Math in preschool

Geometry

Preschool children can use directional words such as “up and down,” and “over and under” as well as comparing words such as “bigger and smaller,” or “longer and shorter.” Additionally, children at ages three to four recognize and name shapes. Naming a shape is mathematics, it is language arts. Mathematics comes in as students recognize and classify the attributes of those shapes. Additionally, students are beginning to compose and decompose shapes. For example, they may be able to make a square with two triangles.

Measurement

Three-year olds can lay two objects side-by-side and tell which one is longer. By age four, children begin to use non-standard units to measure things. For example, they can tell you how many shoes long a desk is, although they need to use many shoes. They are not yet ready to use one shoe repeatedly.

Children in preschool do not learn to tell time, but they are learning the concept of time. They talk about yesterday, today, and tomorrow.

Algebra and Patterns

Preschool children do algebra by recreating patterns and making their own patterns. Children can recognize, describe, extend, and create patterns from a simple repeating pattern such as “red, blue, red, blue” to a more complex pattern such as “red, red, blue, red, red, blue. ” They also notice growing patterns such as “1, 2, 3, 4” or “2, 4, 6, 8.”

Problem-Solving

Problem solving is critical at all levels. Allow students to solve a problem without stepping in too quickly. Children begin to link words and concepts; therefore, teachers can begin to use story problems for teaching mathematics. In kindergarten, the words should be simple and short and by first grade, students begin to write their strategy in the problem-solving process.

Each of these content areas will be further developed in subsequent chapters.

Critical Mathematics Concepts for Preschool Children

Activities in the preschool classroom must incorporate the use of manipulatives and hands-on learning, and the main emphasis should be on number sense. Do not use worksheets or independent practice in the preschool classroom, instead plan activities that will develop a strong sense of number and patterns. The following domains are critical concepts as you teach preschool children to be mathematically proficient:

Counting and Cardinality

Number sense is the foundation for success in mathematics and is the first vital skill for preschool children (Resilient Educator, 2021). The ability to count accurately is a part of number sense, but also to see the relationship between numbers, such as addition and subtraction. Children should be able to demonstrate simple counting skills before kindergarten. This includes counting to 20, ordering numbers, identifying how many are in a set without counting (subitizing), and understanding that the quantity does not change regardless of the arrangement of the items. Additionally, preschool children should understand cardinality, in which the last number said is the number of items in the set.

Operations and Algebraic Thinking

Mathematical ideas become “real” when teachers and students use words, pictures, symbols, and objects. Young children are naturally visual and can build those relationships between numbers and the item represented; therefore, teachers must use pictures and objects to clarify that relationship. As children learn to count, they will learn that the number symbol represents the number of items shown.

Patterns are things that repeat in a logical way. Manipulatives can help children sort, count, and see patterns. An AB pattern means that two items alternate, such as red, blue, red, blue, red, etc. ABC patterns means that three items are in the pattern, such as bear, cow, giraffe, bear, cow, giraffe, etc. Students will learn to make predictions about what would come next in a pattern.

Number and Operations in Base 10

Preschool children begin to understand that the number “ten” is made up of “ten ones,” although this is a difficult concept. Teachers should allow children to count on their fingers one to ten.

Showing students the meaning of the words more, less, bigger, smaller, more than, and less than can help young children understand estimation.

Measurement and Data

Finding length, height, and weight using inches, feet, pounds, or non-standard units is measurement. Also in this skill area is measurement of time. Teachers should ask their students to notice objects in their world and compare them, for example, “The stepstool is bigger than the chair. Do you think it will fit under the chair?”

Sorting is a skill that preschool children should do often. One way to sort is by color; another way is by another attribute. Teachers can ask students to count the toys in a basket, and then sort them based on size, color, or their purpose. Check out this excerpt from the book Exploring Math and Science in Preschool by the National Association for the Education of Young Children – Sorting Activities for Preschoolers by William C. Ritz.

Geometry

Spatial sense is geometry, but at the preschool level it is the ability to recognize shape, size, space, position, direction, and movement. Teachers can talk with children about shapes – count the sides or describe the shape. Furthermore, talk with children about shapes in their world, such as “The pizza is round,” or “The sandwich is a rectangle.”

Calendar Time

Morning calendar time is a daily part of many preschool classrooms. There is a ritual when children sit on the floor and talk about today, look at yesterday, find out about tomorrow, and write out the date. Understanding that time is sequential is critical for young children. They think about before and after, later and earlier, and future and past events. According to Beneke, Ostrosky, and Katz (2008), preschool children generally cannot judge distances or lengths of time. For example, they do not understand that a field trip is in five days and differently than if it is in eight days. And it is different for young children to judge units of time. And although a true understanding of calendar dates comes with maturity, using the calendar to teach other concepts is also valuable time spent in the classroom. For example, vocabulary (month, year, weekend), sequencing (yesterday, today, and tomorrow), and patterns (Monday, Tuesday, Wednesday). They also begin to recognize numbers. Additionally, teachers can use calendar time to teach social skills, colors, letters, and integrate science as they talk about the weather (Beneke, Ostrosky, & Katz, 2008).

Manipulatives

Manipulatives are the mainstay of a preschool mathematics classroom (Geist, 2009). Math  are physical objects that are designed to represent explicitly and concretely mathematical ideas (Moyer, 2001). Students need time to explore and manipulate materials in order to learn the mathematics concept. According to Carol Copple (2004), children should be given many opportunities to manipulate a wide variety of things and teachers should provide children to “mess about.”

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.” Students at all grade levels can benefit from manipulatives, but especially at the elementary level. Using manipulatives can

• provide your students a bridge between the concrete and abstract.
• serve as models that support students’ thinking.
• provide another representation.
• support student engagement.
• give students ownership of their own learning.

Adapted from “The Top 5 Reasons for Using Manipulatives in the Classroom.”

Everyday activities can be used to promote mathematics. For example, during snack time children divide up snacks, count plates, and notice the one-to-one correspondence between the number of children and the number of napkins needed.

How to Teach Maths to Preschoolers

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Children start developing their mathematical skills while they are still babies exploring their environment and continue into their preschool years.

By the time they are learning formal mathematical concepts in the first grade, the foundation for success is already set.

Here are some tips for how to teach maths to preschoolers at school or at home by using hands-on activities and following a concrete-pictorial-abstract approach.

Early maths refers to the mathematical concepts and skills a child builds informally during the first few years. These are also called pre-maths skills or early numeracy skills.

It is essential to first develop these before trying to introduce concepts that are too advanced.

When wanting to introduce your child to maths, you may immediately think of numbers and try to teach your preschooler how to count, recognize the numbers and add or subtract them, but these are really some of the more advanced early mathematical skills.

It’s important to first understand how children learn mathematical concepts.

The three stages of learning any mathematical concept are concrete, pictorial and abstract.

In the concrete stage, children need to physically experience a concept. They need to develop an understanding of one item by holding one block.

By playing with concrete objects, children form the concept that there can be one object, multiple objects, less objects, more objects, etc.

Many mathematical processes are going on while a child is building a tower of blocks next to his friend. Concepts such as more, less, one more, not enough, how many, plenty, fewer, take away and add on are picked up.

Children compare objects and learn that a value can be attached to objects.

In the pictorial stage, which follows the concrete stage, children are able to see a picture of objects and understand that it represents real objects.

For example, a child can look at a picture and understand that the 4 leaves represent 4 actual leaves.

Later on, a child can see a dice with 4 dots on it and assign the value 4, knowing that the dots could hypothetically represent any object.

They would then be able to add the 4 dots on one dice to the 3 dots on another and say there are 7 dots altogether.

This is the final stage of understanding a mathematical concept. It means that a child can look at a sum, e.g. 4 + 3, written in number symbols, and add them without concrete objects or pictures.

The child has matured enough to understand that the symbols 4 and 3 represent a number of objects to be added.

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Preschoolers are mostly in the concrete stage.

In fact, up until the third or fourth grade, any teacher worth their salt will still introduce a new concept in a concrete way before moving onto books or worksheets with examples to solve.

When children understand a concept concretely, it is then much easier to solve abstract problems.

This means that in the preschool years, trying to push a child to count pictures of objects or understand the value of the number symbols is premature and will cause frustration.

You may want to expose your child to numbers (e.g. playing with wooden numbers like these or magnetic number tiles) or rhymes that teach counting, but do not expect your child to understand the value of these numbers yet.

The best way to teach preschoolers mathematical skills is through their main medium of learning – play!

This means that during these early years children don’t need formal lessons, activity sheets and workbooks, or anything that looks more like “real work.”

Here is a list of just a few basic everyday opportunities that double up as the perfect preschool maths activities.

1.

Playing with foam or wooden shapes familiarises your child with basic geometric shapes, as well as their properties. It teaches shape recognition.

2.

Cut basic shapes out of colored paper and make a picture out of them. Children learn to join 2D shapes together to make different forms.

Tangrams (like these) are great for making pictures with shapes.

3.

Puzzles are excellent for developing visual perception and will build a child’s understanding of geometry.

Choose good quality wooden puzzles with a wooden tray.

4.

Pegboards are another great activity for building mathematical skills. They develop number concept and geometrical knowledge.

5.

This may not seem like a math activity, but building forts and other structures and climbing inside them is the first step in a child learning about space and shape. These early play sessions are a must!

6.

There are so many benefits of playing with blocks and that children should have opportunities to play with manipulatives daily. Also offer beads, counters or other construction toys. (read about the benefits of Lego too).

Playing with blocks is the first step in building a number concept and every child should have a good set of wooden blocks at home. This set is perfect for the classroom or home.

7.

When children play in the sandpit and make mud pies and other structures, they begin to use terms such as “I need to make another one,” “There are 3 cakes” or “I made one for each of us.”

8.

Counting songs are a fun way for a young child to learn to count forwards and backwards. This is known as rote counting. They also learn about increasing and decreasing quantity in songs such as “5 Green Bottles. ”

9.

Let your child play with foam, rubber, wooden or plastic numbers in the bath or on a magnetic board. Because they are physical objects, your child can touch them and feel their shapes.

This is far more meaningful to a young child than looking at numbers on an activity page. With time, they will naturally learn to recognize them and know how they are formed.

10.

Playdough is one of the best substances out there, with some amazing benefits. Take the previous activity a step further and mould the numbers out of playdough.

This sensory activity will imprint the numbers in your child’s mind far quicker than trying to write the numbers on paper.

11.

Provide containers of different sizes and shapes and let your child discover the basics of capacity while having fun in the bath or sandpit.

Baking is a great mathematical experience. Let your child be involved in measuring the ingredients to introduce them to units of measurement and quantities.

12.

Ask your child to measure certain objects – such as a book, table or room – using body parts such as hands or feet, and later objects, such as a block or book. Children must first learn to measure length using non-standard items before they can be introduced to standard measurements.

13.

Find opportunities daily to talk about time. Use the daily routine as a starting point. Discuss concepts such as the time of day (morning, afternoon) as well as clock time (“I’ll pick you up at 12 ‘o clock when the school bell goes”).

14.

Give your child different objects and ask him to feel which are heavy or light and to compare the weight of different objects. Use a balancing scale (or make one) and place various household items on it.

15.

Problem solving can be the most, um… problematic, of all the maths tasks! Children in the grades often struggle to visualize problems and what they actually mean.

They often resort to guessing operations (e.g. it says more so I should add) without having any idea what the problem is actually about and how, when visualized, the solution is usually so logical.

The best way to prepare your child for problem solving is to give non-stop opportunities to actually solve real problems!

You need to train your child to develop their critical thinking skills.

You don’t necessarily need to be giving mathematical problems, just general problems that require training the brain to think, and think outside the box!

Allow many opportunities to:

• Build puzzles
• Solve brainteasers such as tangram puzzles
• Solve riddles
• Play games that require thinking
• Play with construction toys (e. g. figuring out how to make a bridge that doesn’t fall)
• Discuss problems and solutions during storytime
• Ask your child for solutions to everyday problems

As you can see, most play experiences have hidden opportunities for learning maths.

Learn to recognize them and use them to consciously teach certain skills. Remember to introduce new vocabulary and ask questions constantly during play.

Introduce words such as: heavier, lighter, longer, shorter, earlier, later, more, less, more than, less than, fewer, extra, not enough, altogether, left, another, full, empty, matching, same, different.

I hope you’ve enjoyed reading this article and have some new ideas to try!

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school preparation, mathematics, counseling

In preschool children, personal qualities, attitude to learning, skills of logical and spatial thinking are most actively formed. They absorb information quickly by memorizing it. Pay attention to the development of the child at an early age. Even in the younger groups of kindergarten, the baby performs minimal mathematical operations. He counts toys when he puts them in the box, forks and spoons when he helps set the table, he knows how many children go to his group. Gradually, teachers teach the kids to sit at the table. Perform simple counting actions on sticks, and also give the concepts of “more-less”, “higher-lower”, “further-closer”.

If the child does not attend kindergarten or the quality and quantity of developmental activities leave much to be desired, you can sign up for general developmental lessons. There, younger and older preschoolers are prepared for elementary school, while paying attention to the formation of elementary mathematical concepts. Preparation with experienced teachers for the school curriculum will help to acquire basic mathematical knowledge.

But not all parents can take their child to extracurricular activities. Parents, grandparents can work with the child. But in order for the classes to be as useful as possible, you need to get advice from a teacher-psychologist.

Pre-school activities

Young children are not yet ready for purposeful learning. They do not have motivation and physiological readiness for long intellectual work. The main activity for preschoolers is a game, so the formation and development of abilities should take place in a playful way. Teaching methods offer many games that allow you to master mental counting and learn numbers. They help to learn how to add, subtract, get acquainted with geometric shapes.

Do not force a preschooler to do tasks that are not interesting to him. If there is no interest, then the task does not correspond to the age, developmental level or personal characteristics of the child. Perhaps he is tired, something is bothering him. It is necessary to offer a different task or change the type of activity, identify and eliminate the cause of discomfort (the desire to have a snack or play with friends).

How to conduct math classes

Preparing for elementary school involves learning using didactic materials and frequent changes in activities. Part of the lesson, the kid solves interesting mathematical problems, then plays active games, where you also need to apply counting skills, choose geometric shapes or numbers. The child sculpts, draws, makes crafts.

Various tasks should be offered that develop counting skills and creativity, the ability to think logically and analyze, and draw conclusions independently.

It is important that the preschooler speaks as much as possible, commenting on his actions and the progress of solving problems. This contributes to a better memorization of information, develops thinking with speech, teaches you to clearly express your thoughts.

Possible difficulties

Teaching and shaping the thinking of children requires patience, knowledge of child psychology, age characteristics. Younger preschoolers can concentrate their attention when solving a problem for 10-15 minutes. Attempts to force or persuade the baby to practice writing numbers or drawing a little more will lead to a negative attitude towards classes.

Older preschoolers are selective in their choice of games. If the task is too difficult or too simple for them, it will not arouse interest. A change in activities and a variety of tasks are needed in order to captivate the game.

At any age, it can be difficult to understand and remember the material. In order to accurately establish the causes of difficulties in studying the foundations of mathematics, to find ways to overcome them, you need a consultation with a neuropsychologist or a teacher-defectologist.

Activities with multiple children

If there are two or three children of different ages in the family, you can work with each one separately, or you can bring them together. But preschool age is a period when there is a rapid physiological and intellectual development. Even a difference of one year can be very noticeable. Therefore, before starting classes, developmental consultations with a neuropsychologist are useful. He will tell you how to properly organize the learning process in a playful way. Advise on how to make it interesting for preschoolers to study. Then the younger ones will not feel “stupid” next to the developed elders, they will not lose interest in learning. Some assignments must be individual. We also need co-op games. For joint classes in preparation for school, it is important that the psychotype matches. Sometimes it is more useful to conduct separate training.

Whims and unwillingness to do mathematics

The formation of logical or spatial thinking requires the child's emotional involvement in the learning process. He should be interested - only then he will comprehend the information and be creative in completing tasks.

If the child does not want to study, postpone the training for a while. If this is repeated regularly or the preschooler loses interest in classes after 5-10 minutes, a consultation with a neuropsychologist or psychologist is needed. These problems may arise due to pedagogical errors of adults and difficulties experienced by the child (fatigue, difficulty concentrating, hyperactivity). Neuropsychological correction will help to eliminate these shortcomings.

Advice for parents

Mathematical development before elementary school will be effective, enjoyable and will help instill a love of learning if the following rules are followed:

comprehensively develop abilities, paying attention to logical thinking and the ability to creatively approach tasks.

Parents who are planning to start introducing their children to the exciting world of mathematics would benefit from counseling on the development of mathematical abilities. The specialist will select a technique taking into account age, level of development and education. Tell parents what is especially important to pay attention to in education.

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See also

Mathematics education in the preschool educational institution

Mathematical education in the preschool educational institution.

Modern approaches to the formation of the foundations of the mathematical culture of preschoolers.

The entry of children into the world of mathematics begins already in preschool childhood. Mathematics is a universal method of cognition of the surrounding and objective world, and its role in modern science is constantly growing. Changes in conceptual approaches to determining the content and choice of methods for teaching mathematics at school, the widespread use of modern educational technologies have also determined the requirements for the mathematical preparation of preschool children.

Today "mathematics is more than a science, it is a language". The study of mathematics improves the culture of thinking, teaches children to reason logically, educates them in the accuracy of their statements.

Traditionally, there are four lines in the content of mathematical education of preschool children: arithmetic, algebraic, geometric and magnitude. Today, taking into account the renewal of the content of preschool education, a fifth content line is added - algorithmic (schemes, models, algorithms). The use of information in a symbolized form contributes to the development of the ability to act mentally, develops logical and creative thinking, and imagination.

The adoption of the Federal State Educational Standard for preschool education will require the need to provide, as a prerequisite, the possibility of self-realization of the child at all stages of work on mathematical development in the preschool education system.

Mathematical material should be revealed during excursions, acquaintance with literary works and small forms of folklore, games with natural material (water, sand, beans, peas, cereals), through game exercises with sensory standards, household items, constructive and didactic games , in problem situations. All these forms vary according to age.

During their stay in kindergarten, a graduate must learn to apply mathematical knowledge and ideas in practical activities that are significant for him: play, children's experimentation, design, work, art and visual.

And as a result of self-realization, the child will develop learning motivation. Thus, the priority tasks of continuous education of children will be solved.

The concept of mathematical education in the Russian Federation

The importance of mathematical education is evidenced by the adoption of the Concept for the Development of Mathematical Education in the Russian Federation (December 24, 2013 (No.

Modernization of the content of curricula for mathematical education at all levels (with ensuring their continuity) based on the needs of students and the needs of society in general mathematical literacy, in specialists of various profiles and levels of mathematical training, in high achievements in science and practice;

Popularization of mathematical knowledge and mathematical education.

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