relation to their objects of study. The separation, useful in some stages of study and in their specific development, was often simplistic and damaging both in scientific elaboration, to meet the challenges that nature and the future offers us, and in didactic transposition of knowledge. Studies in general education and cognitive psychology, and more recently neurosciences, show that aspects of different disciplines are formed and stimulated in parallel, and also motion and cognition are linked in the brain. The research confirms that cognitive experience is linked to the body and to emotions, more than school organizations often wanted to recognize. Therefore, inter-, multi- and trans-disciplinary approaches better relate to the objects of study, to teaching methodologies, and to teaching research methods. To analyze these issues, I present reflections from my Astronomy teaching experiences with students of different ages in Italy and elsewhere, and I present open questions about teaching and learning, in and out of school, and about teacher training.

Dificultades de Aprendizaje en Matemática en los niveles iniciales:Investigación y formación en la escuela italiana Ivonne GONZÁLEZ*, Guido BENVENUTO**, Nicoletta LANCIANO** *Universidad Santo Tomás, Chile **Universitá di Roma La Sapienza, Italia (Recibido 3 Junio 2016; Aceptado 18 Julio, 2016) RESUMEN:La presente investigación se circunscribe en el ámbito de la evaluación de las dificultades de aprendizaje en matemática inicial, tiene por objetivo profundizar en el conocimiento de la Competencia Matemática Temprana (CMT) a través de la observación e interpretación de las estrategias utilizadas por los niños para resolver tareas de tipo relacional y numérica. La investigación tiene la intención de poner un especial énfasis en romper la barrera del error como sinónimo de fracaso y avanzar hacia mejores estrategias de potenciamiento y prevención de las dificultades de aprendizaje en un contexto de investigación y formación histórica en la escuela italiana. En términos metodológicos, se trabajó con docentes de los niveles iniciales de escolarización (escuela de la infancia y primaria) y dirigentes escolares de 14 establecimientos de diversidad geográfica, territorial y sociocultural de las ciudades de Roma, Terni y Trieste, los que participaron en los años 2012, 2013 y 2014 en la validación para la población italiana del Early Numeracy Test-R (ENT-R Difficulties of Learning in Mathematics in the initial levels: Research and training in the Italian schoolABSTRACT:This research concerns the field of assessment of learning difficulties in mathematics in the early years. It aims to deepen the knowledge of Early Mathematical Competence (in spanish CMT: Competencia Matemática Temprana) through observation and interpretation of the strategies used by children for solve numerical and relational tasks. The research intends to place special emphasis to break the stereotype that considers error as a failure and move toward better strategies of empowerment and prevention of learning difficulties in a context of research and training in the Italian school. In terms of methodology, we worked with teachers in the initial levels of schooling (primary and preprimary school) and school leaders from 14 schools located in different geographical, territorial and socio-cultural contexts in the city of Rome, Trieste and Terni, who participated in the years 2012, 2013 and 2014

This paper describes one of the phases of a broader research carried out by the Science Education Research Group (SERG) from State of São Paulo (UNESP, Brazil), which has evidenced the distance between the academic production of the area of Astronomy Education and the knowledges and practices of students and teachers in Basic Education. In this text, we seek to investigate the singularities found during the stages of translation and adaptation of a specific didactic material, in the form of a school diary – Il Diario del Cielo (The Diary of the Sky) -, originally created and idealized to the reality of the Northern Hemisphere (Rome, Italy) and adapted to the reality of the tropical belt of the Southern Hemisphere (Bauru, São Paulo, Brazil), as well as discuss the potential of this material, to work with concepts of phenomena related to Astronomy, in a training program of continuing training for in-service teachers in Secondary and High School in the area of sciences. Topics such as: the visible horizon, the time of birth, climax and sunset and the Moon, the duration of the day according to the time of year and the latitude of the place of observation, equinoxes, solstices, seasons, phases of the Moon, among others, are approached from a sequence of didactic activities developed with students, in regular schools, according to the bases of Position Astronomy. Among the results found, the data obtained evidence that teachers were in favor of the proposal, approving the use of the astronomical diary, offering them moments of reflection on what they know about the contents worked, what they learned during the course and the feasibility of an incorporation of the contents discussed to their daily practice, and can be understood as viable and relevant to potentialize and enable the teaching of astronomy concepts in basic education. It also stands out, among the results, that the need to record daily the data from the active and systematic observation of the sky and the environment in a diary, besides to reveal an interdisciplinary character, involving different areas of knowledge, also points to the need to diagnose, discuss and reflect on the student's difficulties in developing the habit of daily written record as well as the teacher in managing the contrast between times of astronomical phenomena (cycle day and night, lunar cycle, seasons of the year, eclipses, among others) and those of the school, between the open spaces for the sky and the confinement of the classrooms in schools, making the task of teaching about astronomical contents more difficult. Also points out the expectations and challenges faced by the teachers in relation to the teaching of astronomical phenomena, considering the relations of similarities and spatio-temporal differences between the realities of the North and South Hemisphere contexts, as well as the initial training of teachers, compromised by the way and the quality, or even by the inexistence of the same, which leads to the incipient domain of the disciplinary and pedagogical knowledges focused on Astronomy and sometimes the feeling of incapacity and insecurity, when working with the theme in schools