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Cognitive and metacognitive skills in building geometric cognition for ages 11 to 14
Product: Book
Trim size in cm: 21x29,7
Pages: 261
ISBN: 978-88-590-0919-1
Publication date: 01/11/2015
Suitable for: Lower secondary 1st level (ages 10-11), Lower secondary 2nd level (ages 12-13)
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Developing geometrical competences is a series that offers a complete programme in geometry – divided into two books: from ages 6 to 11 and from ages 11 to 14 – which starts with the identification of plane figures and related formulas for perimeters and areas and goes on to solids, to theorems and to analytical geometry, all in a simple way which can be readily used by every student.
The main feature of this programme is making pupils work so that it is them who build geometric concepts, starting with visual spatial abilities, and work out the formulas they need themselves, in a creative and personal way.
The program offers activities on manipulating figures — from the complex to the simple and vice versa — and building geometric formulas, starting with simple expressions to solve, then gradually reach more complex geometrical problems.
Designed both for individual or small group work in the class, the first volume is specially written for primary school, the latter is addressed to secondary school.
- PLANE FIGURES
Noun or measure?; From straight lines to figures; Identifying figures; Measuring; Congruence; Calculating the perimeter; From the area to dimensions; The circle; Angles; Traslation, symmetry and congruence; Similarity.
- THEOREMS
Pythagorean theorem; Euclid's first theorem; Euclid's first theorem; Thales' theorem
- ANALYTIC GEOMETRY
Increasing and decreasing line; Parallel lines; System of intersecting lines; Parabola and hyperbola
- SOLID GEOMETRY
Dihedrals and trihedra; Polihedra and solids of devolution; Volume, weight and diagonals; Surfaces
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.
