Mathematical Thinking in Children: Number Sense - Literature review Example

Mathematical Thinking in Children: Number Sense Name Institution Date Mathematical Thinking in Children: Number Sense Introduction Early childhood development programs have been keen to establish a way through which children will grasp content at such a tender age [Val091]. Color, pictures, and songs have always proven to be the best way of sparking children’s memory. Children tend to enhance cognition abilities when these three approaches to learning are used. Number sense is one of the trickiest aspects for children to grasp yet it is an essential factor for developing mathematical sense among children. Without number sense, children may find it hard to develop the aspect of logic needed in mathematical operations. Number sense can be defined as the children’s flexibility and fluidity when dealing with numbers. Alternatively, number sense can be defined as the ability to understand numbers as well as the ability to use the numbers effectively [Bob05]. A child with number sense is capable establishing the relationship between numbers; possess knowledge of the symbolic representation and ability to use number sense in real life. ECD experts have established that the process of learning in children takes place in stages through what has been identified as natural developmental progression. The same approach has been cited as relevant when focusing the concept of number sense in children. This paper will delve into the aspect of number sense development among children. Development of number sense According to Jordan et al. (2006), most people develop number sense at an early age with the age of two identified as the genesis of number sense. At this age, experts have identified that children can identify two or three objects in the sense of counting with understanding develops. Piaget, a known scholar on the issues of child development, identified that mental power develops when a child approaches the age of four years. Piaget suggests that a four-year-old child can easily identify four objects without counting, but still every child’s cognitive ability depends on s certain pattern of arrangement. For this reason, Piaget suggested that children require an additional strategy to enable identification of objects more than four. The unconscious cognitive ability of a child may only recognize four objects but would need a conscious ability to recognize six object or groups of six objects. The strategy to be adopted in ECD training should enable a child to develop a greater sense of number, which will enable it to use the numbers in various academic and real life applications. All the procedures of training number sense should adhere to the natural developmental progression. Development of number sense can be split into six phases which every child has to undergo [Val091]. The emergent phase, matching phase, quantifying phase, Partitioning phase, factoring phase and the operating phase are the three distinct phases. Emergent Phase In the emergent phase, a child is capable of developing a sense of bigger or smaller as a primary means of differentiating sizes of objects [Wes13]. It is during the emergent phase that a child is also able to differentiate the spoken numbers from other spoken words. The emergent phase is further characterized by the ability of children to differentiate written numbers from other written words or symbols. The emergent phase provides children with the ability to share or distribute portions while making use of number sense in the social sense. Matching phase In the matching phase, the children can identify five objects at a glance even if some may not be in a position to use names to identify the numbers (Jacobs et al., 2010). It is at this stage that children may start learning how to use names of numbers to count. Children are also capable of recognizing the sequence in which numbers appear such as one, two, three and four. At this phase of numeracy, development children can easily respond when asked to provide four spoons. Teachers can use the child’s ability at this stage to indoctrinate basic number principles such as counting sequence. Number story problems can also be used to enhance number sense among children in the matching phase. For instance, a teacher may use a family situation to teach basic numeracy operations such as addition and subtraction. Quantifying phase Children are likely to enter the quantifying stage between the age of five and six [Bob08]. The quantifying phase allows a child to possess more sense of numbers in such a way that he or she may understand that numbers remain constant unless an addition or subtraction is done. The quantifying phase allows children to apply for numbers in logical operation such as distribution, addition, and subtraction. Children who complete the quantifying phase are capable of using the sense of numbers to continue with education. The sense of numbers provides young learners with the capacity to understand various mathematical and logical expressions involving numbers. The partitioning phase The partitioning phase has been established to take place in children between the age of six and nine years. At this stage, children are capable of differentiating numbers from objects and as use such numbers in representing objects [Jul05]. For instance, children will understand that whole numbers can be used to count any object. If the children used numbers to count mangoes, he or she could use the numbers to count chairs. The sense of understanding the independence of numbers and their use is important in defining the partitioning phase. Children at this stage also have the ability to use numbers in representing groups as well as using numbers in representing each group member. Other capabilities of children at this stage include; ability to double count during multiplicative operations; establish an inverse relationship between numbers, and substituting mathematical operation to find an answer. For instance, when a child is provided with a mathematical operation such as, the child will be able to change the version of the question to get an answer. One way of changing this question would ask, ‘what do I add to 20 to get 24?’ Factoring stage The factoring stage occurs in children between the age of 9 and eleven years. It is during the factoring stage that learners develop an additional capacity to indulge multiplicative thinking. According to Clements et al. (2004), children are capable of engaging cognitive and visual ability to identify the multiplicative situation. The factoring phase is also characterized by the ability of children to connect with groups of numbers as well as the ability conduct mathematical operations such as multiplication and division. Additional mathematical knowledge such as place value of digits in numbers, visualize and use fractions in mathematical operations as well as real life situations. The sense of number in children at this stage is greatly developed, which paves the way for the final phase of number sense, the operating phase. Operating phase It has been established that most learners attain the operating phase between the ages of eleven and thirteen. The previous stages must have played a role in ensuring that children understand the numbers regarding application and the basic applications used to manipulate numbers (Carruthers and Worthington, 2006). At this stage, children are capable of manipulating numbers using both primary operations as well as secondary operation. Learners can either use a single arithmetic operation or effectively handle several operations in the same case. Learning trajectories According to Clements and Sarama (2010), use of learning trajectories enables ECD experts to answer basic questions such as objectives to be established, starting point and steps to be taken to establish the identified goals. Researchers have universally developed a common learning trajectory, which has three components. The first component stipulates the goal, which is a mathematical goal. The second part identifies the path through which the children will follow to achieve the mathematical goal. The final part involves identification of the instructional approaches as well as activities to be used in the process. It is the third part that also identifies the specific levels of thinking for incorporating the instructions and activities. Conclusion Piaget is one of the world's known contributors to the understanding of early childhood development. His discovery that children develop in stages has been beneficial in various applications including the acquisition of number sense among children. As discussed numbers, sense in children is effectively developed in six stages. Before identifying the six stages, trajectories have to be established, and this helps in the development of the curriculum. The entire approach of developing numbers sense in children must acknowledge the fact that natural developmental progression plays an important role. References Val091: , (Faulkner, 2009), Bob05: , (Bobis, et al., 2005), Wes13: , (Western Australian Minister for Education, 2013), Bob08: , (Ojose, 2008), Jul05: , (Anghileri, 2005), Read More