Assessing problem-solving skills of 5-6 year old children when being familiarised with numbers in kindergartens

Scientific Essay, 2017

13 Pages, Grade: 1.5





1. Literature review
1.1. Preschool assessment of children
1.2. Problematic situations and the solutions of preschoolers.
1.3. The focus of the program that familiarises preschoolers at the age of 5 - 6 with numbers at kindergarten.

2. Experiment to assess how children at the age of 5 - 6 solve problems related to numbers.

3. Results
3.1 Situation 1:
3.2 Situation 2:
3.3. Situation 3:
3.4. Situation 4:
3.5 The relationship among the children’s answers




The article focuses on problem solving skills of 5-6 year old preschoolers when being familiarised with numbers at kindergartens. Learning materials were designed that include 4 situations in which the children need to suggest their solutions to the problems. The sample is 150 children in some different kindergartens in Hanoi. The result revealed that children had many different solutions in one situation. They had some good ways to solve the problem how to arrange, classify and compare things but their ability to use of the numbers in reality was still limited. Thus, teachers should give children more chances to work with quantity representations in both playing and learning activities in kindergartens.

Keywords: numbers, mathematics, 5-6 year old preschoolers, assessment, problem solving, solution


One of the goals that pre-primary education should reach is to help children form and develop basic psychological functions, competences and personalities as well as essential life skills that are appropriate for their age in order to inspire, maximise their potentials and to give them a good foundation for their next levels of education and life long learning (MoET, p.1). The activities that familiarise the 5-6 year old children with numbers play an important part in developing their perception and knowledge of the world outside, making them ready for the 1st grade in primary schools and developing their problem-solving skills. Teaching through problem solving activities enables preschoolers to understand mathematics representations in an easier and more meaningful way.

It is important to recognise how children solve the problems, how they “think” and “reason” when familiarised with maths symbols. Teachers should encourage them, respect their own ways of thinking so as to know what the children have known, what they can do, and how they do it. In addition, teachers should make a plan for the children’s personal development in the next stages.


1. Literature review

1.1. Preschool assessment of children

Apart from the common features of learner assessment, the assessment of preschoolers has its own features not only because preschoolers have not been taught how to read or write but also because the selection of how to assess children should depend on each of their personal development stages in terms of intelligence, emotions and physical health (these aspects are closely related). The fact that a child develops at a higher speed than normal also makes it difficult to ensure the reliability and validity in assessment.

The purposes of preschool assessment of children:

- Identify exactly the development of each child. This may be his/her development in language competence or maths. Also, the levels or the achievement of a child after a nursery period are identified. For example, the assessment will reveal whether a child can “read” fluently or whether he/she has good hand movements or not; and so on.

- Diagnose the delay in development in children and suggest timely intervention. Thanks to clinical diagnosis,psychologists, educators, or doctors can detect the deficiency in a child’s intelligence, psychology, language competence, physical health or even other kinds of disabilities. The earlier they are detected and intervened, the more chances the child will have so as to overcome them. For example, if the hearing disability in a child is detected early enough, he/she can be taught to communicate and get information in many other ways.

- Make a childcare and education plan for the coming stages. After evaluating the appropriateness level of the childcare and education program that has been done, teachers can make a plan for a better program in the next stages.

The principles of preschool assessment of children:

When assessing the preschoolers, we should follow some principles as follows:

- Many different sources of information should be used to assess a child;

- the assessment must ensure the child’s rights and help develop his/her learning competence;

- the assessment should be fair for all children;

- what and how to assess should be suitable for the child’s age.

1.2. Problematic situations and the solutions of preschoolers.

A problematic situation always contains a certain idea to define, a task to complete or problem to, the results of the research on problematic situations will bring about new knowledge, new perception or new actions for the subject.

A problematic situation is characterised by a psychological state of the subject arised when solving a problem that requires him/her to use new knowledge and new strategies. A problematic situation has 3 main components: the need to perceive or take action of the learners, the search for the unknown knowledge and action strategies; and the intelligence of the subject that is shown by his/her experience and abilities.

Problematic situations for kindergarteners can be suggested by teachers both in playing and studying activities. By observing each individual or a group of children at kindergarten, teachers can find out how the children solve a problem.

Problem solving is a really important stage in education in which learners try to find the best solutions to the problems by making use of their abilities, knowledge and facilities.

5 - 6 year old preschoolers have a new visual way of thinking: mind-mapping and logical thinking. Mind-mapping enables children to reflect objective relationships without depending on their subjective actions or wants. This reflection is necessary for children to acquire new knowledge that they cannot gain from observing things separately and making a generalisation by combining their characteristics (2, p.317). This is an important milestone in which preschoolers at the age of 5 - 6 can solve problems in more and better ways than they could earlier.

“In view of that, we advocate the use of problem solving in early childhood, because we consider it to be the foundation of learning since children develop their intelligence as a result of their intetional actions” (Lopes.C.E 2017, p.252) . According to Vygotsky: “however incipient they may be;... egocentric speech progressively becomes appropriate for planning and solving problems, as the activities of the child become more complex” (Vygotsky 1998, p.27).

Children have different ways of acquiring and explaining scientific and daily life concepts as well as different solutions to a problem due to their different life experiences. Children may have been introduced to maths in different ways by the time they go to kindergarten. They may see letters, telephone numbers, buttons on TV remote controls ...and learn how to use them in everyday life at home or in the “Buying and Selling Corner” at their kindergarten , so they have different experiences with quantity.

1.3. The focus of the program that familiarises preschoolers at the age of 5 - 6 with numbers at kindergarten.

The program that familiarises preschoolers at the age of 5 - 6 with numbers should include (Nguyen Anh Tuyet 2009, p.79):

- Counting to 10 and counting at their own pace
- Identifying numbers, quantity and ordinal numbers up to 10
- Grouping items and count
- Dividing one group into two smaller groups in many different ways
- Matching: matching two items that are closely related.
- Understanding the meaning of different numbers used in daily life such as house number, car or motorbike registration number.

In kindergartens, children learn mathematics through games, toys, the surrounding world and communication or wherever mathematics is available. Teachers should wisely help increase children’s need to explore new things, raise questions for them to find the answers and create problematic situations for them to experience, practise solving the problems and share with each other so that they will have suitable responses in new situations. Identifying and understanding how children solve a problem plays an important role in boosting their development based on their own needs and abilities.

2. Experiment to assess how children at the age of 5 - 6 solve problems related to numbers.

- Purpose of the experiment: To assess different ways in which 5 - 6 year old children solve a problem related to numbers.

- Content of the experiment:

Assessing children when counting the number of sets, adding and substracting up to 10;

Assessing children when comparing the number of different sets;

Assessing children when working with numbers representations.

- Participants:

The experiment was done with the participation of 150 children at the age of 5- 6 (94 boys and 56 girls) in some public and private kindergartens in Hanoi such as Thanh Xuan Nam kindergarten, Tuoi Than Tien kindergarten in Thanh Xuan district, Quang Trung kindergarten in Dong Da district, Van Khe kindergarten and Phu Luong II kindergarten in Ha Dong district. Among them, 7 children are learning Soroban and 11 children are attending Montessori program.

There are 45 teachers taking part in the experiment. They all graduated from kindergarten teacher training college and now are in-service students of K2C at Hanoi National University of Education. The children are selected ramdonly and willing to take part in the experiment.

Time of experiment: From September 15th, 2017 to October 15th, 2017.

Experiment method: Teachers used a survey questionaire with 4 different situations to assess how children solve problems. Teachers read the questions with illustration, observed and took notes on how children answered them.


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Assessing problem-solving skills of 5-6 year old children when being familiarised with numbers in kindergartens
Vietnam National University Hanoi  (Psychology)
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Giap Binhnga (Author)Nguyen Manh Tuan (Author), 2017, Assessing problem-solving skills of 5-6 year old children when being familiarised with numbers in kindergartens, Munich, GRIN Verlag,


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