Why is counting important for preschoolers

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

Why is Number Sense So Important?

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The development of early number sense is critical for children to be able to understand math in later years. There are important developmental skills that all students need in order to conceptually understand math. If there are gaps in these skills, we need to use intervention in order to fill the gaps so that the child can move forward in their numeracy learning.

A Struggling Student

I had this student in my class once, years ago who struggled so much in Math. He was a year behind when I met him in September. This child received extra help outside the classroom as well as the lessons in class that were very hands-on. I had him for two years in a row as part of a looping situation.

At the end of the 2 years, he was still a year behind. While that made me disappointed, I did realize that he had moved forward by a year each time which was a good thing, but there were learning gaps. He did make such good progress because we did a lot of hands-on learning using manipulatives. What I think I could have done to help him understand Math more and not just “do Math” was to be able to identify the learning gap and target those skills.

Understanding Math

Numeracy is different than Mathematics. Mathematics is a body of knowledge and numeracy is the ability to use this knowledge to reason and apply Mathematics knowledge to everyday life. It is not the quantity of Math knowledge that one has that is important, it is the ability to “see” math and use it to function in day-to-day life. Just like early reading comprehension, having number sense will set kids up for success.

Our students need to touch Math and understand quantity. It is critically important that teachers help students develop number sense as an initial skill in their numeracy development. While most initial number sense is developed in the Pre-K, K, and 1st grades, it is developmental and must be nurtured. Whether students have number sense in K or older, the importance is that learning is hands on and conceptual in nature.

Jo Boaler (Professor of Math at Stanford) explains the importance of this in this video where she talks about compression in learning. Watch it here.

Number Sense Practice Ideas

In order to effectively develop number sense in your students, they need lots of hands on practice counting, subitizing and decomposing numbers.

Counting

Counting is one of the important early number sense skills that students learn and use to find out “How Many?” Knowing how to count to 10 is memorization and is an abstract concept. A more concrete measure is to apply their understanding of 5 by counting and using 1-1 correspondence. Young students need TONS of practice counting. There are many things that they can count – simple things like beans or buttons or rocks. Count all the things! Often times, we stop having children count too soon. Click here or the image (affiliate link) to see some math manipulatives and things to count.

Subitizing

When figuring out 5 + 3, does your student count the first 5 fingers out then continue counting 3 more or do they subitize 5 and count on 3 more? Subitizing refers to a student’s ability to instantly recognize a number without counting it like in the case of one hand is 5. Formatively assessing this will help you know what skills they need to work on next. Eventually, students stop looking at and needing their fingers because they can subitize. Subitizing is one skill that our students need in order to develop number sense. So is it okay for students to use their fingers when they are figuring out a problem? Absolutely!

Should Students Use Their Fingers?

According to research, using your fingers gives students a visual not only to look at but also in their brain. The important thing here is that you can observe students working on Math whole class or more closely in a small group and you can use these observations to determine at what stage your student is currently at and what they will need to move forward in their learning.

A great way to practice subtilizing is with 10 frames, dominoes and dice. Dice are handy because they can be used for Math games which reinforce subtilizing while having fun. Kids don’t even know they are learning! (It’s so much better than a math drill, don’t you think?) I don’t know what it is about dice but I just love them! Do you? My favorite dice are the dice within dice set. Need dice? Click here or the image to see all the different kinds of dice.(affiliate link)

Decomposing

When kids can subitize, it makes learning how to add and subtract much easier. Another important element of early number sense is when students are able to decompose, that is, take a whole number and identify the parts. ie. 5=2+3 . As students become more numerate, they apply this to larger numbers. ie. 25=20+5

As your students are learning and growing with practice in these early number sense skills, they are building a confidence in their Math ability. It is so important to develop this early confidence so that they don’t “fear” Math like many adults do. Many of us did not learn this way, rather we learned processes and memorized formulas. No wonder Math fear developed in many people over the years. With hands on lessons and practice, our students will be more engaged in their learning and inspired to learn more.

Math in the “Real World”

It is also important for students to be constantly thinking about Math in real life scenarios because there is Math everywhere! In future posts, I will be looking more closely into breaking down the math progressions so that you can more easily identify where your students are at. Knowing this will help you to target the skills they need and fill in any learning gaps you may see.

While many of these skills are built in preschool and 1st grade, some students in 2nd, 3rd or beyond may not have learned these important skills. What kinds of things do you see in your classroom that students struggle with in Math?

More About Number Sense

Due to the popularity of this post, I wanted to elaborate on some of these concepts discussed here and provide some activities to help you teach number sense. I have added a new number sense post to the blog with more detail on teaching number sense and tips for intervention for those students showing learning gaps.

You can find the new post here or by clicking this image.

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90,000 features of the perception of the concept of counting in preschool children | Mathematics consultation on the topic:

Peculiarities of perception of the concept of counting in children

of preschool age

Modern children get acquainted with numbers early and get great pleasure from rhythmic counting: one-two-three-four-five. But ... quite often this ability to count is only external, and the calculation itself is mechanical.

How to help a child learn to count intelligently, in which mathematical games do the first counting skills develop well?

Before the age of three, it is absolutely not necessary to introduce the baby to numbers and numbers. It is much more important to develop a sense of quantity (a sense of size, color, shape and other mathematical concepts), and thereby lead to the perception of an abstract number.

That is why it is more useful not to memorize numbers by heart, but in the most ordinary life situations to act with familiar objects, learning: what is a lot, and what is little or one at a time, what is more, and what is less or the same.

In mathematics, the important thing is not the quality of objects, but their quantity. Operations with numbers themselves are still difficult and not entirely clear to the baby. However, you can teach your child to count on specific subjects. The child understands that toys, fruits, objects can be counted. At the same time, objects can be counted “between times”. For example, on the way to kindergarten, you can ask your child to count the objects you meet on the way.

In the period before the numerical teaching of children in mathematical representations, a sensory basis for further mastery of counting is formed: the dismembered perception of the totality, the practical establishment of element-by-element correspondence, a general quantitative assessment, which stimulates the need to determine a certain number of objects by a specific number. Many children, even before systematic learning to count, use numbers to determine small populations.

The greatest difficulty for children is to achieve the result of counting, that is, the result, generalization. Developing the ability to answer the question "how much?" in words many, few, one, two, the same, exactly, more than ... speeds up the process of children's understanding of the knowledge of the final number when counting.

During the development of counting, children have difficulties in coordinating numerals with a noun in gender, number, case (in the process of counting, when summing up). These mistakes are natural. Their correction is facilitated by the use by the teacher of such techniques as explanation, the correct selection of visual material, its constant variation in the same lesson, attention and control of children's counting activity. In case of a mistake, it is useful to invite the child to name one of the listed items and choose the right word; one, one or one, and also think about how he will say about two objects: two or two.

By the age of six, children usually have good numeracy skills. When practicing counting, preschoolers should understand that any inaccuracies and errors affect the result. That is why we must strive not to miss an object and not to count one object several times, to remember from which object the counting began, to coordinate

word-numerals with nouns when counting.

Children learn the sequence in naming numerals, quite accurately correlate the numeral with each object of the group (element of the set), learn the meaning of the final number. In the process of further education, work continues on the development of counting skills.

Thus, as a result of the development of counting activity, children begin to understand the quantitative meaning of a number (a number serves as an indicator of quantity) and realize that it does not depend on the spatial and qualitative features of a set (groups of objects).

Sometimes it happens that if a child is often read the same book, he remembers it so well that he retells it by heart, turning the sheets in the right place. From the outside it looks like he can read. But it is worth giving him an unfamiliar text, and it is clear that this is not so. A similar story can happen with the account. The only difference is that an adult does not always clearly understand how the conscious count differs from the unconscious count. This happens because some things that are obvious to an adult are sometimes a mystery to a child. So the studies of the famous psychologist J. Piaget (later these studies were called "Piaget's sign") showed that young children do not understand that the amount of water will be the same in a narrow glass, where the water level rises high, and in a wide one, where the water level low They do not understand this even when water is poured in their presence, and they see that its amount has not decreased or increased. If the baby is asked to compare several large objects with similar small objects, and asked which objects are larger in number, he will point to large objects, even if their number is clearly less. Moreover, if several objects of the same shape are laid out in front of him, and then these objects are moved apart so that they occupy a large area, while asking a question, there are more, fewer or the same number of objects, he will argue that their number has increased. Some children, having memorized the ordinal count, do not know how to count correctly, that is, to assign one object to each number in sequence. Difficulties also arise if it is required to continue counting from a given quantity. All these difficulties speak of a still unformed concept of number, which should be worked on. Otherwise, this concept may not be formed in the first grade, which will significantly slow down the process of mastering the subject of mathematics. You can check whether a child can count consciously with the help of a simple test.

1. Place 2 apples and a pile of 3 peas in front of the child. Ask what more apples or peas?

2. The adult claps his hands, and the child, with each clap, puts down one button.

3. Ask the child to bring as many toys as they have pencils in their hands, without counting either. Now ask each toy to give out a pencil.

4. Take 7-10 coins of the same denomination. Lay them out in front of your child, but don't ask them to count them. Move the coins apart with him so that they occupy a large area. Ask, have there been more coins, fewer coins, or the same number?

5. An adult shows and says to a child: “There are four pencils here”, then adds three more and asks: how many pencils will there be in total?”

But even if the child copes with all the tasks, a complete understanding of the concept of number may never come if he does not realize that this mathematical concept is an abstraction. Often the child does not even have to think about it, because the adult deliberately invites him to count specific single objects. We have already said above that a simple account is not a guarantee of the development of mathematical abilities. The understanding that a counting unit can include several objects, or that a different number can correspond to one object, depending on the measure used, leads the child to a deeper understanding of the concept of number and already contributes to the development of the prerequisites for mathematical thinking. Such a correct introduction of a number, and, moreover, presented in a right-hemisphere way, that is, figuratively, unfortunately, is very rare (modern preschool programs do not set themselves such a task at all). Basically, learning comes down to practical counting, and even if a child counts large and small objects, and then compares them in quantity, and not in size, he does this not because of understanding, but because he was taught that way. Work on overcoming the sign of Piaget on the example of plasticine, water, bulk material, the study of the concept of number with the help of measurements, the figurative presentation of the abstractness of a number - this is what contributes to the development of mathematical thinking.

But it is impossible to achieve the development of the prerequisites of mathematical thinking by studying the concept of number and teaching conscious counting alone, because the subject of mathematics is a broader concept that includes many directions. So let's talk about what else needs to be worked on.

The teacher should take into account that counting skills, like any other, will develop with repeated repetition, exercise, as a result of organized learning. Therefore, tasks where children apply counting skills and reinforce them should be interesting and varied.

It is necessary to pay attention to how correctly children perform movements in the process of counting activity, since in its structure it is a certain system of actions subordinate to each other, consisting of private operations: this is the selection of each object of the set, the correlation of a numeral with it, retention in memory number sequences.

Highlighting and displaying each counting item is a skill that develops gradually. At first, in order to achieve the correct counting result, the child needs to move objects or touch them. Step by step the steps are getting better. The child only points at objects with his finger or hand at a distance, then he singles out each object with his eyes, sometimes helping himself with rhythmic movements of the head.

Speech action in the process of counting activity goes the same way: from external, expanded action (loud naming of numerals, pronouncing words in a whisper) to internal action (naming numerals by moving the lips, and then silently, without moving the lips).

Teaching children to count, it is necessary to include various analyzers: kinesthetic, visual, speech-motor, auditory, tactile. For this, game exercises are used, where it is necessary to count by ear, by touch, to count movements. For example, the teacher suggests counting as many toys as the children hear the hammer blows; jump as many times as the beats of the tambourine sound; clap their hands as many times as they can feel for the balloons in the bag. Children count a certain number of sounds with open and closed eyes, and then count the indicated number of objects or perform certain actions. These exercises are playful. Performing a didactic task, they bring some relaxation, which is necessary in mathematics classes.

All this involves the use of visual material: toys, various objects, images, etc., as well as sounds, movements.

Children practice counting objects according to a pattern or a given number. A numerical card with a certain number of circles, a subject picture with several images of toys or recognizable objects, geometric figures located on a flannelgraph can serve as a sample. Children count the number of objects, keep this number in memory, in accordance with it they count small counting material or toys.

The number can be set using a verbal instruction or a displayed digit. For example, count as many toys as there are windows in a room; count as many bones as there are seasons; count as many circles as the number shows.

It is advisable to make visual and counting material more diverse from lesson to lesson, to complicate tasks. First, children count objects as many as the pattern indicates. Then the number of counted items can be increased or decreased relative to a given number, correspond to the next or previous relative to the named number, show the number one unit more or one unit less than the named number.

The teacher relies on the children's ideas about the features of counting activity and offers them tasks in which the base of the count changes. Children are shown that a certain group can be conditionally taken as a unit of account, for example, two, three, four, five, ten items. The result is a new number. The topics of such tasks are included in the quick wit tasks. For example, it is proposed to determine how many chickens are perched if six chicken paws are visible. Taking two chicken paws as a unit of account, the children correlate the proposed amount with the unit of measurement and get the answer: three chickens are sitting on a perch.

Counting by a given base deepens the understanding of the meaning of the unit. The activity of the account rises to a new, higher, conceptual level. The established ideas about counting activity are used in the further mathematical development of the child, when children come to an elementary understanding of the basics of the decimal number system. The study of the numbers of the second ten, counting in tens, hundreds, lies on the prepared favorable basis.

The practice of teaching counting to preschoolers has shown that its success is influenced not only by the content of the material offered, but also by the form of presentation, which can arouse children's interest and cognitive activity. To do this, it is necessary to use such methods when knowledge is not given to children in a finished form, but is comprehended by them through independent analysis, comparison of the essential features of objects and phenomena, and the establishment of interdependencies.

The organization of the lesson should help the child to turn from a passive, inactive observer into an active participant. The form of the lesson should be mobile and change depending on the tasks. It is necessary to move away from the frozen school-lesson forms of teaching and search for various options for conducting a lesson,

For example, it is important how close the child is to the teacher or to the scene of action with objects, whether he can directly participate in what is happening. The organization of classes in small groups contributes to mutual learning and mutual verification, stimulates cognitive communication and interaction of children. For a joint search for an answer, discussions are very useful. The need to explain the methods of action of a friend, the opportunity to ask a question, to doubt the correctness of the decision, to offer one's own version, as a rule, makes everyone active. With such an organization, an atmosphere of cooperation arises within the team. Children quickly get involved in the search situation, readily help each other, trying to solve a game or practical problem.

The leading activity of preschool children is play activity. Therefore, classes, in fact, are a system of didactic games, during which children explore problem situations, identify essential features and relationships, compete, and make “discoveries”. During these games, personality-oriented interaction of an adult with a child and children among themselves, their communication in pairs, in groups, is carried out. Children do not notice that training is in progress - they move around the room, work with toys, pictures, balls, LEGO cubes ... The entire system of organizing classes should be perceived by the child as a natural continuation of his play activity.

Ordinal and quantitative counting for preschoolers

11/24/2020

To teach a child to count even before he becomes a first grader? Easily! To do this, you need to awaken in a preschooler an interest in mathematics and simple calculations. Of course, the game will help in this! Playfully, you can learn not only to count, but also to distinguish a quantitative account from an ordinal one. Forgot what it is and what is the difference? We invite you to refresh your knowledge.

Mathematical counting is an action for counting something. The school teaches ordinal and quantitative counting. Let's talk about them.

Content:

What is a quantitative account
What is an ordinal account
Ordinal and quantitative accounts - 5 differences
- Targets
- Numerals
- Questions and answers
- Direction
- Meaning
Reinforcement games
- "On the clouds" with an ordinal score of
- Game for quantitative and ordinal counting - Rainbow-arc
- Game - Luntik's birthday
Helpful Hints

What is a quantitative account

A quantitative account implies the answer to the question: "How much?".

As soon as the child remembers the question, he will understand what is required of him. Of course, information is best absorbed in the form of gaming exercises.

Example: Place objects in front of your baby. Ask him a question, give him the opportunity to count and answer.

The game can be gradually made more difficult. For example, adding or removing some of the items, grouping according to characteristics, etc.

What is an ordinal score

An ordinal score is associated with the question: "What is the score?".

It's simple. Again, the game and objects, preferably something different from each other, for example, felt-tip pens. Ordinal from the words "order, in order", this will help the child remember the main question. Ask him to determine the serial number of any of the items.

To complicate the game tasks, swap items, take away or add new ones, inviting the child to explain how and why the serial number changes.

Ordinal and quantitative accounts - 5 differences

Only the account is common between them. You have to count to get the answer to the question in the end. Everything else is different:

targets;
numerals;
questions;
direction;
value.

Difficult at first glance. For a preschooler, it may even be incomprehensible, but if you play a little, everything will become clear!

Goals

A quantitative account is used to count something. The end goal is to determine the total number. An ordinal count is needed to determine the number of an item in an ordered set.

A simple example. Arrange the fruits in a row: apple, pear, tangerine, orange and pomegranate. A quantitative account will help us calculate how many fruits are on the table - 5.

Ordinal is needed to determine the ordinal number of each fruit in the row. The apple is the first, the pear is the second, the tangerine is the third, the orange is the fourth and the pomegranate is the fifth. The same can be done from right to left, the serial numbers of fruits in this case will change.

Numerals

Ordinal counting is impossible without ordinal numbers (indicate the order of an object in a series of sequences), and quantitative counting is impossible without quantitative ones (indicate the quantity).

For example, one, two, three are quantitative, the first, second, third are ordinal numerators.

Questions and Answers

It is easiest for children to remember how the ordinal count differs from the numeral count by asking questions. "How?" - numeral, "what, what number?" - ordinal.

This example game can be played all day long until the child memorizes the information. Ask questions about everything around him. For example:

How many legs does a stool have?

How many fingers are on the hand?

How many rooms are there in the apartment?

What floor are we on?

What candy do you eat?

Direction

To calculate how many items in total, it does not matter how to do it from right to left or vice versa. The goal is to determine the total. You can find out the number of an item in a set only after specifying the direction. Ordinal numbers change depending on whether you count from right to left or vice versa.

Example:

Can you show the third bird from the right?

What color is the second house on the left?

These are tasks for determining the sequence number with direction. Explain to the child that the total number of objects does not change when the direction changes.

Meaning

The quantitative score indicates the totality of items, and the ordinal score helps to determine the place of each.

Games for reinforcing the material

"On the clouds" with an ordinal score

An interesting game for reinforcing the ordinal score with the smallest. To play, you will need any small toy smaller than an A4 sheet. The toy is the main character of the game. She will ride on fluffy clouds.

Ordinary white sheets of A4 format are suitable for the role of clouds. By the way, by inviting your child to imagine the sheets in the form of funny clouds, you will push him to dream up a little.

So what needs to be done. Lay out the sheets-clouds in a row. Place the toy on any of them. Start asking questions:

How many clouds do we count?

Are all clouds the same?

Can you show me where the toy sits?

How can we find out which cloud she is riding?

Answering the questions, the child will count the clouds, he will be able to find out for himself that the toy is sitting on the first, second or third. You can play this game for a long time. The toy will soon get bored on its own cloud, it will want to transfer to another one, and then to the next one, and so on. As you play, keep asking your child probing questions.

Number and Ordinal Counting Game - Rainbow Arc

You will need multi-colored identical objects. Ideally 5-7 colors. It can be anything - from building blocks and cubes to carved figures from cardboard, balls, plastic plates, etc.

To reinforce quantitative counting, simply ask your child to count objects. Complicate the tasks by grouping them by color or some specific features.

When practicing ordinal counting, invite your child to name the number of an object by color and vice versa. For example:

What color is the third ball in a row?

What is the blue cube on the right?

Show me the second clothespin from the left, what color is it?

Change objects, direction of counting, number before the child begins to lose interest in what is happening.

Game - Luntik's birthday

If the child does not know or does not like Luntik, you can replace him with any other cartoon character. So how to play.

Together with your child or on your own, you need to cut out 5 identical balloons on a stick from cardboard. Under one draw a birthday cake. The purpose of the game is to fix in the mind of the child the idea that the serial number always points to a specific object and depends on the direction of the count.

The essence of the story is as follows. Luntik has a birthday. All the guests decided to give him a balloon. But someone could not resist and prepared a birthday cake for the birthday boy. Luntik knows that a surprise awaits him. The caterpillars told him about this in secret. But apart from the fact that the guest who brings the second ball will have a surprise, he does not know anything!

Task: Find the second ball and make sure that Luntik gets a cake with it. To begin with, try to do it for the birthday man. For visibility, let him begin to count from the wrong end, skip the balls or swap them. The main thing is to clearly show the baby that the direction of the account affects the final result.

Variations of the game are different. You can swap balls, pick up, add, etc. Each time the child must determine what has changed, why, what has become the serial number of the ball with a birthday cake.

Helpful Hints

To get kids under 4 interested in counting in the summer, tell them that it will help them find out the total number of items and find a place for each.