Children number learning

Help Children Understand the Meaning of Counting — Better Kid Care — Penn State Extension

Topics include: learning about measurement, learning about patterns and sorting, and learning about shapes and space.

Teaching children to count involves more than helping them learn the numbers one to ten. It involves helping children understand the meaning of numbers.

Children learn the meaning of numbers when they are developmentally ready. For instance, children ages two to three might move things as they count, but they might count to three while moving four things. This shows that while they might know the numbers in sequence, they are not able to use them to count. At this age, it’s great to count together with a child, just for fun. You might count the steps as you walk up them or the buses as they go by. This helps children begin to move towards matching one thing at a time with the number as they say it.

Three- to four-year-olds are still learning to understand quantity. While they can count up to five, they are growing in their understanding of what numbers really mean. By age four to six, children can match the numbers one to ten with ten items; this means they are really counting with meaning. They can solve simple problems, such as how many cookies you will need for each person to have one. By the time children reach the ages of five to seven, they can count items and match them; for example, putting five stamps on five letters.

You can help your child learn to count by making counting a fun part of your day. Count socks as you sort them; count the juice boxes in your refrigerator; count the cars and buses going by. The more experience children have with counting, the more they will learn the meaning of numbers. Understanding the meaning of numbers takes experience with counting lots of things, and you can help by giving your child this experience regularly.

Learning about Measurement

Giving your young child a chance to measure things can help her understand both how and why people measure things. Find real measuring jobs for children to work on. Will this table fit here in this space? How tall are you? How much bigger is the plant than it was a month ago?

Inches, feet, and other units of measurement don’t make much sense to a young child. Teach your child to measure with a simple object, such as a shoe. Check how long the rug is with the shoe, or measure the height of a plant with blocks. Then give her a ruler to work on measurement problems. How big a block do we need to fit this space?

Learning about Patterns and Sorting

You can help your child get ready for math by giving him chances to think about patterns and to sort things. This skill is both fun and important in learning math. You can use things that you can find outside: pinecones, leaves, sticks, etc. Lay out a pattern with these objects (leaf, leaf, stick, stick, stone) and then repeat the pattern and ask your child to make the same pattern. Most children enjoy this simple game.

You can help your child develop sorting skills when you do your household chores. Ask your child to put the blue towels in one pile and the white in another. As children grow you can challenge them to use two different ways to sort. You might say, “Can you sort these towels by color and then put all the large towels in this basket and all the small ones here on the shelf?”

Learning about Shapes and Space

Take time to notice shapes and talk about them with your kids. Shapes are everywhere. A simple walk is a great time to talk about them — you might see the rectangles made by the fence posts, or the circular manhole covers. As you pick out shapes, your children will learn how to do this as well.

Children learn best about sizes, shapes, and how things fit together by playing. Blocks are a great toy to teach these spatial relationships. Building structures helps children figure out how things can fit together. They learn about what it means to double things in a practical way, when they discover that they need two blocks to fill a space. When children understand the real-life meaning of these things, the idea of multiplying by 2 makes sense.

Parent Count December 2007

When Do Kids Learn Numbers and Start Counting?

Starting counting is a significant milestone in children’s development. Though it seems like children learn when they start school, they start learning numbers just as soon as they start exploring the world around them. Other skills they have like identifying shapes help build on what they actually already know.

Counting is taken for granted often. However, there is a lot of research about where our capacity as humans to do math comes from. Some scientists suggest that we are all born with the innate sense of number in our brains.

Though we think that counting has to be taught, we are born with an instinct that the neuropsychologist Brian Butterworth explains as something similar to the idea of color. We perceive the ”blueness” of the sky just as we can perceive the ”threeness” of a group of objects.

When is the Perfect Time for the Children to Learn Counting Numbers?

Of course, having this instinct for the number of objects when we are born doesn’t mean that we don’t have to learn the names and the symbols of numbers to develop that instinct. Children start learning math as soon as they are out in the world and there are certain math milestones most children reach around approximately the same age. However, as we always mention, children develop at different rates. This means that if your child doesn’t have the skills listed for their age group, just be patient and on the lookout.

Similar to reading and talking, counting and math skills and thinking can be introduced to the child from the start. Studies show that children as young as 12 months can have a sense of how many items are in a set that is up to three objects thanks to their innate sense of number. When children start making the connections between the language we use to count and this innate sense, they learn counting.

Counting everyday objects around the house can be a great start for parents to count along with their children. Children may first learn the numbers in a different order, and may even repeat and memorize a sequence of numbers or counting. It is just like singing the ABCs. Songs could be great helpers in teaching children how to count. Children develop the ability to understand the actual concept of counting generally around the ages of two and four. By the age of four, children usually can count up to 10 and/or beyond.

You may notice that your toddler is skipping some numbers along the way, like jumping from 3 to 6. This is called pre-counters where toddlers start saying numbers in no order. This is very typical for two-year-olds especially. Don’t worry, as they are just beginning to develop their skills. When you notice this happening, model the correct way of counting and they will hear you do the counting the correct way. Keep them exposed to counting and numbers as much as you can, just like what you are doing with reading.

Following the pre-counter stage comes the chanters level. Children may say numbers and count but do this in a sequence. Meaning that they group these numbers. You can observe this when if you interrupt them, they will have to start over rather than continuing from where they left off. Then, reciter children can verbally count to 5 and so on. However, this is still pretty advanced for a child at this age so it should not be expected right away.

Children at the age of three to four can typically advance to a level of math that is a one-to-one correspondence. They can point at objects and count them. You can practice with your child this skill easily. For instance, to start off easy, put their toys in a straight line and have your child point to each toy as they count them. This behavior model can be used with infants and toddlers to develop their counting skills.

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What is Rote Counting?

Rote counting is the simplest number concept that children can develop. It is the ability to say numbers in order from memory, so it basically consists of counting numbers sequentially. Most children find it easy to count by rote. Usually, this skill begins developing before children recognize numerals. When the child is exposed to counting and numbers both at home and at school, they start to develop together.

Through rote counting, children don’t actually count the objects, they just say the numbers in their correct sequence. It’s like going 1, 2, 3, 4, 5, etc. Here, the child doesn’t count objects or actions. Rote counting is just saying a sequence of numbers, and the simplest way is starting from one and counting upwards. It is a core skill related to early maths.

Once the child gets the hang of it, rote counting can also be done backward and starting from different points. When the child grasps this concept and gets this knowledge, they can apply it in different ways and contexts.

The importance of learning rote counting comes before the ability to count objects. Rote counting gets into the picture when a child sees five toys and wants to count them. They would have to have the sequence of numbers in their head first in order to work out how many toys there actually are. If rote counting is not established at first, other skills like addition, subtraction, times tables or money may not be learned accurately. Repetition is the best possible way to rote learning.

Rote counting can be developed and practiced easily with your kid. Try to incorporate counting in your daily routine with your child. You can count the items you got from the grocery store, or create or use counting songs as they will be catchy enough to help your child learn rote counting more quickly. One of the good counting song examples is 1,2,3,4,5 – Once I Caught a Fish Alive.

Math Skills in Different Ages

Each child develops at a different rate than others. However, there is an age group where certain skills develop to take as reference. Here are math skills that children acquire at different ages:

Age 0 - 12 months - Babies

Starts to understand basic cause and effect relations
Starts to understand sizes and relative sizes, like small and big
Starts to understand words related to quantities
Starts to predict the sequence of events, like opening the door means mommy is coming

Age 1 - 2 years - Toddlers

Can use fingers to show how many years old they are as they understand that numbers mean ”how many”
Can match certain basic shapes, like putting the triangle in the triangle hole
Can understand words indicating comparison or measure like behind or faster
Can start to recite numbers but may skip some

Age 3 - 4 years - Preschoolers

Can compare and contrast height or size
Can recognize shapes around
Can sort things out based on color
Can make the connection between numerals and number names, like 2 and two
Can count up to 20

Age 5 years - Kindergartners

Can add by counting their fingers on one hand
Can follow very basic maps
Can draw symmetrical shapes
Can understand and follow directions that have multiple steps

Age 6 - 7 years - First and second graders

Can understand and know the difference between 2D and 3D shapes
Can count to 100 by ones, twos, fives, and tens
Can write and understand numerals from 0 to 100
Can write and recognize the words for numbers from one to twenty
Can do basic addition and subtraction up to 20

Age 8 - 9 years - Third graders

Can know how to do multiplication and division
Can do addition and subtraction
Can handle money
Can use paper and pencil to solve math problems

Basic and Fun Math Games for Counting to 10

We have gathered some basic and fun math games that will develop your child’s sense of numbers, counting, and math!

Count with Dominoes!

In this game, you can use dominoes to practice counting and maths. You can draw your child a worksheet where you will separate the page into boxes. You can then give your child a domino for them to count the dots on the two sides.

If you would like to put math into the game, you can put one addition or subtraction, where the child will write or tell the numbers and the result. You can also play this game with more than one child to turn it into a competition!

Toy Car Race!

You can play this game with some toy cars, cardboard tiles, and dice. You can race your child or you can have your child and other children play at the same time. The goal of the game is to move 10 tiles to get your toy car to finish the race. The number of tiles can be increased depending on which numbers you would like to work on.

Your child will roll a die and lay down a tile to move their car forward. However, in order to get to tile 10 at the end, they have to roll the number they need. Going over is not allowed. This will help your child practice counting as well as some basic addition.

Makeshift Weight Station

You won’t need much for this game. Get a clothing hanger and hang two plastic cups on either side of the hanger. Have your child drop small items into the cups to see which items weigh more or less. Kids love this game and putting items in the cups. Have your child or multiple children guess what weighs more first! You can also ask them to guess how many of the objects in the cup weigh the same.

10 Rocks

This is a great outdoor activity to learn counting and math. Prepare buckets with numbers on them. Have your child look for and gather rocks and put them into the buckets to complete the number on the bucket. You can also add some other features into the mix, for instance, have your child look for 5 big rocks for the big rock bucket and 10 small rocks for the small one.

In Russia, the number of parents who give their children family education is growing

It is quieter at home

For example, in the Crimea, over the past four years, the number of children studying at home has doubled - from 535 to 1208. The motives of parents who chose the family format for them , were different. Someone was not satisfied with the quality of education and the psychological climate in the classroom. Someone wants to increase the effectiveness of a child's education through modern educational methods or focus on subjects that will be useful for entering a university and a future profession.

- At school, my son Pasha faced the banal cruelty of other children, and that's why I transferred him to family education, - said Maria Rogova, a resident of Sudak. - And after a while it turned out that he was better prepared than the children who communicated with teachers every day. At home, I distributed the time of classes so that the assimilation of the material for the child was as effective and comfortable as possible. But in September 2020, Pavel nevertheless returned to the classroom. True, already in a different school.

In the Rostov region, the number of "family families" has doubled over the past five years. According to Yulia Grichanichenko, the mother of a fifth-grader, the main advantage of such education is the opportunity to give children a broader and more modern education, and to do it in a fun way. "Now there are thousands of programs, videos, lessons on the Internet on all topics of the school curriculum," she says. "This greatly enriches the same textbooks."

In Izhevsk, according to the general education department of the city administration, last year 401 children studied in the format of family education. And, as the head of the department, Elena Ivanova, says, about the same number of “family” students, plus or minus ten people, visit each year.

As a rule, parents of "home" children do not advertise that their children study at home - they do not want to hear words of condemnation. For example, Maxim (his parents asked not to give his last name) went to a regular school in the first and second grades. But dad and mom noticed that their son was losing interest in learning, and decided they could teach him themselves. Now Maxim is going to the fourth grade. He studies well, and he likes that he does not have to run to the lessons by eight in the morning.

If before 2020 ten thousand people studied in the family format, now about 13 thousand children study under the guidance of fathers and mothers

- And more and more parents are interested in the possibilities of family education, - says Galina Rezvanova, director of the Novosibirsk school N 96. - When a child is transferred to a family format, he is excluded from school, returns textbooks, loses access to the school library, gym. But some moms and dads still decide to educate their children on their own. Each family has its own reasons for this, but we should not forget about the pandemic, many parents think that it is better if their child is constantly nearby.

"Children studying at home are more independent - that's a fact. In addition, they are more satisfied with life and calmer - after all, they study in a family atmosphere," says a family psychologist from Khabarovsk. It all depends on them, and also on the methodology that parents use in teaching.

School is safer

In St. Petersburg, as of the end of the 2020-2021 academic year, 3,651 children were enrolled in family education. But local education officials are not at all inclined to exaggerate the effectiveness of such training. For example, if parents succeed in teaching according to the primary school program without difficulty, then difficulties may arise with the organization of the systematic preparation of the child for passing the final certification. But the most negative consequences of studying outside the walls of a general education institution, as experts emphasize, is the blurring of the boundaries between education and recreation, which does not give the child the opportunity to manage his time wisely, as well as the lack of socialization.

- Most of the time, these children are within the family, do not communicate with peers, do not face various life circumstances, which means they do not learn to adapt to the constantly changing conditions of society, - Sergey Tarasov, Chairman of the Committee for General and Vocational Education of the Leningrad Region, notes.

According to the Ministry of Education of the Nizhny Novgorod Region, in the 2020-2021 academic year, 803 children studied outside educational institutions in the region, and for some of them the issue of passing intermediate certification was an "edge". “Because the law says that the development of an educational program is necessarily accompanied by a regular school,” explained “RG” in the Nizhny Novgorod Department of Education. “To pass an intermediate or state final certification, “families” are enrolled in an educational organization that operates on educational programs that have state accreditation. And here it is important to remember that the unsatisfactory results of the intermediate certification are recognized as academic debt, and if it is not eliminated, the child will definitely return to school."

As a rule, parents of "home" children do not advertise that their children study at home - they do not want to hear words of condemnation

Costs are comparable are comparable.

However, fathers and mothers of "families" still have to fork out for textbooks - we recall that ordinary students receive them in schools. At the same time, those who study at home manage to save on school uniforms. Both of them, depending on academic performance, sometimes also have to hire tutors.

Parents have the right to decide on the choice of the form of education themselves, but they are obliged to notify the district department of education at the place of residence or at the location of the school in which the child studied before or was attached to. Also, moms and dads need to conclude an agreement on the same certification with any chosen school. The certification procedure is determined by federal law and internal regulations of the educational institution. For example, at school N 319 in the Petrodvortsovy district of St. Petersburg, certification is carried out twice a year. The deadline for submitting an application for passing the intermediate certification is no later than the first of December and the first of April. “But at the request of an external student, an educational organization has the right to set an individual deadline for conducting intermediate certification,” is also indicated in the school Regulations on the organization of education in the form of family education and self-education.

A World Fit for Children (Simplified Declaration and Action Plan)

Action Plan

B. Goals, strategies and actions

2. Providing quality education

38. Education is essential.

Education is one of the human rights.
Education is a key factor in reducing poverty and child labour.
Education is a key factor in promoting democracy, peace, tolerance and development.

What are the problems?

Over 100 million children of primary school age, most of them girls, do not attend school.
Classes with a large number of children are taught by untrained and poorly paid teachers.
Many schools are overcrowded, unsanitary and poorly equipped.
One third of all children do not complete the fifth grade of school, ie. do not reach the minimum required level of basic literacy.

What do we want to do?

39. As agreed at the World Education Forum in Dakar, it is important to ensure that, by 2015, all children have access to and have the opportunity to receive free, compulsory and quality primary education. We will also strive to gradually provide secondary education. As a step towards achieving these goals, we must achieve the following:

a) Expand and improve integrated early childhood care and education systems for both girls and boys, especially for the most vulnerable and disadvantaged children;

b) Reduce by 50 per cent the number of out-of-school children of primary school age and increase the net enrollment rate of children in or in alternative quality primary education to 90 percent by 2010;

c) Eliminate by 2005 the disparity between girls and boys in primary and secondary education; and achieve gender equality in education by 2015, with a focus on ensuring that girls have full and equal access to and opportunity to receive high quality basic education;

d) improve all aspects of the quality of education so that children and young people achieve recognized and measurable levels of learning, especially in numeracy, literacy and basic life skills;

e) ensure that the educational needs of all young people are met by providing access to appropriate education and life skills programs;

f) Achieve a 50 per cent increase in adult literacy rates, especially women, by 2015.

How are we going to do it?

40. To achieve these goals and objectives, we will implement the following strategies and measures:

Develop and implement specific strategies to ensure that school is easily accessible to all children and adolescents and that basic education is affordable for all families.
Promote innovative programs that encourage schools and communities to be more proactive in identifying dropouts, out-of-school and out-of-school children, especially girls and working children, children with special needs and children with disabilities, and assisting them in enrolling in school, its attendance and successful completion of training with the participation of governments, as well as families, the public and non-governmental organizations as partners in the educational process. Special measures should be taken to prevent and reduce the number of dropouts due to the need to go to work.
We understand that:
- education must be of good quality;
- teachers must be qualified;
- non-formal education and alternative approaches provide valuable experience;
- With this in mind, it is necessary to bridge the gap between formal and non-formal education and ensure their complementarity.
Ensure that all core curricula are:
- open to children with disabilities and children with special learning needs;
- fully covered such children;
- took into account their needs.
Ensure that indigenous and minority children have access to quality education on the same basis as other children. Efforts must be made to ensure that this education is provided with respect for their heritage. Efforts must also be made to create opportunities for learning so that indigenous and minority children can develop a deeper understanding and preservation of their cultural identity, including important aspects such as language and spiritual values.
Develop and implement specific strategies to improve the quality of education and meet the learning needs of all children.
To create with children a learning environment that is comfortable for them, where they feel safe, protected from abuse, violence and discrimination, and healthy and encouraged to acquire knowledge. Ensure that curricula and materials fully reflect the promotion and protection of human rights and values such as peace, tolerance and equality between men and women and take advantage of every opportunity presented by the International Decade for a Culture of Peace and Non-Violence for the Children of the World (2001–2010).
Strengthen early childhood care and education systems by providing services and developing and supporting programs for families, legal guardians, caregivers and communities.
Provide education and training opportunities for adolescents to enable them to secure sustainable livelihoods.
Develop, when appropriate, and implement programs to enable pregnant women and adolescent mothers to continue and complete their education.
Urge the further development and implementation of programs for children, including adolescents, especially in schools, to:
- prevention and cessation of smoking and alcohol consumption;
- detection, counteraction and prevention of trade in narcotic drugs and psychotropic substances and their use.
This will be done, inter alia, by promoting media campaigns to raise awareness of their harmful effects and the dangers of drug addiction, and taking the necessary measures to address the root causes of this phenomenon.
Encourage innovative programs to encourage children from low-income families to enter and attend schools and not be forced to work at the expense of their studies.
Develop and implement programs that address disparities in school enrollment between girls and boys, and gender biases and stereotypes in education systems, curricula and materials, regardless of the argument.
Raise the status, morale, training and professionalism of teachers, including early childhood educators, by providing them with adequate remuneration for their work, as well as opportunities and incentives to improve their skills.
Develop flexible, participatory and accountable governance and management systems for educational institutions at the school, community and national levels.
Address the special knowledge needs of children affected by crises by ensuring that learning takes place during and after crises, and implement training programs to build a culture of peace in a way that contributes to the prevention of violence and conflict and contributes to the rehabilitation of those affected.
Provide accessible conditions and opportunities for recreation and sports in schools and communities.
Embrace rapidly evolving information and communication technologies to support affordable education, including open and distance education, while reducing inequities in the availability and quality of education.
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