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Fold to unfold – Fundamental Geometric Elements
Product: Book
Trim size in cm: 21x29,7
Pages: 136
ISBN: 9788861379411
Publication date: 01/11/2011
Suitable for: Primary 2nd level (ages 8-10)
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After an introduction on the cognitive aspects of geometry, on shape and space representation and their relations to the different developmental stages, each of the 3 books present several simple activities, ordered by degree of difficulty, that teach how to fold paper and learn to recognize shapes according to cognitive processes such as naming, comparing, classifying, constructing / deconstructing and recognizing. All activities only require the use of papers and colors.
This education program aims to help students to build their knowledge of geometry on solid foundations starting from primary school up to secondary school.
Vol. 2 – Fold to unfold – Fundamental Geometric Elements: how to fold papers and recognize geometric entities such as: all kinds of angles, bisector, axis, segments, sum and difference of angles; multiple angles; submultiples angles with bisection, classification of individual or pairs of angles; relations between classes of angles, activities with protractor.
- Folding and cognitive psychology
- Folding and learning geometry
- Bibliography
- Introductory activities. Let's fold!
Naming (Straight lines and points; Angles; Right angles; Straight angles; Full angles and zero angles; Bisectors; Segments; Mid-points and axes; Points, segments and angles in symbols)
Comparing (Concave and convex angles; Free angles; Right angles and their peculiarities; Straight angles and their peculiarities; Full angles and their peculiarities; Angles which are greater or less than other angles; Congruent angles; Vertically opposite angles; The characteristics of angle bisectors; The characteristics of an axis of a segment; Comparing segments)
Building and taking apart (Consecutive and adjacent angles; Sum of angles; Difference of angles; Sums and differences; Special sums; Multiples of angles; Submultiples of angles with bisections)
Classifying (Classification of individual angles; Classification of pairs of angles; From the object to the class; Relationships between classes)
Recognising (Recognising right angles; Recognising acute and obtuse angles; Recognising concave and convex angles; Recognising bisectors; Recognising axes; Recognising and building congruent segments; Recognising and building congruent angles; Recognising complementary and supplementary angles)
The disc of angles (Activities with the disc of angles)
Edited by Daniela Lucangeli – Università di Padova
This collection comprises a series of books which offer didactic programmes on calculation, geometry and problem solving, departing from traditional methods. Translating the latest research findings on numerical and logical scientific cognition into practical teaching strategies, the various books aim to build up cognitive processes in order to develop innate numerical intelligence.
What is numerical intelligence? We talk to Daniela Lucangeli
When do we develop numerical intelligence?
At only a few days old, a child recognises quantity way before being able to name it with words. Various scientific studies have demonstrated how a new-born baby in his mother’s arms discriminates 1. When dad arrives he discriminates 1 different from 1 and when the nurse arrives 1 different from 1 different from 1. Not only this, but within these 3 the baby is able to recognise greater than, less than and equal. Recognising quantity – which is the basis for counting – is in fact an innate skill, which has developed over thousand of years of evolution of our species.
If numerical intelligence is innate, why do we have difficulty with numbers?
Just like the fact that we don’t learn to speak unless somebody teaches us, we don’t learn to develop a competence if we don’t practice it in the right developmental stage. Generally, children practice the mechanisms of quantity only when they start school…too late! To give you an idea it’s like getting our children to practice talking from 4 years onwards. This is why in order to develop numerical intelligence and build competences on numbers and quantity it is essential that we act in the first five years of a child’s life.
What is the role of parents and teachers in developing numerical intelligence?
Through games, adults facilitate and speed up the processes of maturing and optimising learning. Like a spoon, which mixing coffee and sugar, facilitates and speeds up the transformation process and enables you to drink a tasty beverage in a short time.
THE TOPICS OF THE COLLECTION
NUMERICAL INTELLIGENCE AND CALCULATIONS CALCULATION STRATEGIES GEOMETRY PROBLEM SOLVING MATHEMATICS AND MAGIC
NUMERICAL INTELLIGENCE AND CALCULATIONS
Scientific research has demonstrated that the ability to understand and work on quantitative aspects in real life and to distinguish number and estimate it is a potential which is innate in children. These processes, however, should not be left, as often happens, to develop naturally; they require educational strategies and interventions designed to develop them.
An original and creative approach to arithmetic operations (and not only!) which are often an important milestone for youths of all ages. These books offers a series of strategies, which are part of a lengthy research project dedicated to eastern methodologies, in particular Vedic mathematics, and they are accompanied by observations and illustrations which provide a link between far eastern and western didactics. The manual, which contains a selection of techniques and strategies, comes complete with three books of in-depth explanations, full of examples and exercises for children and youths.
Developing geometrical competences A complete programme in geometry, divided into two books (from ages 6 to 11 and from ages 11 to 14), which starts with the building of geometric elements, the main plane figures and related formulas for perimeters and areas and goes on to solids, to theorems and to analytical geometry, in a simple way which can be readily used by every student, on the edge of reasoning.
Geometry with paper An original and exciting practical programme based on folding paper in order to develop and build geometric competences in children at primary school and the beginning of lower secondary school, by stimulating their curiosity and creativity.
Problem solving in 6 steps A wise, thoughtful owl and a quick, cunning fox guide children through the second stage of primary school in a complete programme for developing problem solving abilities. The owl with its reassuring manner will give instructions, whilst the fox will encourage metacognitive reflection in order to activate the self-evaluative processes needed for the stable acquisition of good problem solving skills.
Magically minded 1 A collection of fun recreational mathematical activities — to be carried out under the guidance of the «magician-teacher» — which stimulate pupil’s reasoning and curiosity.
