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Development of spatial thinking, geometry and physics What can parents and preschool teachers who interact with young children do to promote their development? Emilio Balzano Università degli Studi di Napoli Federico II. Geometry skills are innate.

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Development of spatial thinking, geometry and physics

What can parents and preschool teachers who interact with young children do to promote their development?

Emilio Balzano

Università degli Studi di Napoli Federico II


Geometry skills are innate

Researchers examined how the Mundurucu think about lines, points and angles, comparing the results with equivalent tests on French and US schoolchildren

The Mundurucu do not even have words for geometric concepts

The Mundurucu showed comparable understanding, and even outperformed the students on tasks that asked about forms on spherical surfaces.

"The education of Euclidean geometry is so strong that we take for granted it's going to apply everywhere, including spherical surfaces. Our education plays a trick with us, leading us to believe things which are not correct."


Naples experience Kids, Teachers, Parents involvement

The experiences represent the first step of a complex and innovative programme of lifelong-learning initiatives connected to science education which is being developed by the Faculty of Science at the University of Naples.

The results obtained within this project are based on the collaboration and sharing of experience of the research groups in Science Education and Pedagogy of our University.


At the University level, the project activities consisted in the organization of a number of basic courses addressed to worker students and students with difficulties in following the regular courses. These courses integrate the usual traditional teaching strategies with some special activities conducted by tutors with science education research background. The courses involved around 500 students (around 70% passed the final exam).


At the teacher training level, several courses have been organized involving around 150 kindergarten teachers. The aim of these courses is to build in the adults (teachers and parents) the awareness of their role of cultural “mediators” between the pupils (with their models of the world and their cognitive styles) and scientific knowledge. Laboratorial activities in the kindergarten classes conducted by university researchers involved around 600 pupils.


Our findings come from the

  • interviews with university teachers and students
  • and from
  • analysis of audio and video recordings with kindergarten teachers and pupils’ parents

Parents’ involvement

This experience originated from a possibility offered by the Municipal authority of a collaboration between schools, university, and the science museum in Naples.

Paying particular attention to the affective dimension of learning (parents’ involvement; small group activities) and to the relationships between art-science, science-language, etc. we work with two multidisciplinary areas: ‘Light, Colour and Vision’ and ‘Water’.


An important component of our research is an understanding of the reciprocal impact of science and the culture on each other.

The theoretical framework draws on ideas of critical teaching and incorporates affective and cognitive practices set within socio-cultural contexts. Language mediates thought in a dynamic, interactive way and the social interaction between pupils and adults is essential for learning and development.


Lev Vygotsky's theories concerning optimizing of potential through assistance, support, or instruction

  • An approach that would maximize the growth and development of children, including:
  • mentoring,
  • adult and parental involvement,
  • community involvement
  • the use of humor,
  • emotional education,
  • personality development,
  • critical thinking
  • metacognitive aspects
  • dynamic assessment

"Learning is more than the acquisition of the ability to think; it is the acquisition of many specialised abilities for thinking about a variety of things.“

Lev Vygotsky, Mind in Society, 1978

Lev Vygotsky Known for:

Zone of Proximal Development

Sociocultural Theory

Guided Participation

emphasis interests
  • Science in the social and cultural framework
  • Scientism vs. Science as a human enterprise
  • Science as a process
  • Role of models and theories
  • Predictivity and uncertainty
  • Science-mathematics-technology relationships
  • Gender

National Research Council-NAP

How People Learn:

Brain, Mind, Experience, and School: Expanded Edition

How Students Learn



Ready, Set, Science!: Putting Research to Work in K-8 Science Classrooms

Learning Science in Informal Environments: People,

Places, and Pursuits



  • The Teaching-Learning Paths for Number, Relations, and Operations
  • The Teaching-Learning Paths for Geometry, Spatial Thinking, and Measurement

Cognitive Foundations for Early Mathematics Learning

“Over the past two decades, a quiet revolution in developmental psychology and relatedfields has demonstrated that children have skills and concepts relevant to mathematics learningthat are present early in life, and that most children enter school with a wealth of knowledge andcognitive skills that can provide a foundation for mathematics learning...

At the same time, thesefoundational skills are not enough—children need rich mathematical interactions, both at homeand at school in order to be well prepared for the challenges they will meet in elementary schooland beyond.”


A large body of research has examined a set ofnumerical skills, including infants’ ability to discriminate between different set sizes, their abilityto recognize numerical relationships, and their ability to understand addition and subtractiontransformations.

“The study of numerical knowledge in infants represents a major departure frompreviously held views, which were heavily influenced by Piaget’s (1941/1965) numberconservation findings and stage theory. These older findings showed that children do notconserve number in the face of spatial transformations until school age, and they led many tobelieve that before this age children lack the ability to form concepts of number (see Mix,Huttenlocher, and Levine, 2002, for a review).

Although Piaget recognized that children acquiresome mathematically relevant skills at earlier ages, success on the conservation task was widelyregarded as the sine qua non of numerical understanding”


Spatial thinking

“Viewing or imagining an object from different perspectives in space and moving or imagining how to move an object through space to fit in a particular spot links spatial relations with the parts and features of objects and shapes. .”

Composing and decomposing shapes and objects are part of a foundation for later reasoning about fractions and about area and volume.

Through their study of geometry and measurement, children can begin to develop ways to mentally structure the spaces and objects around them. In addition, these provide a context for children to further develop their ability to reason mathematically.


result of the work of a Commission, charged by the Board on Science Education of the National Research Council, to give indications, validated by research, on the problems and effects of the introduction of "National Standards" (USA, 1995) about Science Education

  • some recommendations suggested for future research works:
  • "what" to teach and "when". The systematic under-estimation of students' cognitive potentialities is stressed by the authors who maintain that science has to be presented to learners as a process of building theories and models. They also think that it is necessary to identify a few "core ideas" of the discipline and design how they can be progressively developed, over grades K-8 levels, using strategies based on models of learning
  • "how" to teach. Learners have to be involved in activities about the above mentioned components of proficiency; adults have to support and guide them. Teachers have to be educated to transform their knowledge about disciplines, about students' learning processes, about different teaching styles and strategies into professional competences.

Learning Science in Informal Environments:

People, Places, and Pursuits

There are many research-based frameworks for understanding interest and motivation and therole they play in the learning process.

• Curiosity—The visitor is surprised and intrigued.

• Confidence—The visitor has a sense of competence.

• Challenge—The visitor perceives that there is something to work toward.

• Control—The visitor has a sense of self-determination and control.

• Play—The visitor experiences sensory enjoyment and playfulness.

• Communication—The visitor engages in meaningful social interaction.



Parents were invited to support the scientific-linguistic development of their children making some real and also “mental” experiment at home.

With this aim workshops have been proposed for the parents (a large majority being mothers from a poor part of Naples) in order to explain the aims of the project and to improve the feeling of self-esteem when science at home is involved.

Everyday examples have been proposed in order to improve the mothers’ ability to reasoning and discussing scientific issues (makeup colours, discothèque changing colours, etc.).

Teachers have also been invited to share experiences with other teachers in order to gain competences on how to organise their work.


The experience was based on the integration of lab works in ordinary class activities with the involvement of researchers. Workshops with parents and visits to local museum were part of the project activities. The main aim was to involve pupils, teachers and parents in a game of correlations between phenomena and modeling.

Chosen a topic we proposed every-day phenomena (with coloured shadows, water lens, floating bodies of different shapes/materials in large transparent tanks of water, coloured boxes where the children could enter under different coloured lights,) and ask pupils to find rules and explanations through continuous discussion with guidance of their teachers.

parents activity kaleidoscope
Parents activity - Kaleidoscope

Make multiple images of yourself.

Duck Into Kaleidoscope will createhundreds of images of - whatever you place inside it. The basic kaleidoscope is a triangle, but mirror tiles can beformed into other shapes and angles as well.


In 6 years, we involved approximately 100 full classes (kindergarten level pupils of 4-6 years) from different social conditions.

The experience has been very well received by teachers, kids and parents.

Evidence is based on: -interviews; -sheets of observation; -workshop participation; -quality of the communication of phenomena made by kids in final science festival events; -the permanent laboratory activities in schools.

Teachers and parents consider very productive this experience but require more work with researchers and stability of the project.

 In the current school year the work will be supported by regional-European funds in the framework of Life Long Learning Programme.



evidences show that there is some kind of relation between family involvement and children performances.

families where parents are able to help their children doing mathematics and science are more likely to get better performances that families where this does not happen.

there are not a relevant number of researches in that field in Europe

in Europe there is no tradition doing "mathematics workshops for parents/families".

we have to fill that gap


According to Vygotsky, cognitive development does not happen just in the head of the child

it is a process of learning to operate with physical, symbolic, and cognitive tools in ways that in themselves change cognitive processes.

infant begins the process of knowledge acquisition with a set of core principles that guide and constrain future cognitive development

core principles are either innate, or are given by simple perceptual information such as a sensitivity to contingency


Knowledge acquisition is guided by the core constraints, and also by the ways in which surrounding adults behave—the social, emotional, and cultural contexts within which learning takes place.

The kinds of innate or early-developing core principles postulated include physical principles like solidity and continuity of objects, conservation and invariance, etc.

three-year-old children can reason by analogy

We have a great opportunity to share in the family-school communities cognitive aspects.


The results presented show that the development of educational paths and training programmes based on a meta-cognitive approach and focused on the enhancement and exploit of individual resources and background knowledge of learners is an effective strategy in order to motivate and actively involve people, regardless of their age, education level, profession and of the socio-cultural context in which they live.


The possibility to reflect on learners’ learning experience and cognitive configuration has been particularly useful in order to promote their awareness of diversity and functional to the development of meta-cognitive paths that bring into dialogue the individual learning styles and different disciplinary epistemologies. We think this a particularly relevant issue as long as the difficulties generally experienced in the access to some kind of knowledge (especially scientific knowledge) are due not to a lack of preparation or to insurmountable cognitive deficiencies, but simply to a lack of mediation devices and meta-learning contexts.