PRE-TEACHING CONCEPTUALIZATION

Application of the concept BODMAS (Brackets Of Division Multiplication Addition Subtraction) in solving mathematical problems.

**Concept **

“BODMAS” (Brackets of Division Multiplication, Addition and Subtraction), pre-teaching conceptualization will use both figures and language arts at students in grade 4 level. As a result of the lesson activities, students will gain a deeper understanding of how the concept works through assistance and actually application of the concept by themselves. They will further understand how to solve mathematical problems that may appear to be complex at their level.

B rackets Do first

O order of

D ivision

M ultiplication

A ddition

S ubtraction Do last

Learning needs to be active, constructive, intentional, cumulative and metacognitive. All these properties and attributes of learning will be factored in ensuring that students benefit from the concept. Furthermore, education needs to be activity centered as Piaget suggested. This ensures that students understand the concepts. This unit will also factor in various levels of Bloom’s cognitive taxonomy. These levels include knowledge, comprehension, application, analysis, synthesis and evaluation.

Analysis- Student will be expected to discuss the concept of BODMAS, come up with problems and solve them using the concept. They will also be required to define the concept of BODMAS and state how it can be applied in solving mathematical problem. Based on their knowledge and understanding of various ways of solving mathematical problems, they will be required to incorporate this knowledge in understanding the concept. For example they will elaborate and define the term BODMAS which means Brackets of division multiplication addition and subtraction. An example of a problem is (2/5 +3/4) of 4/6÷ 5 x 3/4=. The procedure of solving the problem will be based on BODMAS. The first step is to identify the problem in brackets (2/5 + ¾) and solve it, then goes to the next step of ‘O’ which means Of, after this, is to Division and lastly Multiplication as the order of the word goes. This will give you an answer= 23/200. The concept of the formula is for the student to figure out the way the problem is formulated and begin with solving problems in that order that begin with brackets, goes to OF, then to division, multiplication, addition and finish with subtraction.

Synthesis- Student will also be expected to have synthesized the information taught. To ensure this is achieved, they will be required to handle a mathematical problem that requires them to use all the components of the concept of BODMAS. They will also formulate their own problems and use the concept to solve them to ensure that they understand the concept. An example of a problem that contains all the issues in the formula is (3/5 +3/4) of (4/6 +1/2) / 4/6 x 3/4=

**Structure**

The first lesson will be introduced on day 1 and the concept is expected to be taught in one week.

Day 1 On day 1 I will have an improvised big letters that are joined which spells out the word BODMAS. All students will then be directed on how the lesson will be carried out. They are going to be informed about the concepts that they will be learning for the week and what is expected of them. Day one will be introduction of the unit to the students. They will be familiarized on the concepts. The acronym or rather the concept of BODMAS will be defined to them.

Day 2 The concept will then be explained deeper to enhance their understanding. For instance, the functioning of the concept will be explained. Students will be taught on the meaning of each letter in the acronym. B means brackets, O means of, D means division, M means multiplication, A means Addition and S means subtraction. Students will therefore, comprehend these meanings.

Day 3 On day three, students will be expected to write and define what the concept is and how it can be used to solve mathematical problem. For example, they will begin writing simple problems such as 2+3-4=. In such like example, they will use addition and subtraction. Therefore, because addition is before subtraction in the formula (BODMAS) it will be the first to be used. The answer will be 1.

Day 4 They will be given a real problem to solve to find out the level of their understanding. An example of a problem is 5 +3 of (6 +3) / 7 x 9=. This problem requires application of the formula BODMAS. Therefore, they will begin solving it by solving problems in brackets then proceeding on to others in the order of the wordings in the formula (BODMAS). This problem relates to a real world problem that students will encounter. For instance, they will be able to calculate problems relating to prices of commodities when send to buy various goods by using knowledge of addition, subtraction and multiplication.

Day 5 I will have to use the concept to solve complex mathematical problems and will expect students to improvise their own problems and use the concept to solve the problem. I will solve a problem and require them to formulate their own problem and solve using the formula. Students will also be required to solve other student’s problems. These problems will have to relate to real world problems such as 3 x 5 + 4 ÷5= or if you have ten mangoes, each costing 5 shillings, how much will it cost to purchase mangoes for 100 people if every person is to get one mongo? Other examples is (½ + ¼) of ¾ ÷1/2 x 2=>

**Prior knowledge**

Grade 5 students are well versed in language and in numbers. Because the concept is a combination of numbers and words, student’s level of understanding of the concept will be tested by giving them a written exercise that will help in determining their level of understanding. The test will include a list of names including, brackets, division, multiplication division, subtraction and multiplication. Students will then be expected to write a sign that shows the meaning of the word. This test will help in gauging their level of recognition of the concepts. The figure below shows how this will look like;

Brackets | of | Division | Multiplication | Addition | Subtraction |

() | of | ÷ | X | + | – |

**Developmental level**

According to the Piaget’s theory of cognitive development, students at grade five fall in the concrete operations stage. Therefore, students are able to apply rules of concrete and logic in their thinking and solving problems. They are able to order objects and understand the sequence of such objects. The first test to determine their prior knowledge is in tandem with the views of Piaget because they observed the names in the table and indicated the symbol they thought to indicate the description in words.

**Anticipatory test**

This is an important stage in the pre-teaching conceptualization and it is a continuation of the prior knowledge. I will endeavor to make the lesson more interesting to the students from the onset of the lesson. To create interest in the lesson, I will take the students to a shopping center and buy them a number of things including, pens, books and sweets and require them to divide amongst themselves. After that I will go back to class and introduce the topic. The first stage where student will be required to mark the right symbol on the description will help me assess the level of their understanding. This will give me background information on how to handle the lesson to ensure that all students understand the concept. They will be also required to tell me why they used the various symbols to ensure that they all understand the concept. For instance, students should be able to mark the addition sign on the scale provided. Then after ensuring that the students have grasped this first step, I will then explain what the concept means. This will be aimed at widening their scope of understanding of the concept. At this stage for example, I will have to go through the letters one by one in a systematic way from bracket to the subtraction using real examples to make the lesson interesting as well as ensure that they understand the concepts. I will involve them by requiring them to improvise signs with local materials such as sticks that will be used in teaching.

On day three, the students will be required to have understood the concept. They will be required to write them systematically and to have understood what they mean and how the formula can be used to solve problems. After this, they will then be given a real problem to solve using the concept. A more complex problem to solve using the concept on their own will again given. They will also be required to come up with their own problem and solve it. This will allow me to know whether the students have mastered the concept and how they are working.

**Motivation**

In learning process of BODMAS, motivation is important to ensure that students cooperate and work hard towards attainment of their goals. The way material is delivered to students matters a lot. Therefore, as Piaget’s recommends, it is important to create an environment that is conducive to promote effective learning. Intrinsic and extrinsic motivation is central to the effective learning process. I do believe in rewarding efforts in a positive and enthusiastic manner. Students at this level require a lot of care and encouragement. Therefore, to ensure that they are motivated to learn, I will praise them for performing well, use tangible rewards to encourage them especially slow learners to work hard. When administering punishment, it will not be done in front of other students to ensure that the self-esteem of the student is sustained. The students who lag behind will not be criticized but will be critiqued in a constructive manner in order not to feel inadequate. Furthermore, students will always be given feedback on the questions they ask to ensure that they are not discouraged. In teaching the concept of BODMAS students will be motivated to have interesting in the concept through involving them in collecting and improvising materials to be used in class, letting them disagree and argue among themselves and encouraging them to never fear to make mistakes. Examples of materials will include boxes and writing materials. They will also be motivated through promises of tangible rewards such as pens and books for those that will perform well in the assessments.

**Discovery of new skills**

In learning, students’ discoveries enhance their learning experience and enhance their understanding of mathematics concept. Students will be able to discover new concepts in solving mathematics problems since the concept will broaden their level of understanding mathematics concepts. Example of a mathematical problem that will enhance their understanding is 4 x 5-5+2 / 6=. The concept will allow student to have insight in handling problems related to the above. Through interaction between teachers and students, students will be able to broaden their understanding of the concept even better and these skills will enable them to develop sharp skills in other related areas. In using this Concept of BODMAS, they will discover how it is easy to solve complex mathematical problems without having to strain their minds. These skills will also be relevant in their normal daily lives as they will have to encounter such problems. An example of a complex problem is one that requires the students to use a range of mathematical decision to solve. A good example is where, a student encounters situation whereby he needs to buy a range of products from a vendor, sort out bad ones, and divide the good products to a certain number of people. This is a complex mathematics problem that require application of this concept and which shows the discovery of new skills.

**Creativity**

I do believe that students enjoy learning if they enjoy what they are doing. The teacher has the responsibility of arousing curiosity among students in order to ensure that they remain creative. The presentation of the concept is one way of enhancing creativity which will definitely impact on the creatively of students. The improvised letters is a sign of creativity. Furthermore, I will design the lesson in a way that inspires students such as including fun and creativity in the lesson plan. Students will be given an opportunity to be creative by requiring them to come up with their own mathematical problems. They will also be required to read further on the topic to discover various ways in which they can solve their problems. For instance, they will be required to design such acronyms to help them solve other complicated mathematical problems. Example of these problems that students will be expected to come up with include; 3/5+4/9 of (3 x 3/6)/ 7=?

**Exceptionality**

This can be categorized into two groups. Those students that are quick in understanding and those who are slow learners. As a teacher, I am required to ensure that my lesson benefits both the students to ensure that the difference in their performance is minimized. To fill this gap I will modify my lessons by modifying the instructions. I will simplify my explanation to ensure that the slower learners catch up with the res of the class. I will also consider some additions; I will create some few minutes with slower learners to ensure that they can understand the concept to be able to catch up with the faster learners. For instance I will give them less complex sums such as 4/5 of 2/4 x (3-5) –2= to help them catch up and understand the concept. This sum is straightforward but requires the students to use the formulae consistently. Even as the slow learners will be handling this problem, quick learners will be introduced to other problems to ensure that they do not idol.

**Measurement and evaluation **

Measurement and evaluation are important in determining whether the students understood the concept or not. In this lesson, I will measure their understanding by giving them two tests. The tests will test both their understanding of the application of the concepts and synthesis. On application, they will be given problems that require application of the concepts. In synthesis, they will be required to apply the information they learn and come up with different problems and provide solutions to them. Evaluation will be done on how best they can handle the tasks. The level of participation of the students in class discussion will also be used in evaluations. Problem that will measure their understanding and application of the concept in real world will be given to them. The problem will require that they apply the concept taught to find a solution to it. In solving the problem they must be able to demonstrate that they understand the concept. Therefore they should o this by writing the formula and defining it, then using it to solve the problem. An example of such a problem is whereby Mary bought 20 mangoes of which 4 were rotten. Mary has three children. How many mangoes will she give to every child order for her to remain with four mangoes?

**Application and transfer**

This concept will help the student to develop all round intellectual skills that will enable them to perform well in other subjects. Since the concept has aspects of language, it will also allow students to have a good understanding of language. The concept further cuts across all other subjects as it gives the students’ broader understanding of the basic of mathematics, which the society always applies. Additions and subtraction, multiplication and division make larger part of our lives and therefore important. Example of a problem that will help to assess how the concept is applied is in a family of 10 people, they consume 4 kilograms of flour everyday. How many kilograms will they require if two more people join the family? How many kilograms will they consume if the family members reduce by 4 people from the original ten? In solving this problem, students are required to first define the problem before applying it. This will help them find the right answers. It will help the students to know how to add, subtract, multiply and divide.

**Reference**

Summers, M., & Kruger, C. (2003). **Teaching** sustainable development in primary schools: theory into practice, Curriculum Journal, 14(2): 157.

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