The basic foundation of mathematics involves addition, subtraction, multiplication, and division. Therefore, instructors should ensure that children at their early ages of learning the subjects understand these four operations. Developing meanings to these operations through interpretation and understanding of the relationships among them is essential for children's success in relating the mathematical problems to real-life situations (Chamberlin & Powers, 2012) . For children to better understand the operations, contextual problems act as the primary tool.
First, children should understand the structures of the four operations for them to structure their reasoning and separate information during the mathematical problem-solving process (Kilday & Kinzie, 2008) . The two main categorical structures for the operations are additive structures that involve the multiplicative structure, including multiplication and addition of numbers. Understanding the structures is significant even for children with disabilities as they can develop meaning to real-life situations and decide whether to add or subtract. Familiarization with the characteristics of the operational structures can help children solve different problems related to what they have learned in class.
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Addition and subtraction operations can be structured according to the relationships involved in a given problem. Addition and subtraction involve; change problems for joining and separating, part-part operations, and comparing operations. Change problems that focus on joining or adding comprise three quantities: initial value, change value, and result. These three quantities can be interchanged in various ways to solve problems relating to addition and subtraction. On the other hand, part-part-whole operations deal with a combination of two parts to form one entity. These problems aim at finding an unknown variable within the presented structure. On the other hand, comparison problems involve making a comparison of two quantities to get an unknown part through addition or subtraction.
Since the operations might prove difficult in some situations, children can learn modelling techniques to relate the situation to real life and act upon the operations (Kilday & Kinzie, 2008) . Teachers and instructors should understand that the main problem among children in the subject is deciding which operation to use. Therefore, planning the operations structure through contextual applications helps them determine the right operation to apply. One possible method of teaching addition and subtraction is the use of models. Models such as number lines, bar diagrams, and counters help children to solve addition and subtraction problems easily. However, learners should understand some basic properties of the operations, such as a commutative property of addition that allows for changing the order of addends without impact on the result. Some children might find it comfortable beginning with a particular value in a problem depending on their preferences and psychological mindset. Also, additional operations involve the association of variables to be added. Therefore, a child should be introduced to the associative property of addition to understand that it does not matter in which order to put the values together, but adding means getting the combined value of the numbers.
Multiplication and addition problems also take different structures such as combination, area, equal groups, and comparison. For example, in multiplication, a learner should know that the whole is a combination of several sets or groups. Also, through the use of area structures, children can learn the calculation of areas by modelling the problem to equate to the product of measures. Also, combination problems help children understand the multiplication operations by determining probabilities by understanding how many sets are possible to make up a given combination. Using contextual teaching is relevant in teaching multiplication and addition as it helps learners understand the other related variables that might present complexity such as remainders and decompositions. However, the main focus lies in analysing the problems and applying the relevant structures for problem-solving.
References
Chamberlin, S., & Powers, R. (2012). Assessing affect after mathematical problem solving tasks. Gifted Education International , 29 (1), 69-85. https://doi.org/10.1177/0261429412440652
Kilday, C., & Kinzie, M. (2008). An Analysis of Instruments that Measure the Quality of Mathematics Teaching in Early Childhood. Early Childhood Education Journal , 36 (4), 365-372. https://doi.org/10.1007/s10643-008-0286-8
