Mathematical understanding and more
"Let's visit Numberland" was developed to appropriately address the evolving interest of small children in counting, sets, numbers, comparing, and geometric shapes. It supports children to build the bridge between the understanding of math they were born with ('1,2,many') and the formal language of mathematics we developed to describe and handle things. In Numberland, Children acquire a profound, well structured mathematical understanding of the number range 0 to 10 (building the fundamental basis to their mathematical understanding) and the numerals to 20.
Yet the children benefit far beyond the matter itself: Language, self-esteem, concentration and cognition, motivation and creativity, social, motor and music skills are enhanced as well.
The edge of "Let's visit Numberland" lies within the embracing approach: The concept allows a child to experience the entire aspects of numbers with the entire self, i.e. body, mind and spirit. This way, children in their daily play develop a multi-faceted, positive image and a deep, lasting understanding which they can build on.
As an open and didactic concept, „Numberland“ is not a programme but rather a central theme that helps strutcturing. The specific elements encourage both children and staff to bring in own ideas. It can be easily adapted to individual needs and age brackets. Popular and estalished activities can be brought in and „Numberland“ can be a trigger for the further exploration of topics, e.g. bees with their six legs and their hexagonal combs.
"Let's visit Numberland" combines findings from brain research, developmental psycho-logy, educational science and didactics of mathematics. It is consistently designed from a child's perspective and, therefore, considers how small children see the world, builds on what they know already, what they can understand, like, and need. This explains why "Let's visit Numberland" is so highly moti-vating for children.
It is very natural for children to travel to a country where numbers live: For a while, children regard regard everything around them as being alive. Anything magic strongly appeals to small children and going with that is a strong emotional thinking.
In addition, children of that age need tangible experiences of the inherent abstract character of mathematics.
On their fantastic, cheerful journey to „Numberland“, the children meet the numbers 1 to 10 as nice, living characters who motivate them to deal with mathe-matical aspects and coherences. Number Lane shows the way to Number Town where each number lives in its characteristic, geometrically shaped garden. The children furnish these gardens with houses, towers, and other things going with the number.
There is a cheeky goblin messing around and a nice fairy sorting things out. Tales and music, lots of active games and other things children love complement the experiences.
We could prove that within only ten weeks children aged 3 to 6 gained the mathematical competence and understanding they normally would have achieved only within one year. The same was true for the language competence of the children - a highly important finding since language is the key to education.
The findings were also true for under-privileged children with partly very poor understanding of the German language. A second study from the University of Heidelberg confirmed our results.
Summary of the research results (pdf, 274 KB)
Full article on the research study (Translation of the article published in German journal) (pdf, 2 MB)
Nursery schools, preschools, primary schools and special schools in Germany strongly benefit from “Numberland” which they adapt to their special needs. 40.000 books have already been sold. „Numberland“ has started to find its way to Texas, Poland, Russia, Romania, Bulgaria, India, and Thailand.
Teachers approve the concept as an optimal preparation for school and even use it in first grade. In industrial Ludwigshafen with many underprivileged children, teachers diagnose a higher base level and more self-esteem, leading to more motivation and participation.
Kindergarten and preschool teachers alike are enthusiastic about the all-embracing advancement of the children. They appreciate how well our open concept can be combined with their schedule and how individually it can be realized.
Children usually get completely absorbed in a “Numberland” project and transfer it into their daily play.
Number Lane shows the figures 0 to 10 (or 20) and leads the way to Number Town. By moving on Number Lane and playing numerous fun games on it, children become familiar with the ordinal aspect of the basic numbers.
Walking forward and backwards, the children make first experiences in addition and subtraction. The important knowledge of successor and predecessor is easily adapted.
Number Lane can also be used to combine ordinal and cardinal aspect.
Number puppets animate the abstract numbers, communicating that numbers are something nice and lovable.
They may tell a tale, help arranging their garden, or be part of role plays.
The Number Gardens correspond to the geometric aspect and are arranged in a circle, representing Number Town. Access is strictly limited! Children may pick 4 bricks, 4 pens, or 4 beans and place them in the garden. Thus, they experience the cardinal aspect as well as invariancy.
A horse is also allowed due to its 4 legs. Yet it also has 1 tail, 2 eyes, 2 nostrils...
Children are strongly motivated to find out, discuss, and decide where to put an object. This fosters cognition, language skills, social competence - and general knowledge.
Each number needs a house and, obviously, Number One’s house has 1 window, Number Two’s has 2, and so on.
The trick is that as of Number Six, each number gets two houses: Number Six’ house has 5+1 windows, Number Seven has 5+2, etc.
This concept corresponds directly to the children’s hands. It transports the idea that numbers can be decomposited. And, highly important, it supports children acquire simultaneous entry of quantities.
The children build a Number Tower in each garden which gives a linear visualization of the number.
If realized as fourcolored bricks, the children can make experiences with various aspects of numbers as well as possible decompositions.
Hodgeypodgey the Goblin and the Fairy of the Numbers
These two figures account for the magic thinking of children. Especially Hodgeypodgey the Goblin is highly appreciated because ever and again he messes around in Numberland. The children love to find out what is wrong and to correct the mistakes. The goblin is also a perfect scape goat for own mistakes...
But there is also the Fairy of the Numbers who can be called with a spell and who helps to get things right again.
Children love tales and enjoy stories about numbers. For example, to cure the sick Four, a tea is made out of four bits of four different herbs out of her square herb garden. After four minutes brewing time, four spoons of honey are added and stirred four times - curing immediately...
The children can listen, talk about the tales, make role plays, and so on. Interesting details for the general knowledge are embedded in the tales and, possibly, picked up later on. Or how about making up your own number tale?
Rhymes, music, and singing have highest value for children. We composed a refrain and songs for each number. Their beat and number of tones correspond to the number as well as the content does to our number tales.
As an alternative or in addition, popular nursery rhymes or songs can be included as well.
My book of Numbers
“Let’s visit Numberland” offers lots of areas of creative work. A folder going along with the project is highly treasured by the children and a good document of a child’s development.
Games and Activities
Each visit to Numberland can be the basis for lots of activities around the specific “number of the week”. Fun games, related songs or rhymes, designing or moulding, exploring specific questions, sports or outdoor activities...