Table of Contents 1.0 Introduction 2 2.1 Objective 4 2.0 Definitions and Explanatory Concept 3.2 Conceptual Knowledge 5 3.3 Procedural Knowledge 5 3.4 Understanding Relational 6 3.0 Teaching and Learning Topics “Time” 4.5 Approaches,strategies and resources used 8 4.6 Proposed teaching and learning activities 10 4.7 Important of understanding Relational in Learning and teaching 12 4.0 Teaching and Learning Topics “Money” 5.8 Approaches,strategies and resources used 13 5.9 Proposed teaching and learning activities 16 5.10 Important of understanding Relational in Learning and teaching 18 5.0 Conclusion 19References 20 |
Topic 1 ► EFFECTIVE MATHEMATICS TEACHING LEARNING :
SIGNIFICANCE OF AN INTEGRATED APPORACH AND
MAKING CONNECTIONS
► INTRODUCTION
Approach is usually meant by the direction or directions we are taking to achieve the target. In the broader approach also signifies "to come near to in Any Sense" or the path taken to do something. Selected approaches are usually based on theories or generalizations tertentu.Untuk purpose, then, every teacher should know the appropriate and integrated approach of teaching and learning strategies to attract students to get into the classroom and learn. Teachers also need to be skilled in using these approaches or restructuring activities and other teaching and learning sessions that can run smoothly and achieve their learning objectives.
So, due to that teacher should be skilled in this topic. This is because, after studying this topic, the teacher will be able to describe the different models in the teaching process as well as be able to compare and contrast between teaching models. In addition, teachers will also be able to compare and contrast between the implications of teaching models. By learning and learning strategies, teachers will be able to explain the strategies of different teaching and specify the measures and appropriate techniques of effective teaching and learning process. Each teacher will use a different approach to teaching the same subject in different ways according to the teaching style (Ragbir, 2010). The success of an integrated approach is usually determined in terms of the extent to which students engage in the process of teaching and learning. While teaching and learning strategies was a guru wisdom in choosing approaches, methods, and techniques based on the objectives to be achieved. By knowing and applying teaching approaches and strategies that are appropriate, then the class will run smoothly and interesting.
Objectives
Materials Methods Teacher Pupil
Evalution ABM Strategy Feedback
1.0 OBJECTIVES
In this report, I will learn and be able to: 1.1 Read to obtain details or facts 1.2 Read to obtain the main ideas about the concept of knowledge, procedural knowledge and understanding of the relationship 1.3 Plan teaching and learning activities to help pupils solve daily problems related to money up to a value of RM100. 1.4 Know the importance of conceptual knowledge to procedural knpwledge and bring about relational understanding 1.5 Know to plan teaching and learning activities for number 1 to 10 1.6 Identify the major mathematical skills related to addition within 10 1.7 Know to plan teaching and learning activities for addition within 10.
Topic 2 ► DEFINE CONCEPTUAL KNOWLEDGE, PROCEDURAL KNOWLEDGE AND RELATIONAL UNDERTANDING
► INTRODUCTION
In order to teach the topic-topics mathematics effectively, we will need to know some learning aspects about numbers. Sulman (1986) uses the term Pedagogical Content Knowledge in relation to the teaching of a topic. According to him, teachers need to master two types of knowledge: (a) Content knowledge of the subject matter involved (b) Ways of representing the subject matter that makes it easy for pupils to understand.
2.1 Define Conceptual Knowledge
Conceptual Knowledge is knowledge of ideas, concepts and relationships. Concepts are typically composed of many facets based on our experiences and how much we know about a particular idea. They can contain facts, ideas, feelings, relationships, senses, words, images, skills and so on. They usually occur in the form of schema and they are derived from the natural world. Here are some examples of conceptual knowledge typically found in math.
Angle, area, decimal, fraction, percentage, difference, division
What do you know about each one of these concepts?
2.2 Define Procedural Knowledge
Procedural Knowledge is knowledge of the procedures, rules, formulae, symbols and special words we use in mathematics. Unlike conceptual knowledge, procedural knowledge is arbitrary knowledge and a function of.
Here are some example of procedural knowledge typically found in math. (a) Multiplication algorithm such as 12 x 8. (b) Symbols describing referents such as $, in., cm, (c) Division as sharing equally 45÷5 (d) Area of a particular shape such as one curbed surface
2.3 Define Relational Understanding
We can look at understanding from two perspectives, both of which fulfill particular functions in our lives. They are instrumental understanding and relational understanding.
Instrumental understanding is, for the most part not good. It is isolated, fragile and disempowering. It is usually very tentative and difficult to act upon with any degree of confidence. It is at the opposite end of the continuum of understanding from relational understanding. It can be a rule without reason; a piece of rote memorization and can lead to the most amazing misconceptions. Sometimes, however, we need instrumental understanding just to "get by".
Relational Understanding is good. It is robust, connected, rich and full of interconnecting ideas.
Relational understanding is constructed by the learner through disequilibrium, assimilation and accommodation. When we have relational understanding we are empowered and have confidence in our thinking. We can drive a car quite easily with just an instrumental understanding of how the car works. But what if it starts to make a loud knocking noise while driving home late at night. Do you stop immediately to avoid expensive repairs and risk being stranded on a dark lonely road late at night or do you drive home safe in the knowledge that the knocking sound is nothing more than a piece of wire wrapped around the axle. Relational understanding can occur between pieces of conceptual knowledge, between pieces of conceptual knowledge and procedural knowledge and between pieces of procedural knowledge . Wouldn't it be great if we had a relational understanding of everything. Is that possible?
What is possible is that we should want to develop in our students the desire to have a relational understanding of those things that are important in our world.
Topic 3 ► TEACHING AND LEARNING TOPICS “TIME”
► INTRODUCTION
Tick-tock…Tick-tock… Tick-tock…Every second, each mionute, throughout a day, a week, a month or a year:time moves on unrelentlessly regardless of what is happening us. Throudhout history, people have sought various ways to neasure time and keeping time has been an important part of human culture. Our pupils will be able to learn the topic of time effectively if we could plan the systematically. A well-organised conceptual development of time will be very helpful for our pupils to understand the concept of time better. We should use physical materials eg. Clocks, clock face,etc and other representations such as picture cards, time cards,etc to help chidren develop their understanding of concepts involving time.
3.1 Approaches, strategies and resources used Top of Form
3.1.1 InductiveApproach In this approach, the teacher will give students as many examples and will conclude (Shahabuddin, Rohizani, 2008). This inductive approach is centered learning of students and it encourages students to be directly involved in education. It is member the opportunity to students to make their own conclusions about a concept.
In this approach, students will be responsible for active participation is required in the learning process. Teaching and learning process will not be boring them. Pupils also often use the technique of discovery and questioning techniques to draw conclusions on the questions posed by the teacher. They also analyze the information and reasoning in finding that reasonable conclusions. This approach can be used in all studies to encourage students to think the relationship between things.Measures inductive approach is as follows: 1. Before the process of teaching and learning, teachers introduce appropriate examples; 2. Teachers should give more explanation related to curriculum content; 3. Specific examples given by teachers must be varied, adequate and appropriate; 4. Materials educational assistance can be provided to help the students understand the conditions or regulations the problem;
3.1.2 Management of the Teaching and learning in Mathemtaics
Activities in t he classroom, all students in the same activity.Activities are usually based on information communicated by the teacher through the explanation, instruction,storytelling, question and answer session at the end of learning.
3.1.3 Playgroup
Group activities are very important because through rhis activity children learn to share and wait thier turn to take part. When playing in a activities group, the teacher ust ensure that each group involving both sexes and different races. Group shall be in small quantities so that all chidren can engage or participate. The main obejective is to form children to be able to work together to complete the given task.
3.1.4 Individual Activities
In addition to activities in the classroom and group of teachers to hold individual activities. There are instances when individual activities suitable for chidren because it provides an opportubity for chidren to be independition and to allow teachers to give individual instruction to children.
3.2 Proposed Teaching And Learning Activities
Example for Knowledge of Time in Everday Life : Activity 1 Using Alternative Strategies to Compute the Time before an Event, after an Event and the Duration of an Event Learning Outcomes: * To compute the time before an event; * To compute the time after an event; and * To compute the duration of an event. Materials: * Activity Cards * Writing paper * Colour pencils Procedure: 1. Divide the class into groups of four or more. Each group is given a different colour pencil and a piece of writing paper. 2. A set of ten Activity Cards are shuffled and put face down in a stack at the centre. 3. When the teacher gives the signal, pupils will begin solving the questions in the first Activity Card drawn. 4. Once they are done with the first card, they may continue with the next Activity Card 5. At the end of 20 minutes, the groups will stop and hand their answers to the teacher 6. The group with the highest score is the winner. 7. The teacher summarises the lesson on using alternative strategies in computing the time before an event, the time after an event and the duration of an event. Examples of the Activity Cards: ACTIVITY CARD 1 Chong Siew Gaik left home at 7:40 in the morning. She walked for 15 minutes to go to school. What time did she reach the school? She reached the school at ____________________________. |
3.3 Important of understanding Relational in Learning
Relational understanding is the product of a learning process where learners are engaged in a series of carefully designed tasks which are solved in a social environment.
Learners make discoveries for themselves, share experiences with others, engage in helpful debates about methods and solutions, invent new methods, articulate their thoughts, borrow ideas from their peers and solve problems − in so doing, conceptual knowledge is constructed and internalised by the learner improving the quality and quantity of the network of connected and related ideas.
The effects may be summarized as follows: * promotes self-reliance and self-esteem * promotes confidence to tackle new problems * reduces anxiety and pressure * develops an honest understanding of concepts * learners do not rely on interpretive learning but on the construction of knowledge * learners develop investigative and problem-solving strategies * learners do not forget knowledge they have constructed * learners enjoy mathematics.
There is no reason to fear or to be in awe of knowledge learned relationally. Mathematics now makes sense - it is not some mysterious world that only ‘smart people’ dare enter. At the other end of the continuum, instrumental understanding has the potential of producing mathematics anxiety, or fear and avoidance behaviour towards mathematics.
Relational understanding also promotes a positive view about mathematics itself. Sensing the connectedness and logic of mathematics, learners are more likely to be attracted to it or to describe it in positive terms.
Topic 4 ► TEACHING AND LEARNING TOPICS “ MONEY ”
► INTRODUCTION
Children generally understand that sen is part of Ringgit. They can also count collections of sen and Ringgit to determine the total amount of money.
Money reinforces place-value concepts because it uses the base-10 system. In counting number, 10 pieces of 10 sen coins for a 1 Ringgit note,etc. This skill is much needed in counting coins and establishing money equivalence.
The ability of children to estimate prices and perform mental computations on money are also important mathematical skills in handling money in their daily lives.It helps them tosave time doing long calculations and can also be used to evaluate the reasonableness of price of items on sale, when exact answers are not required. 4.1 Approaches,strategies and resources used
What is a problem and problem solving?
It has been said “one person’s problem is another person’s exercise and a third person’s frustration”(NCTM,1969). Thus, the word “problem” seems to cause confusion to teachers in the classroom. There is a need to address this “problem” issue before the problem solving issue could be examined.
In this article, problem solving in mathematics is meant to cover a wide range of problems:verbal and non-verbal problems, and routine and non-routine problems. The following are two examp;es of verbal and non-verbal routine problems.
Simulation Model
1. the act or an instance of simulating
2. the assumption of a false appearance or form
3. a representation of a problem, situation, etc., in mathematical terms, esp using a computer
4. Mathematics the construction of a mathematical model for some process, situation, etc., in order to estimate its characteristics or solve problems about it probabilistically in terms of the model The models Konskrit
Simplify | symbolize | | |
the real world mathematical world
review estimate
forecast Decision Making Skills
Decision making is a mental process in which one acts to choose a best choice of several options available based on specific goals and criteria. Robin Forgarty & James Bellanca (1990) teach them thinking categorizing thinking skills to make decisions as critical thinking and defines it as "making a choice based on reasoned judgment". They give words a synonym of "decision making" and "judging, choosing, selecting". They also provide a menu to use these skills on acronyms JUDGE
J→Jot down occasion for decision
U→Use brainstorming for Toggle
D→ Decide on best possibilities
G→Gauge positive and negative outcomes
E→Express selection; decide.
Mathematics In The Environment And Everyday Life
Relationship between mathematics and students' daily lives is very clear and concrete. An example is the student uses mental arithmetics to choose foods that can be purchased with the amount of money they have and they are addressed by adding and subtracting before buying. This is a mathematical and certainly they do not realize it. If they are aware of this mathematician, sure all students think math is easy and fun.
Observation that I made during this learning process is that students are very fun and they can easily understand how to solve the problem added decimal. This is because in addition to understanding the concepts, they can apply that new knowledge with concrete activities. My idea was supported theory of cognitive development byJean Piaget in the book Mok Soon Sang (2009) which states the development of children aged 7 to 12 years are in their concrete operations. At this point they need to be manipulated for material goes with getting a learning experience directly.
4.2 Proposed teaching and learning activities
Some teaching-learning activities to illustrate the solving of story problems in real-life situations involving money of up to RM100 are as follows:
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Activity 1
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Learning Outcome:
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* To solve daily problems involving the addition or subtraction of money of up to RM100.
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Materials:
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*Sets of newspapers
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*Writing paper
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Procedure:
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1. Pupils form groups of four.
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2. Give each pupil in the group a different set of newspaper.
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3. Tell each group that it is the newspaperÊs 50th Anniversary. In conjunction with their
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anniversary celebration, they are doing some charity work.
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4. The publisher of the newspaper has generously given each group RM100. The money will
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be used to buy food for an orphanage.
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5. Each person in the group is to study the advertisements found in the newspaper provided.
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6. Next, the person is to write the name and cost of one or two items of food that he or she
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feels would be of use to the orphans. 5. -------------------------------------------------
Using the round robin format of the cooperative learning technique, members of the group discuss each item selected and why it was chosen. One member of the group functions as a recorder. 6. -------------------------------------------------
The group will have to come out with a final list of items to be purchased. The group may need to make adjustments to keep the total cost below RM100. 7. ------------------------------------------------- Prepare a bulletin board to display all the groupsÊ lists of items. The displays help pupils recall what they have learnt and it is also a means of seeing the practical application of mathematics.
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Activity 2
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Learning Outcome:
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* To solve daily problems involving addition of money up to RM100.
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Materials:
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* StoreÊs weekly advertisements from supermarkets.
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* Writing paper
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Procedure:
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1. Instruct each pupil to draw on a sheet of paper, five columns and label each column: Monday,
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Tuesday, Wednesday, Thursday and Friday.
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2. Show the pupils the canteen menu and instruct them to study the menu.
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3. Each pupil is to select a drink and a snack from the menu to be consumed each day.
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4. Have the pupils calculate the actual cost for all meals within that five days.
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5. The students may have to adjust their selection of food to ensure the total cost falls below
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RM100.
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6. Have the class determine the most well-balanced meal that can be bought at a moderate cost.
4.3 Important of understanding Relational in Learning and teaching topic Estimation and Mental Computations on Money
As children mature and their knowledge on computations on money increase, you need to offer activities that help them develop the skills for estimating prices and doing mental calculations. You need to help children see how estimation and mental computations on money can help them to:
(a) Save time doing long calculations;
(b) Evaluate the reasonableness of prices of items on sale; and
(c) Solve problems when exact answers are not required.
The best way to help children value the use of estimation is for you to practise estimation with them. Once children understand what they are doing, they will see that estimation is a useful way to judge whether a price is reasonable or not. Three common processes for estimating sums include rrounding numbers, front-end estimation and ccompatible numbers. Under a teacher’s careful guidance, children will learn to use one or more of the processes skilfully
5.0 Conclusion
We can know something, or we can know and undertand it. We know that the sun rises in the east. To understand what that means is quite another thing. We can know that 2 x 6 =18: to understand what that means is really what ot”s all about. We can look at knowing, or knowledge, as comparising two different sets or groups of knowledge:conceptual knowledge and procedural knowledge. Knowledge is something we either have or do not have. We either know something or we do not know it.
Understanding is much more complex than knowing. It is much more difficult to state categorically (or assess) that you understand something or you do not understand it. We can also understand things at different levels depending upon our level of development and experience and familiarity with that particular thing.
Based on the plan of teaching used by the teachers in this paper, children as young as preschool age are actually very interested in learning mathematics. Teachers must play a role that will attract children to feel that passion does not fade as we move into the school environment and finally a stage that much higher.
Strong basic knowledge in mathematics is important in our society that lead to a more developed country based on Science and Technology. Our students need to have a strong understanding of basic mathematical concepts that will enable them to pursue their studies at a higher level. To ensure the future of State, and assesses whether we need a more effective approach in teaching children the basic thoughts about metematik from the early stages of schooling.
References
a) Books 1. Murugiah s/o Velayutham, Kao Thuan Keat, Wong Woy Chun ( Second Edition, August 2012) HBMT 2103 Teaching of Elementary Mathematics Part 1 ; Open University Malaysia, Selangor 2. Novak, J. (1998) Learning, Creating and Using Knowledge: Concept Maps as Facilitative Tools in Schools and Corporations; Lawrence Erlbaum Associates, Inc; New Jersey, pp 24-25 3. Dr.Siti Fazlili Abdullah, Wang Woy Chun ( Second Edition, April 2012) HBMT 1203 Teaching of Pre-School Mathematics ; Open University Malaysia, Selangor 4. Azizah Ngah Tasir, Gomathi Naidu ( December 2011) HBSC1103 Teaching and Learning of Science. Open University Malaysia, Selangor 5. SE.supplies(M) Sdn.Bhd (2010)., Mathematics For Year 2 Activity Book 2, Malaysia Book Publishers Association, Shah Alam, Selangor 6. SE.supplies(M) Sdn.Bhd (2010)., Mathematics For Year 2 TextBook 2, Malaysia Book Publishers Association, Shah Alam, Selangor
b) Internet 1. http://www.mathsisfun.com/worksheets/time.php 2. http://erlc.ca/resources/resources/mathnewsletters/number%20sense.pdf) 3. https://commons.wikimedia.org/wiki/File:MetroDF_Línea_2.svg 4. http://www.bbc.co.uk/schools/ks2bitesize/maths/ 5. http://lms.oum.edu.my/ 6. http://dictionary.reference.com/browse/approach 7. http://eprints.uthm.edu.my/2276/1/baharom_uthm.pdf 8. http://en.wikipedia.org/wiki/Simulation
