## Question:

## Answer:

### Birth to Two Years

#### Babies

Babies develop thoughts and concepts through their self-performance. For a newborn baby, observing the events happening around them helps them to understand the relationship between cause and effect. Seeing the running water of the taps, they learn that it is the time for taking bath. Playing with the toys exposes them to different sounds (Bjorklund & Causey, 2017). Playing with the same toys on a daily basis helps them to classify the sounds. This is also applicable for the mathematical development. Minute observation of the people around them supports their understanding regarding the relative size. This includes their self, their parents and others. It is at this stage, where they develop an understanding that they are small and the parents and the others are big.

Babbling is the form of communication, which the child reveals. However, with the advent of maturity, communication takes a slow yet gradual progress. Herein lies the grasping of words, which includes quantities. Countering this, expressions through hand also makes the child acquainted with the numeric (Bjorklund, 2013).

#### Toddlers

Here, the child slowly and gradually learns to walk by holding the hands of the parents. Along with this, they learn to use fingers for projecting the numbers. Apart from this, the toddlers can recite the numbers; however, some goes missing, as their memory is not that active. One of the other skills, which the toddlers develop, is the understanding of the basic mathematical language. This is done by exposing the child to the different positions of the numbers, which helps the child to learn the words, “under”, “behind” among others (Chu & Geary, 2015). Playing with the numbers and shapes enhance their clarity about their similarities and differences. This reflects their learning about the shapes and numbers. Filling the containers or emptying them supports the toddlers to learn about the quantities and measurements (Rouder & Geary, 2014).

#### Pre-schoolers

Penetrating into the threshold of schools reflect the attainment of maturity at the lower level. Here, the children get to learn the numerical shapes as well as the other shapes, which are present in their surroundings. Doing the projects at this stage generates within them the capability to segregate the things according to their characteristics. This is also applicable for the numbers. Reciting the numbers like rhymes makes the pre-schoolers learn the numbers up to 20 (Demetriou, Shayer & Efklides, 2016). Here also the hand expression proves beneficial in terms of enhancing the acquaintance of the pre-schoolers towards the names of numerical figures. Allowing the students to do the basic things by themselves enhances their awareness regarding cause and effect. However, supervision is of utmost importance in this case to safeguard the children from accidents.

Two years is the foundational age for initiation of the learning process. This includes every subject including mathematics. According to the viewpoints of Purpura et al., (2015), a screener is important for preschool students in terms of testing their numerical skills. Diversified sample selection helps in measuring the progress of the preschool students in terms of the used pedagogies towards the basic and fundamental mathematics. According to the source, this screening is done through two stages. In the first stage, 393 students were selected for performing the instructed maths. Here, item response theory framework was used to detect the capability of the students. As a matter of specification, the items selected were 24 in number. After analysing the achieved results in the first stage, the researchers moved on the second stage, where 129 preschool students were asked to solve certain mathematical problems (Purpura et al., 2015).

Mathematical learning is considered as the stepping-stone towards the decision-making of the children, especially the preschoolers. Provision of proper guidance through the means of skilled and experienced teachers provides the opportunity to attain an easy grasp over the fundamental mathematical solutions. Making effective and judicious use of the gained experience is of utmost importance for the teachers in terms of preparing the students towards their cognitive development. Herein lays the appropriateness of the word “help” as mentioned in the book, Helping children learn mathematics (Reys et al., 2014).

Rational behaviour is expected from the teachers for levying proper mathematical learning to the children. Within this rationality, consciousness towards the needs, demands and requirements of the children, is one of the essential components in the behaviour of the teachers. Imparting the knowledge of the basic mathematical skills to the students in a play way method is the main proposition of the book, Play at the centre of curriculum. Maintaining consistency in the provision of this pedagogy makes the savior in the life of the children in terms of attaining proper mathematical and cognitive development. Viewing it from other perspective, inclusion of play-based learning within the curriculum helps the preschool authorities to achieve positive results in the form of better performance of the students (VanHoorn et al., 2014).

### Mathematical concept for birth to 2 years

#### Shapes

#### Learning experience

I will cut the vegetables and fruits into different shapes and gives these to the child. Then I would talk about these shapes with the child. During the process, the children would learn about different shapes and colours.

Teaching pedagogies

I will make the children see the process of cutting out various shapes from the fruits and vegetables. This would generate interest within the children regarding copying me. They would pick up one shape and form certain concepts and ideas, through which they can compare the shapes.

Methods of assessment

I would jot down my performance as well as the grasping power of the children in response to the undertaken activities.

#### Mathematical learning outcomes

The children would learn the skills of organizing things and comparing them according to their characteristics.

#### Two to Three Years

Until the time of three years, the children acquire much of the skills. In terms of mathematics, a child of three years learns to count the numbers on the fingers. Here, consciousness regarding the counting of 6 on the second hand is on a higher level. This consciousness enables the child to easily identify the large and the small numbers (Iuculano et al., 2014). Drawing is one of the favourite hobbies of the children of this age, so if they are asked to draw the shown figures, they do it very easily. This is because of the liking and interest, which they develop towards drawing. One of an interesting fact here is the ability of the children to pick up the number, which relates with their age. Observation of the things in their surroundings helps three year old children to form certain concepts. This is also applicable for the numbers, with which they play. Regular acquaintance to the numbers and their names helps in memorizing them, which is an example of the mathematic and cognitive development (Cankaya & LeFevre, 2016). In this age, the children can tell the sizes of the two objects placed side by side. This is by expressing the size through finger expression.

### Mathematical concepts for two to three years

### Drawing numbers

### Learning experience

I will draw a number and ask the children to draw the same number on a paper. I would encourage their efforts. Next I would draw different animals out of the number. For this also, I would encourage the children to draw something creative out of the number.

#### Teaching pedagogy

While drawing the number, I would tell the students about the process of copying the number of shape, which they are being shown. Next I would encourage the children to follow the instructions and draw the same number. I would praise their drawings. As a sequential step, I would tell them the method of making something creative from the drawn numbers. I would first do it myself. I would encourage the children to pick different numbers and draw something creative.

#### Methods of assessment

I would take notes of my as well as the children approach towards the proposed activities.

#### Mathematical learning outcomes

These drawing activities would enhance the creativity of the children from the budding stage itself, sharpening their memory.

#### Three to Five Years

Expected cognitive and mathematical development in this stage

By the fourth year, the children learn to speak the basic words like bigger, smaller, and heavier among others. Along with this, they learn the aspects of addition, subtraction, multiplication and division. This is mainly done through the means of objects. Regular practice helps the children to attain an easy grasp over these mathematical aspects. Viewing it from the other perspective, addition generates within them the concept of more and subtraction generates the feeling of less. Here, there are variations in the understanding power. Some of the children show more and less through the finger expression, while others use speech (Verdine et al., 2014). Showing the pictures of the times of the day, seasons and telling them the names enhances their learning in these aspects. However, regular practice yields best results.

Regular observation of the patters and shapes around them enhances the capabilities to make the shape out of their memory. Energy and enthusiasm to explore enhances the creativity of the children at this stage. In terms of mathematics, if they are given an object, they can differentiate them from the other objects on the basis of colour, size, and shape among others. Out of this exploration, they learnt a lot. For example, if out of anger, the parents say a word, which the child fails to understand, they adopt many methods to find out the meaning of that word. This is also applicable for the mathematical calculations, shapes and patterns (Mix et al., 2016). In the process of exploration, they gain an understanding that this shape is like this and is different or similar to the others due to its characteristics.

If graphs are shown to a four year old child, they relate the more and less effect with it. However, this is obviously with the help of the parents and the teachers. The bars in the graph help them to understand which factor is more and which is less.

### Mathematical concepts for three to five years

#### Exploring numbers

#### Learning experience

I will take the children out and tell them about the plants, leaves and flowers. In this, I will teach them counting of the leaves, flowers and plants. After this, I would give them tasks regarding applying the counting in their surroundings.

#### Teaching pedagogy

I will count the number of trees, flowers and animals in the surroundings and tell the children to recite with me. This would generate an interest among them to apply this counting on the other items present in their surroundings.

#### Method of assessment

Observation would be the method of assessment here.

#### Mathematical learning outcome

Observation would help me to assess my performance in terms of the mathematical and cognitive development of the children.

#### Primary (Foundation)

Expected cognitive and mathematical development in this stage

This includes mainly the play group children. Here, the children are provided with the foundational education, which prepares them to cope up with the initial school level education. The method of education here is play based learning, as the interest towards playing is more than studies. The students, through a play way method are exposed to the numbers, shapes, figures and the aspects of measurement along with comparison (Marle et al., 2014). Exposing the children to tests enhances their learning abilities in terms of numbers, their calculations, spotting the shape among others. Maintaining regularity in these tests provides shape to the formed concepts, ideas and thoughts of the children. Along with this, the children are given mathematical projects, which make them independent. The tests help the teachers to assess the learning capabilities of the children. This assessment results in need based teaching, which directly aligns with the development of the children. This assessment is very important as after this, the children would step into the threshold of school (Merkley & Ansari, 2016). One wrong step would aggravate the complexities of the children in coping up with the school level studies. Herein lays the true essence of the word foundation. Exposing the children to the basic and elemental mathematics enhances their preconceived notions about numbers, figures, shapes and patterns. Practicing the learnt skills enriches their cognitive learning, leading them towards a proper development.

### Mathematical concepts for primary (foundation)

#### Interplay with the numbers

#### Learning experience

I would take the numbers, jumble them up and then arrange them in ascending and descending order. Next, I would encourage the children to do the same.

Teaching pedagogy

First I would randomly pick the numbers and arrange them in order. After this, I would encourage the children to randomly pick the numbers. Otherwise they would be conscious regarding picking up the numbers. I would show the children how to arrange the numbers in ascending and descending order.

#### Method of assessment

Here also, observation method would be appropriate in terms of assessing their grasping power in terms of providing them with proper development and nourishment.

#### Mathematical learning outcomes

Interplay with the numbers would enhance the knowledge of the children regarding numbers.

#### Primary (Stage 1)

Expected cognitive and mathematical development in this stage

Till this stage, the children are prepared for entering into the threshold of schools. In this stage, they can tell the basic numeric things like basic addition, subtraction and others. Here, the aspect of mental maths sharpens their memory. Regular practice fades away the concept of using fingers for calculation. One of the other aspects of this stage is the clarity in the expression of the numbers, which helps the students to portray the numbers clearly even in the blank page (Bailey et al., 2014). Children at this stage are expected to reveal matured behaviour in terms of doing calculations or spotting the differences between two objects. Along with this, the expectancy is even higher in terms of measurements. Typical evidence here is the capability in doing projects on filling the containers or emptying the contents of one container into the other and telling the outcomes. However, this is on a play way method and is devoid of any depth.

### Mathematical concepts for primary (stage 1)

#### Mental maths

#### Learning experience

I would tell the children about the process of doing the calculations mentally. I would show them some examples and then tell them to do some themselves.

#### Teaching pedagogy

I would randomly pick certain numbers and show the students the method of subtracting, adding, multiplying or dividing them. After this, I would give them certain mathematical problems to solve.

#### Method of assessment

Here, testing the capability of the students to solve the given mathematical problems is the most appropriate in terms of assessing their grasping power.

#### Mathematical learning outcome

Testing the capability of the children regarding solving the problems helps me to assess their grasping power. This assessment would help me to provide them with the required lesson on mathematics.

## Conclusion

This assignment emerges successful in providing an insight into the development of a child from its birth till the stage 1 of primary level. Out of all the diverse developmental aspects, the focus of the assignment is on mathematical development, which enhances the awareness of the children about numerical values, shapes and figures. Within this, play based learning generates the interest of the children towards studies, which varies from the birth year till the penetration into the first stage of the primary level. The school authorities need to take strict actions regarding the development of the children.

## References

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