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Addition is the first and most obvious of the four operation on numbers and perhaps, the one that children use most frequently in their everyday lives. The ability to add successfully is a basic and it is a reasonable expectation that the vast majority of primary learners should master addition with whole numbers. Success in addition creates a sound foundation for the development of many other numerical skills. Before learning addition in the formal way, learners already had informal knowledge about it.
They already knew that when doing addition, the amount of something become more than the initial amount.
The studies of Mathematical Thinking and Learning reported the foundation that supports operating with numbers and make it clear that learning to calculate is not just a matter of learning a particular calculation procedure, but that it requires an understanding of number relationships and properties of operations. Numbers and its operations are certainly the most important area of mathematics learning for students (Sarama & Clements, 2009).
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Addition is the first and most obvious of the four operation on numbers and perhaps, the one that children use most frequently in their everyday lives. The ability to add successfully is a basic and it is a reasonable expectation that the vast majority of primary learners should master addition with whole numbers. Success in addition creates a sound foundation for the development of many other numerical skills. Before learning addition in the formal way, learners already had informal knowledge about it. They already knew that when doing addition, the amount of something become more than the initial amount.
Addition is one of the basic number operations in mathematics which is familiar for learners. In solving addition problems, students have to think about the meaning of addition and the more efficient strategies to solve it.
The aim of this study is to contribute to the development of strategies for addition by designing instructional activities that can facilitate students to develop strategies in solving adding two-digit numbers.
The central issue of this study is formulated into the following general research question: How can a strategy support learner to solve addition problems up to two digit numbers in the first grade of primary school?
The general research question in this present study can be elaborated into three specific sub questions:
According to the international literature, mental calculation holds an important place in the teaching and learning of mathematics. In particular, it develops problem solving skills, provides opportunities for making calculated estimates and contributes to the understanding of the concept of number (McIntosh et al., 1995; Threlfall, 2002). In addition, it encourages children to manipulate numbers with ease, it is the foundation for the development of calculating skills and it aids the understanding and development of written methods of calculation (Varol and Farran, 2007).
Addition is close to students’ everyday life. Since they know numbers, they immediately learn the number operations including addition. When they realize the amount of something, they will recognize that the amount sometimes increases and decrease. If they add something, the amount will be increased. Improving childrens’ problem solving skills is an important aim of mathematics education. While solving problems students not only use their mathematical knowledge they already gained (Wyndhamn ve Saljö, 1997) but also improve their knowledge and understanding leading them to a better mathematical insight. Therefore, problem solving should be used as the basis for teaching mathematical concepts so that students construct their own knowledge (Peterson, Fennema & Carpenter, 1989).
When addition applies to real things in the world there are functional variations, which carry the different kinds of meaning to which children are sensitive. The real world contexts are not as simple as the number relationships themselves which are an abstraction of what they all have in common.
There are four different kinds of meaning for addition (Orton, J and Orton, A 1999).
Two-digit numbers, and their addition and subtraction, is the topic where students first engage seriously with place value. The main ingredients in learning two-digit addition and subtraction are: a) learning the addition/subtraction facts: knowing the sum of any two digits (meaning, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and, given the sum and one of the digits, knowing the other digit; b) understanding that a two-digit number is made of some tens and some ones; and c) in adding or subtracting, you work separately with the tens and the ones, except when regrouping is needed. Specifically, item c) comprises two situations:
Add two-digit numbers by combining tens with tens and ones with ones. This can be done in stages: add and subtract 1 or 10 from a two-digit number, add single digit numbers or multiples of ten from a two-digit number, add two-digit numbers without regrouping, add single digit numbers to or from two-digit numbers when regrouping is required, and finally, the general case of adding two-digit numbers with regrouping. In adding a single-digit number to (or from) a general two-digit number, when regrouping is required, the parallel with the corresponding addition fact should be emphasized. Both the reasoning and the mechanics of regrouping have already been learned while learning the addition facts beyond 10.
Learners do not understand addition in the simple, undifferentiated way that adults do. A typically adult conception of addition is purely numeric, as ordered triples. For example, the number 4,5 and 9 have addition and relationship which may be written in diff ways. Stripped of these variations, however the relationship between the numbers in that of numbers that fit together in that way. Children however, tend to see addition less simple. Their conceptions may be bound up with calculation with addition as the process of getting an answer when there is a ‘+’ sign. Additionally, they may understand addition in terms of the situations in which they find it. However just as they understand cardinal and ordinal numbers initially as if they are different things (Fuson and Hall, 1983).
Mental methods or strategies are based on knowledge of facts that can easily and quickly be recalled, combined with inference rooted in awareness of how number system functions, including place value. Breaking numbers into parts and operating on the parts separately and changing the numbers in systematic ways. As well as being an important skill to develop in children, work with mental methods is also very revealing to the teacher about children’s addition knowledge and reasoning. It appears to be a skill that children may develop without the intervention of a teacher.
An important aspect of learning addition is the ability to calculate addition using a paper and pencil method. Different methods for manipulating symbols on paper in order to calculate additions have been developed over the years, yet children often invent methods of their own based approaches to mental addition. The FTM (National Numeracy Project, 1999) suggest some methods which may assist children in the development of their understanding and skill with the conventional addition algorithm and which correspond with some of the mental methods that children use.
The addition of numbers to an answer greater than 20 may be done mentally or using pencil and paper. Both written and mental methods draw, in different ways on the ability to add numbers up to 20 mentally.
Mental methods - the methods that are used to calculate addition above 20 are parallel to those used for addition below 20.
Written method – when children have developed meaning of addition, learned addition related knowledge and practised efficient ways of adding mentally, they are ready to be taught an addition algorithm appropriate to their stage of development. Initially this will b with numbers t 50 and the 100, extending to all whole numbers and eventually decimals.
Children need to practise using paper and pencil methods independently of any material support. Paper and pencil addition should be practiced as a paper and pencil exercise, with the apparatus brought back for demonstration purposes.
The strategies that will be used in solving addition are influenced by the numbers involved. The students are expected to use indirect addition also can be a good alternative for problems which require crossing the ten (Peltenburg, van den Heuvel-Panhuizen, & Robitzsch, 2011). It can be assumed that people decide to solve two digit addition problems either by means of an addition depending on which of both processes requires the fewest and easiest steps (Peters, De Smedt, Torbeyns, Ghesquiere, & Verschaffel, 2010).
Besides the numbers involved, the way addition problems are presented also influences the strategies that students will use. Several studies revealed that bare number problems hardly evoke the use of addition, which can be explained by the presence of the plus sign that emphasizes the “add” action, which is equally true for addition words in words problems (van den Heuvel-Panhuizen, 1996). Contextual problems, on the contrary, lack this operation symbol and therefore open up both interpretations of addition (van den Heuvel-Panhuizen, 2005). Moreover, the action described in the context of a problem may prompt the use of a particular strategy. There is a need for providing a learning environment that can support students to apply the addition strategy properly.
Based on available research on the didactical insights, the following design principles might be recommended:
Therefore, this present study tries to provide instructional activities to construct students’ understanding of the meaning of addition and the more efficient strategy to solve addition problems up to two digit numbers based on the design principles above.
This present study is aimed to contribute to the development of a local instruction theory for addition by designing instructional activities that can facilitate students to develop a model in solving two digit numbers addition. Consequently, this study will be based on the design research approach as an appropriate methodology for achieving the research aim since the purpose of design research is to develop theories about both the process of learning and the means designed to support that learning.
Design research consists of three phases; those are preparing for the experiment, conducting the design experiment, and carrying out the retrospective analysis (Gravemeijer & Cobb, 2006).
In this study, a sequence of instructional activities is designed as a flexible approach to improve educational practices for addition in the first grade of primary school. The three phases in this design research are described as following.
The first step in this phase is studying literature about addition, realistic mathematics education approach, and design research approach as the bases for designing the instructional activities. The planning of mathematical activities and the instruments that will be used; and the conjectures of learning process in which teacher anticipates how students’ thinking and action could evolve when the instructional activities are used in the classroom (Simon & Tzur, 2004).
The next steps are conducting a an interview with teacher, and pre-test to investigate the starting positions of the students.
In this phase, the instructional activities are enacted and modified on a daily basis during the experiment. Before conducting the teaching experiment, the researcher and the teacher discuss the upcoming activity. And after conducting the teaching experiment, the researcher and the teacher make a reflection of whole learning process in the classroom, what are the strong points and the weak points. In this study, the teaching experiments are conducted in three lessons in which each lesson needs 40 minutes.
In this phase, all data in the experiment are analyzed.The form of analysis of the data involves an iterative process. The teaching lesson is compared with the students’ actual learning. There should be explained not only the instances that support the guesses, but also the examples that contradict the guesses. Underpinned by the analysis, the research questions can be answered and the recommendation of how the next the lesson should be improved for further studies can be made
The participants in this research were the Grade 1 learners from historically disadvantaged school. Gender was not considered. The school is the government school. Although this was a convenience sample, with school selected on the basis of convenience.
Follow-on prospective participants were identified, the researcher approached and inviting the parents to a brief meeting to ask them for their children to participate in the study. They will be presented with the information sheet and will further be informed about their right to refuse participation and that participation is voluntary. When they agreed to participate, they will also made aware of their right to withdraw from partaking in the study. They will be further informed that the information that they provided in the interviews would also be treated with confidentiality; they will not be required to disclose their identifying details. Finally, they will be presented with consent forms to sign for participation of their children.
Effective teaching of two-digit addition in the first grade requires a multifaceted approach, integrating conceptual understanding with strategic problem-solving. The study’s instructional activities offer a promising framework for fostering addition skills, underscoring the importance of hands-on learning and mental computation strategies. Further research is recommended to refine these strategies and explore their applicability in diverse educational contexts.
Enhancing Addition Skills in Primary Education: Strategies and Insights. (2024, Feb 22). Retrieved from https://studymoose.com/document/enhancing-addition-skills-in-primary-education-strategies-and-insights
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