Challenges — Concept — A Neighbourhood full of Maths — Research Project — Publications — Conferences — Videos — Teacher Feedback
Maths is a beautiful and important language, meant to no less but to enable us to understand and to describe our world. Longitudinal studies underline how crucial it is to master this language, i.e. acquire a true basic conceptual understanding.
The challenge is that maths is an abstract language, while children children start from their concrete world and only gradually build their bridge over to abstract thinking.
The good thing is that all children have an inborn desire to learn this language, making it part of their natural development. It is our responsibility to provide an environment enabling children make the experiences they need and help them structure.
All maths experiences need to be embedded in children’s play – because playing is their way of learning. And this learning is a very individual process, based on each child’s individual experiences, needs, and associations.
Neuroscience and developmental psychology tell us that, when learning something new, we all build on what is already there, on our experiences, knowledge, associations as well as emotions. This is especially true for young children. They are self-centred and live in an emotional world, where everything is alive. They have a black-and-white view and a magical thinking. Anything new is associated with what they already learn – and how they feel about it.
So we need to provide an appropriate environment that helps them making the relevant experiences, structure them, and let the good things happen!
The complexity of numbers
We as adults tend to forget how complex the concept of numbers is and that children need enough time and many experiences to grown into them. Here is a long list of the many important facts:
— Cardinal aspect A number represents a quantity (3 cars, 3 children … 3 is always 3)
— Ordinal aspect Numbers have a defined order (1, 2, 3 …). They also stand for a rank (first, second, …)
— Invariancy Quantities stay the same, no matter how they are placed
— Partitioning Numbers can be split into other numbers/ quantities (Crucial for becoming able to work with numbers beyond 10)
— Subitising Being able to grasp quantities at a glance
— One-to-one-correspondence Each element counts only once, and one elements of a set relates to exactly one of another set
— Calculating A number is the result of an operation (2 + 3 = 5)
— Reversibility Turning 2 + 3 = 5 back by 5 – 3 makes 2 again.
— Operator A number as the multiple of an activity (clap 4 times, hop 3 times)
— Encoding A number encodes a quantity, but also the rank in an order, a house, a birthday …
— Geometric aspect Numbers relate to geometrical shapes
— Musical aspect Patterns in rhythms, beats
— Cultural aspect The meaning of numbers in stories and in cultures
— Measuring We encounter numbers as different measures, i.e. for lengths, volume, weight, time, money.
The Numberland Concept
‘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 their inborn understanding of maths (‘1, 2, many’) to the formal language of maths we developed to describe our world and to handle things. In Numberland, children acquire a profound, well structured conceptual understanding of the number range 0 to 10 (building the crucial 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.
‘Numberland’ is not an academic training but rather a central theme that triggers children to play in this carefully designed environment, and helps them structure their experiences. 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 established, relevant 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.
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.
In a nutshell
On their imaginative, cheerful journey to ‘Numberland’, the children meet the numbers 0 to 10 as nice, living characters who motivate them to deal with mathematical aspects and coherences. Number Lane, starting at 0, shows the way to Number Town where each number lives in its characteristic, geometrically shaped garden. The children decorate these gardens with houses, towers, flowerbeds, and other things going with the number.
There is a mischievous (but not scary) little character messing around and a nice fairy/princess sorting things out. No matter how these two characters are named, children love the good vs. bad. Tales and music, lots of active games and other things children enjoy complement the experiences.
A neighbourhood full of maths
Let’s build homes for our number friends!
While building a neighbourhood with gardens and homes for their living number friends, the children experience all vital aspects of numbers, shapes, operations. It triggers a lot of communication, reasoning, helping each other and can be used to deliberately address an abundant choice of content. They are the starting point for cross curricular activities and support the transition to further, more abstract maths experiences.
All elements are designed to trigger children as well as to transport max mathematical content – structured but still flexible and different.
Imagine, someone invited me to a very special place …
— Number puppets turn abstract symbols into living and lovable characters with distinct characteristics to play with and to talk to. They live in Number Town as happy neighbours.
— A Number Lane leads us into and out of Numberland (from 0 to 10, then 20). So many fun active games we can play on and with it to ensure we always find our way in and out of Numberland.
— Gardens define the property of each number and correspond to the geometric aspect. We decorate these gardens and experience all number aspects at a glance. Access is strictly limited and, therefore, a lot of communication, detailed cognition and reasoning is triggered: “I wonder in which garden this little toy cow may graze?”
— Houses because also numbers need a house to live in, with a matching set of windows and a house number on top of the chimney. Once we understood the concept 1 to 5, we can easily build those houses 6 to 10.
— Towers built with single blocks for the beautiful view in each garden. Much to explore, also when we put them next to each other as an impressive staircase.
— Flowerbeds and a large Meadow for those gardening enthusiasts who love picking / planting / buying flowers or vegetables, exploring numbers, patterns, symmetry, even money.
— Hodgey Podgey and Forgetmenot These two imaginative characters account for our magic thinking. We particularly love cheeky Hodgey Podgey who ever so often messes around in Numberland, so that we have to spot and correct the mistakes! Fortunately, we can also call kind Forgetmenot for help.
— Stories like that of poor Four who is sick! To cure her, a tea is prepared from 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…
Or that of Nine who needs to be rescued by his number friends …
— Number Songs because music, rhymes, and singing have the highest value for our body, mind, and soul. A refrain for the beginning as well as for the end of a visit to Numberland make these visits special. In addition, there are songs for each number the beat of which and number of tones corresponds to the number as well as the content does to the number tales. Popular nursery rhymes or relating songs can be included as well. It is fun to explore the patterns in rhythms and to sing, dance, and make music alongside Numberland.
— My Book of Numbers where I can collect my creative treasures around Numberland, maybe some activity sheets, definitely colouring pages of the number characters and a table to stamp the visits to Numberland. Highly treasured by children and a good documentation of a child’s development.
— Plennnnty of room for creativity, own ideas and needs, for free play, for cross-curricular activities – and to connect with things us children love and need.
— Games and Activities Each visit to Numberland can be the basis for lots of activities around the specific Number of the Week. Fun active games, related songs or rhymes, designing or moulding, exploring specific questions, sports or outdoor activities – whatever is part of the term anyway or an objective can be brought in.
Let’s visit Numberland started as a research project in Germany from 2003 to 2005. The objective was to find out whether combining findings from brain research, developmental psychology, elementary pedagogics, and maths into an emotional and imaginative, open and playful concept had significant effects on learning.
And it had: Friedrich/Munz proved that within only ten weeks children aged 3 to 6 gained the mathematical competence and understanding they would have normally achieved only within one year. The same was true for language skills and for under-privileged children with partly very poor understanding of the German language.
The University of Heidelberg confirmed the findings in a second study from 2005 to 2009.
- Within ten weeks only, the Numberland children gained the mathematical competence and understanding they normally would have achieved within one year; the control group more or less remained the same.
- The same was true for the linguistic competence, both passive and active, of the children.
- The socio-economic background of the children was irrelevant for the gain of competence.
- Both sexes benefit, the girls even a little bit more than the boys.
- The age specific results show a striking development of the children regarding both math and language skills: Naturally the younger children had a much lower base level than the older (red dots). Yet the tasks were all taken from tests evaluating whether or not a child aged 5+ may enter school. So obviously the older children achieved much higher scores (green triangles). But after only 10 weeks of Numberland the under 4 year old children scored on average higher than the base level of the one year older! The same was true for the development of the 4 to 5 year olds compared to the base level of the over 5 year olds who again made significant progress.
- The teachers felt motivated and competent to creatively apply Numberland.
- The second study by Sabina Pauen with a similar test design included 4 to 5 year olds and confirmed the positive effects of “Let’s visit Numberland”. It additionally pointed out that the concept increased the confidence of the staff in teaching math and that they felt very comfortable with the concept.
Description of the Friedrich / Munz research study
During 10 weeks 46 children aged 3 to 5+ traveled to Numberland once a week. Each week they visited one number for approximately 50 to 60 minutes. Whenever suitable, the respective number of the week was picked up during the daily routine (circle time, creative play, sports, meals etc.). The children had access to the material for free play. In parallel, a control group of 46 comparable children carried on with their normal routine and had no access to Numberland. In a second run, this setting was repeated with underprivileged children, many of them having severe language problems and lacking other skills. The charts depict the results of that second run.
Project and control groups were tested before and after the 10 weeks in which the project took place. The tests comprised tasks such as conceiving and building sets of numbers, colors and shapes, remembering numbers, cognition of details, general reasoning powers. Regarding active and passive language skills, the children made a story out of some pictures, were asked what they remembered from a story that had been read out to them, and they had to carry out tasks of differing complexity. The effects of ‘Let’s visit Numberland’ both on math relevant thinking and on language have been tested twice with significant results.
Publication in Peer-reviewed Journal
Gerhard Friedrich, Horst Munz (2006). Förderung schulischer Vorläuferfähigkeiten durch das didaktische Konzept “Komm mit ins Zahlenland”
In: Psychologie in Erziehung und Unterricht, Vol. 53, S. 134-146. München und Basel: Ernst-Reinhardt-Verlag.
-> email email@example.com for a free electronic pdf-copy
Gerhard Friedrich, Viola de Galgóczy, Barbara Schindelhauer (2010).
Let’s visit Numberland – playfully discover the world of numbers. Self-published handbook, ifvl Waldkirch.
Adaptation of Komm mit ins Zahlenland by the same authors (2004), Herder Publishing (long seller with 65k+ sold copies)
NCETM National Centre for Excellence in the Teaching of Mathematics (2011). Focus on…Numberland.
Early Years Magazine, Issue 25/2011, www.ncetm.org.uk
Gerhard Friedrich, Barbara Schindelhauer (2014).
Let’s visit Numberland: An Emotive, Story-based Contribution to Numeracy and Literacy Development.
In: Jörg F. Maas, Simone C. Emig, Carolin Seelmann (eds.). Prepare for Life! Raising Awareness for Early Literacy Education. Results and Implications of the International Conference of Experts 2013. Stiftung Lesen 2014 (pp. 79-85)
Gerhard Friedrich, Barbara Schindelhauer (2015).
Let’s visit Numberland: A highly emotive and efficient reason for reasoning.
In: Mathematical Association, Primary Mathematics, volume 19, issue 1, pp. 13-16. Mathematical Association, www.m-a.org
Further publications (in German) on www.ifvl.de
It has been an honour and a joyful enrichment to exchange thoughts with experts on international conferences!
World Literacy Summit 2020
April 5 – April 8, 2020
Oxford University, UK
Over 160 speakers discuss how to improve literacy skills around the world.
Barbara speaks about how children’s natural interest in the language of maths relates to the topic.
Kick-off Meeting 30th Mar – 3rd April 2020
Start of a new project on creatively teaching maths with partners from Poland, Italy, Bulgaria, Portugal, Cyprus.
Kick-off meeting with Numberland training with Barbara.
The 2019 Autumn Summit: Literacies
Oct 28 – Nov 3 2019
– online event –
Kathy Brodie broadcasts interviews with 20 early years experts.
Among them, Barbara talks about the chances of an emotional approach to the language of maths.
Subscribe to the online summit for FREE here:
Erasmus+ project ‘CLIL Bilingual Education a Step Ahead’, 2014 – 2016
Closing conference 2016
2. Andiner Deutschlehrerkongress / Congress of Teachers of German as a Foreign Language
Santiago de Chile, Chile
Workshop on ‘Let’s visit Numberland – learning a second language with the help of maths’ by Barbara Schindelhauer
BCME8 – British Congress of Mathematics Education
University of Nottingham, UK
Session ‘Let’s visit Numberland – an emotive, story based and practical contribution to numeracy and literacy’
Prepare for Life! – Raising Awareness for Early Literacy Education
International conference by Reading Worldwide / Stiftung Lesen, Mainz, Germany.
Session on the contribution of Numberland to both maths and literacy, held by Barbara Schindelhauer.
Gerhard Friedrich, Barbara Schindelhauer (2014). Let’s visit Numberland: An Emotive, Story-based Contribution to Numeracy and Literacy Development.
In: Jörg F. Maas, Simone C. Emig, Carolin Seelmann (eds.). Prepare for Life! Raising Awareness for Early Literacy Education. Results and Implications of the International Conference of Experts 2013. Stiftung Lesen 2014 (pp. 79-85)
Free download of the e-book: http://www.stiftunglesen.de/download
Delta Kappa Gamma Society
Bi-annual European Regional Conference
Keynote and workshop on Numberland, given by Barbara Schindelhauer.
British education expert Kathy Brodie and Barbara discuss the chances of an emotional approach to the language of maths.
This interview was part of Kathy’s Early Years summit 2019.
Listen to Numberland author Dr. Gerhard Friedrich and see Numberland in action.
What Personal Transition and Early Maths have in common.
Catrin Jacksties and Barbara discover amazing connections.
Please cruise freely among the quick quotes and some more detailed feedback.
Teachers tell us about their children
⭐ They are completely enjoying it!
⭐ They have connected on an emotional level to the characters and are very enthusiastic about the Numberland sessions
⭐ Children in year 1 are so excited about Numberland, they have been talking about it in school and at home
⭐ They even brought their own items from home to decorate the number gardens, and are noticing when particular numbers are said in everyday conversation
⭐ They have become excited about maths and it is so good to see how engaged they are with it all
⭐ They love the fairy tale element and the two characters
The idea that the children have to negotiate, reason and justify whilst relating this to numbers, is what makes it perfect for developing early, yet essential, problem-solving skills.
Numberland has been a delight for our preschool program
I had no idea that it would make such a big impact on our children
Numberland far surpassed my expectations
It is the PreK class’s favorite activity to do at school
Numberland fits in beautifully with the Early Years Curriculum. It is exploratory, learning through play, based on role play, allows children to develop their personal, social and emotional skills and “hands on”
It helps learners to extend their problem-solving abilities.
I very quickly witnessed children who had previously not demonstrated a keen interest in maths became very animated and active in their learning.
We started using Numberland in Year One with a group of children who are struggling counting in general. We are pleased with the response from the children.
… also ignites imagination and creativity
All the equipments promote communication among learners.
A group of girls sat for a whole afternoon making their own characters (one to four) to take home and another group made maps of Numberland, including Number Lane!
Getting children to love maths is something I know lots of schools find difficult but this type of scheme is ideal for making maths fun!
Not only is Numberland itself a great concept but the book is a valuable tool.
Numberland is a fun and exciting way to teach children about the world of numbers.
We were looking for a fun way to introduce numbers and shapes to our learners. Numberland is a fantastic concept.
I highly recommend Numberland to all Pre-primary Schools.
… the concept has great value and offers something different to U.K. and North American early years maths approaches, as I have not seen anything like it in my subsequent explorations or conversations with early childhood education professionals.
… a fantastic experience for children where number work can be easily integrated with other areas in the early years.
Research I have read about early years maths through my studies and my own experience with children validates what is suggested in the handbook.
Our learners have so much fun and can’t wait for the next number/shape to get introduced. They are more motivated and excited with each week.
It also impacted on the children’s speaking and listening skills as the activity sparked some interesting debates and forced the children to think more deeply about their mathematical knowledge as they challenged each other to prove their reasoning.
Holleyhill Primary School, Selston (UK)
The concept of Numberland is working REALLY well for us! Reasoning and maths talk is much more prominent and interest/enthusiasm and creativity in maths is much higher than previous classes since implementing what I could find out from the internet earlier this year. Children are becoming ‘producers’ of maths instead of ‘consumers’. Made my own resources and added some characters borrowed from another source who live in each house. LOVE IT!
Hunsley Primary School, North Ferriby (UK)
When our primary maths co-ordinator and Specialist Leader in Education, Liz Russell, first saw Numberland and its amazing resources at the BCME Conference in 2014, she absolutely knew this was the perfect vehicle for engaging our first wave of Reception children in their learning about number and shape. The tactile resources encourage all of the pupils to create exciting models and use their imagination to fill each numbered house and garden with corresponding items: flowers, ladybirds, animals. When the children took their first ‘visit’ to Numberland, accompanied by a song, they were excited and charmed by the experience.
Each of the stories associated with Numberland have a magical quality which the children have been drawn to and teaching staff have been equally inspired to personalise and develop the use of Numberland resources explicitly to suit our school. On first encountering Numberland’s houses and gardens, the children’s faces said it all – you often strive for awe and wonder in Early Year settings and it clearly appeared that day. The resource was used initially to help support the children’s developing understanding of each number, 1 to 10 – their counting, their quick number recognition and their emerging deeper understanding of what each number entails – as we say, ‘the fiveness of five!’.
Not only does Numberland develop number skills and mathematical knowledge, but it also enhances children’s imagination, fine motor, critical reasoning and communication skills – even their social skills – as they learn to share, collaborate and co-operate. We look forward to further exploring the many possibilities of Numberland with our new Reception class in September.
Amy Langmead, KS1 teacher and maths-coordinator (UK)
In KS1 (Year 1), I had a group of children still struggling with one-to-one correspondence. I did some research and came across Numberland – it was featured on the NCETM. It sounded perfect so I emailed Barbara and ordered a copy. When I received it, I was excited at the prospect of undertaking the concept and ordered the resources needed so we could get started straight away. I initially ran Numberland as a daily intervention for 6 children in my class, they covered the Numberland program for 6 weeks and it had the exact impact I had hoped for. Their one-to-one correspondence was there, along with this new found confidence to question and explain their Mathematical understanding.
From then on, we have used Numberland to teach Maths in Reception during the Autumn Term. The children absolutely love it! They love the fairy-tale style characters, and are developing essential problem-solving skills from an early age. Numberland is the perfect tool for: engaging the children, fostering a love for Maths, developing higher-level problem solving skills, along with consolidating a deep-rooted conceptual understanding of basic number. We have recently had the addition of a Nursery, and this year Numberland has also been used in there. Once again, the children love the characters and the resources and are developing a real love for Maths.
I feel that the structure of the program is what makes it so effective. The idea that the children have to negotiate, reason and justify whilst relating this to numbers, is what makes it perfect for developing early, yet essential, problem-solving skills. The children are led to ‘teach’ the teacher, as it is up to them to explain why certain items are allowed in certain gardens. This style of ‘learning and teaching’ has been proved to be the most effective. As we all know, if we get told something – a rule or a procedure – we are unlikely to retain it on a long-term basis, but if we manage to figure a rule or procedure out for ourselves, by developing links and concepts, it is more likely that we actually understand the concept, therefore it is more likely that we will retain it. This is why Numberland is absolutely perfect for teaching those early number skills. (pdf)
Diane Hess, PreK teacher at the Teddy Bear Junction Child Development Program, Plano, Texas (USA)
This program has surpassed my biggest expectations. I left Carola’s training and just knew I had to incorporate it into our school. I had no idea that it would make such a big impact on our children. I know that we are providing our children with a strong foundation through Numberland.
My team and I have a PreK class of 17 children in Plano, TX. We are now in our fourth week of Numberland and parents are reporting to us that their children are telling them that they have to be at school on the Numberland days. And, not a day goes by that one of our children doesn’t make a reference to Numberland by pointing out the number we are on and finding objects in our world with that number or doing basic math concepts in different settings throughout our day without our prompting. They are excited about it and about the Princess and HodgeyPodgey and will say things like: oh no, HodgeyPodgey is at it again when something happens in our classroom. They also love the stories and the Numberland Number songs as well as the gathering song.
Just to give you an idea of how well your program is working in our school….today is Monday, we did Numberland on Wednesday of last week and today someone mentioned on the playground that they found 3 shovels (we have 3 shovels in our garden bag for Number 3) and someone else mentioned HodgeyPodgey in our classroom. They also reference it when they are adding together objects and will say: Just like in Numberland. The opportunities for this program are endless.
Update March 12, 2013: A day for parents Early in February, we hosted a day for the parents to come in and see Numberland. Our parents have really been curious about this Numberland
that their children go home talking about. It took 3 announcements that day telling the parents that they could leave once the children began setting up the gardens before parents started to leave. I think they were so intrigued by the concept and how engaged their children were that they wanted to see more. It was, in our opinion, a very successful morning.
Carola Hauer-Berry, teacher at the Christian Child Development Center, Lewisville, Texas (USA)
Numberland is a fun and exciting way to teach children about the world of numbers. My class fully embraced the number puppets, their gardens, houses and of course their favorite, the naughty goblin Hodgey Podgey. The fantasy world of the numbers adds an intriguing aspect, the hands-on manipulatives make it a ‘real’ number learning experience.
I have never seen children so excited and motivated to learn about numbers as with Number Land. I also like how all kinds of information is woven into the ‘Number Stories’. (For example – the 6 colors of a rainbow and how to mix colors). Who would have known that learning about numbers is so much fun – what a great concept !!
Reeli Tänavsuu, kindergarten teacher and head in Pärnu (Estonia)
We started to travel to Numberland in November 2011 with 4 groups of children: 2 groups age 3-4 and 2 age 5-7 years old. The children were excited about the number puppets and their small houses. All stories give challenges for them. You just have to see their surprised faces when they discover some connections in the story about the numbers! For example the story about Mayor 5’s birthday – they all got tickets to a birthday celebration and in they go just with 5, but all tickets only show numbers 1 to 4… Suddenly one 5-year girl discovered that she can go in with her friend while she has 2 and friend has 3 on the ticket. Then almost all could go in, but two children couldn’t – their tickets showed 2 and 4 which made 6 instead of 5. The teacher just asked, how they could enter and who could help? Immediately there were two children with suitable tickets, so they combined 3 with 2 and 4 with 1 and joined the Mayor’s birthday party. Is there a better way to develop empathy?
Each activity makes teachers to admit, that there are things to be surprised of on Numberland. They all have said, that every time, they “go to Numberland” with children, there are some wow-moments for them too. They enjoy these moments with their children. Our teachers learn to accept children’s viewpoints, listen to their stories and opinion.
As a new approach to early years mathematics, Let’s visit Numberland was introduced to preschool teachers at their summer school August 2012. It has been adopted warmly – as something they need to teach children playfully, integrate mathematics with other subjects and give children the opportunity to acquire other skills.
Linda MacDonald, Nursery teacher (UK)
Numberland fits in very well with our Early Years Foundation Stage curriculum for Mathematics. The book is great and explains the concept of Numberland very well. I really like the way in which the activities and ideas embrace a whole range of mathematical concepts at the same time.
All of my children are able to name, talk about and describe simple shapes with more confidence and use of appropriate mathematical language. My children are now becoming stronger in number recognition, counting objects reliably and accurately and beginning to order numbers. With some of my children I can already see the improvement in understanding of one more, one less, and the concepts of addition and subtraction.
The children have connected on an emotional level to the characters and are very enthusiastic about the Numberland sessions, love bringing ‘gifts’ to the various Numbers (in the correct quantities!!), are becoming adept at sorting out the problems that the naughty Hodgey Podgey causes, and loved making medicine for the poorly Number 4. A group of girls sat for a whole afternoon making their own characters (one to four) to take home and another group made maps of Numberland, including Number Lane!