The Nature of Maths What is Maths? Why we teach or learn Maths? Why do some people dislike Mathematics?

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1 The Nature of Maths What is Maths? Science of numbers and shapes,quantities and space It involves abstracting,logical reasoning,problem-solving,investigation,classifying etc (A Process) Measurement,probability,statistics,sets,algebra Why we teach or learn Maths? Help in calculations Help us to think and reason logically It is applied in games Learn to read,write and use numbers. Recognition of shapes Measurement of length,weigh,time,money etc It is applied in the study of science and other related subjects It helps us to fit well into society It helps us in estimation and approximation It provides job opportunity Why do some people dislike Mathematics? Peoples wrong notion about mathematics Wrong methods of teaching and learning of Mathematics Lack of TLM's and wrong usage Teacher(not reading enough to update her knowledge) Use of cane(mental) Wrong assignment for teachers Assessment procedure Commentary of achievement(poor.akoko ti) What can we do to develop the interest in pupils for mathematics? Child centered teaching Avoid insults(prevent students from coiling back) Discourage teasing in class Wrong answer analysis Peoples involvement Activity oriented lesson Positive motivation Prepare and use TLM's(questions,appropriate materials

2 Are mathematics teachers born or made? Heredity and IQ level contribute by setting the limit. Environment is there to nurture How Children Learn Mathematics. -What is learning? -How can we notice that learning takes place? Definition Learning is a relatively permanent change in behavior through experience Learning is process of knowledge acquisition through practice,study or exposure,experience etc. Learning mathematics means thinking logically. Learning Mathematics Learning mathematics is a process of developing logical and quantitative thinking abilities. Mathematics becomes functional in the life of children when they develop basic computation skills and can apply mathematics to the world. SCHOOLS OF THOUGHT REGARDING LEARNING OF MATHEMATICS BEHAVIOURIST DEVELOPMENTALIST Behaviourist(Characteristics) Behaviourist see learning as a connection between both stimulus and response This is seen in how questions are posed for an answer to be given by students. They place great emphasis on the environment They regard the child's mind as empty pot to be filled with knowledge Developmentalist(Characteristics) In learning the mental processes of the child must be taken into account(level of maturity must be taken into account. thinking ability) Children can not learn the same content as adult. Individual children differ in the way they learn. Learning is a personal experience and the job of the teacher is to facilitate this process.

3 Jean Piaget's Developmental Views. Piaget's Four Stages Of Mental Mental Development Sensory Motor Stage(0-2) 1. Children are mostly without language 2. They learn to physically control objects in the environment.(keep your eyes on babies. children explore a lot.) 3. Towards the later part of this stage they become aware of others and language begins to develop.(mum and daa way of talking) Pre-Operational Stage(2-7) 1. The children can not perform the four basic operation of mathematics mentally since they cannot relate to the abstract state of thinking. 2. They have difficulty conserving height,length, mass,volume, capacity and other forms of measurement.*demonstration..observe the struggle for big bowls...use two sticks and balance it to test their response to height.* 3. There is no reversible thought process that will allow for logical thought. 4. They are very good at imitating others even they may not understand what someone does. 5. They have difficulty putting things in their natural order.(wearing OF SLIPPERS) 6. They see only their point of view and do not realize that,other might not see the world the way they see it. 7. They also focus on one attribute of a situation at a time.(dont COMBINE CONCEPTS) 8. They are strongly influenced by visual data. Concrete Operational Stage(7-14) 1. They begin to develop a logical system of thought.*they begin to reason and think logically 2. They 3. They begin to group things into classes 4. They cannot combine series of operations to perform a complex task 5. They can reverse thought processes and other event in time.*he is ware of closing time,break etc 6. They can conserve time,quantity,height etc 7. They are able to perform mental action rather than using physical action to perform them. Formal Operational Stage (14 and above) 1. They can deal with the abstract in both verbal and mathematical situation. 2. They can reverse thought processes. 3. The can conserve height,volume,time etc 4. They can perform mathematical operation based on abstract thought alone.

4 Jerome Brunner's Theory Of Learning Theory: any subject or topic can be taught effectively in some intellectually honest form to any child at any stage of development He talks about: 1. En-active 2. Iconic 3. Symbolic Enactive Stage At this stage the child can express many coordinated movement without being able to express this knowledge. Iconic Stage This is a stage where children can make mental pictures of concrete objects. Visual and perceptual organization dominate at this level. Symbolic At this stage of development the child can perform mental manipulation on abstract symbols. (Graphical and pictorial representation) Zoltan Dienes theory Of Learning Principle of Multiple Embodiment Each concept should be presented using as many different situations and examples as possible Richard Skempt Concept Formation Mental object which result when we abstract from a number of examples which they all have in common. Concept of a higher order than those that a person already has cannot be communicated to that person by definition. Instead it can be done by arranging for the person to encounter a suitable collection of examples on that concept. Since in mathematics examples are almost invariably other concepts,the concept used in the examples must already be formed in the minds of the learner. PRIMARY AND SECONDARY CONCEPTS Primary concepts are built from sensory experiences such as seeing,smelling,tasting,feeling, hearing. How a primary concepts can be achieved? Provide more red bags or items for children for them to identify with their senses. Secondary concepts they are formed by combining primary concepts

5 Difference between concept and a skill. A skill is the ability to physically and mentally complete a task. Skills are observable and easily measured whereas Concept is a comprehensive idea about something. Summary Application of learning theories for effective teaching and learning of Mathematics Children can understand concept better when they can relate it to the ones they already know. Use the child-centered approach in teaching. The child must discover thing for himself under the guidance of the teacher All children need concrete experiences throughout the primary and JHS,however older children may need fewer than younger children. And also children of high ability may need less than those of low ability. Children learn better when they are involved in practical activities and discovering things for themselves. The lesson must be activity-oriented under the guidance of the teacher Mathematical thinking is an essential part of problem-solving and children will think for themselves when they are given the opportunity to ask questions Methods of teaching should accommodate the natural taught processes of the child. (Children should be confronted with appropriate experiences that will challenge their existing knowledge of taught) During teaching,show that mathematics is very useful in both career and everyday life. Children learn better in a lively and enjoyable atmosphere. The attitude of the teacher towards the children and the subject should promote the desire of the children to learn Learning Mathematics should be devoid of boredom and coercion(use of force to cause someone to do something) Encourage students or pupils to work in small groups for difficult learning task. (Mixed ability or Ability Group) The presence of concrete learning experiences helps to bring meaning to the symbolic representations. In every mathematical lesson,children should be able to do talk and record their work. PROBLEM-SOLVING AND INVESTIGATION What is a problem? A problem is any challenging situation which is accepted by the one involved and by which one finds a solution.

6 Investigation and Problem-solving compared? Questions? Arrange 1,2,3,4,5,6,7,8,9. Arrange the numbers in the boxes such that when you add them horizontally they are the same as well as vertical and diagonal.( Mathematical investigation is an act of finding out in mathematics. In an investigation there is no immediate goal or steps to take rather, its a process of trying out things and getting wrong answers and trying over again till success is achieved Steps involved in problem-solving 1. 1st reading to be aware of the problem 2. 2nd reading to understand the problem to find out what the question is demanding 3. Think about the technique,strategy formula to use or data collection 4. Start using or apply the right solution. 5. Check the validity of result. Question? Twice a number plus 2 equals 13. George Polya's problem-solving Model Understanding the problem Device a plan Carrying out the plan Looking back John Mason's Problem-solving Model 1. Entry Phase what do I want and? what do I know? what can I introduce?

7 2. Attack Phase 3. Trying out getting stuck and finally reaching the Aha! 3. Review Phase Check result reflect upon it and check it on a wider concepts Gender Issues In Mathematics Gender refers to characteristics attributed to men,women,boys,girls in a society. This characteristics may be related to natural ability emotional or physical ability. Gender therefore is the social roles assigned to the male and female by society Sex is the natural difference between a man and a woman. This is predetermined and we cannot change it.from the above definition gender is socially constructed and sex is biologically determined. Gender Bias when you give unequal treatment to individuals based on their social roles then you are gender biased. Gender Equality refers to equality and access in participation in both sex Gender Sensitivity If anyone acknowledges the existence of gender bias and attempts to work against it then we can say that person is gender sensitive. So gender sensitivity is the situation where on recognizes the existence of gender bias and work against it. Gender Stereotype It is a situation where one has a fixed idea about what something or somebody is or what something should be which is wrongly believed to be true in all cases. Reasons of Low Participation of Girl Child in Learning Mathematics Attitude of tutors towards girl-child when learning Mathematics Wrong notion about the subject Mathematics

8 NUMBER WORK Number Chart Learning to count * ** *** **** one two three four Cuisenaire rod White 1 Red 2 Light Green 3 Violet 4 Yellow 5 Dark Green 6 Black 7 Blue 8 Brown 9 Orange 10