Special Methods In Teaching Mathematics

Page |1 SPECIAL METHODS IN TEACHING & LEARNING MATHEMATICS. Topic 1: Introduction to Maths

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Definition of mathematics

That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations

ROLE OF MATHEMATICS • • • • • • •

modeling and simulation; mathematical formulation of problems; algorithm and software development; problem-solving; statistical analysis; verifying correctness; Analysis of accuracy and reliability

Topic 2 : introduction to Mathematics General Principles of teaching Mathematics • • • •

Easy to difficult Concrete to abstract General to specific Specific to general Principles

Easy to difficult

Explanation • •

Concrete to abstract

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General to specific

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Specific to general

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Example

Maths should be taught from easy to difficult concepts. From lower level to higher level of difficulties

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Basically, we learn about number first than operation. If we don’t know about numbers then how to operate?

In the concrete stage, the teacher begins instruction by modeling each mathematical concept with concrete materials Abstract stage, the teacher models the mathematics concept at a symbolic level,

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(e.g., red and yellow chips, cubes, base-ten blocks, pattern blocks, fraction bars, and geometric figures). The teacher uses using only numbers, notation, and mathematical symbols to represent the number of circles or groups of circles, operation symbols (+, –, ) to indicate addition, multiplication, or division.

Teach maths from general topic and narrow down to specific concept. Usually, the introduction of the topic tells the general concept of the topic, then it tells specific items of the topic

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First we learn about general things about money then we learn about the monetary skills, value, the operation involve money and etc

Learn maths form specific to general concept. Focuses on the sub-topic first then to the main topic

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We learn about the monetary skills first then discusses about issues/experience involving money.

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Nadiah binti Abu Bakar

Teaching Concept of mathematics •

In order for students to develop their innate number sense, and a working knowledge of the above concepts, they must have : ○ a great variety of interactions with their environment, ○ exploring and manipulating, comparing, arranging and rearranging real objects and sets of objects.

Many of these types of interactions and experiences occur incidentally for sighted children, but the blind child is at great risk for missing valuable and relevant incidental information. So, teachers & parents should provide both structured and informal opportunities to handle and explore, note likenesses and differences, match, group and classify, order, and experience other relationships with real objects to prepare them for understanding the same relationships with numbers Concept of Mathematics 1. 2. 3. 4.

Classification Sequence One-one correspondence Conservation

Concept

Explanation

• Classification

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Sequence / Ordering

Involves discrimination, matching, and grouping or categorizing according to attributes and attribute values. Begin working on simple discrimination and matching with objects that are familiar to the child and that occur naturally in his or her world (e.g., shoes, toothbrush, squeeze toys, blocks, etc.),

It is ordering objects, then quantities, and eventually numbers, according to specific given criteria.

Example (Example) classified according to : * Shape (square, circle, triangle, rectangle) * Size (large, small, big, little) * Weight (heavy, light) * Length (short, long) * Width (wide, narrow, thick, thin) * Height (tall, short)

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ordering from largest to smallest

Activities •

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Give children numerous opportunities to use everyday items for matching and categorizing: eating utensils, grooming tools, foods, and toys for function; shoes and shoelaces for matching by size or length. Children can explore shapes and size by building with Legos and Unifix blocks; Ask the studnts to help in sorting different sizes of books, different colour paper or different shapes of legos.

working in this area with real objects on the basis of quality (e.g., ordering family members' shoes or belts according to attributes such as length). Having family members or class members line up according to height can also help to facilitate understanding of sequence To practice positional ordering, have a student line up the rest of the children in a group, and then identify each as first, second, third, . . . last.

Page |3 One-to-one correspondence

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Understanding relationship

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conservation

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Knowing that a given amount remains the same though its appearance may change.

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They can place one sock inside one shoe or one shoe on one foot; they can get one napkin or snack for each member of the family or class; They can place pieces in one-piece puzzles.

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The value of RM1 is same as 2 coins on 50 cents.

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Have the child compare/match/sort groups of objects into sets; then have him or her identify the number of items in each set, Expressing them by name and by some pattern (e.g., clapping or ringing a bell the same number of times as the number in the set).

give them a ball of clay and let them divide it into smaller amounts as they wish, and then combine the smaller shapes to demonstrate the constancy of amount

Topic 3 : Causes of failure & Problems of learning Mathematics Mathematics disabilities are: • • • •

the child is having persistent difficulty learning mathematics tends to perform poorly on classroom math assessments compared to the rest of the class. For example, the child may have trouble remembering what the teacher has taught she may have difficulty using effective strategies to solve math problems.

Causes of failure Cognitive

Explanation • •

Level of cognitive ability (maybe it slow & very weak) Brain injury/ disabilities

example Slow-learner

Intervention Teacher has to explain briefly, clear & easy to understand.

Cerebral-palsy Emotional

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Students readiness / emotional and health condition

Bad health condition. So, no mood to study.

Physical

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Depends on their Physical abilities

Blind, deaf or psychomotor problems.

Blind-use Braille Deaf-use sign language

Problems in learning maths among LD students Problems

Explanation

Example

Intervention

Page |4 Visual/ auditory

Perception = pengamatan

Blinds- hard to learn by visual

perception

To use eyesight & hearing to learn

Deaf – hard to learn by audio

Memory

Ability to keep & store knowledge or anything

Students with difficulties to remember information & concept

Ask student to write a note about the important topics.

Language

Difficulties in understanding language & maths concept.

Maths concept : first, last, then, more than, less than & etc.

Teacher uses simple & direct language so that student easy to understand.

Abstract thinking

Ii is hard for LD students to think abstractly.

To imagine something/ concept.

Use concrete materials to teach them before ask them to relate to abstract concept

Readiness of their cognitive to study

Some kids- 5years old already can count

(penaakulan) Metacognitive

Student needs a lot of practices about size, distance and space.

Some kids- 7years old still cannot count Social

Exposure from family & friends. Through TV, daily life activites & etc

Reading

Abilities to read

Family taught them how to count stairs, money and let them go to the market.

Teach them maths by social skills.

How to solve problem if they cannot read?

Teach them thru symbols or concrete materials.

Nadiah binti Abu Bakar Topic 4 : Problem of Learning Mathematics. Styles of learning Mathematics • • •

Stages of cognitive developmental Methods of understanding Information processes

Topic 5 : Strategies in teaching Mathematics

Teaching strategies Exploration

Explanation

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Polya model

Obtaining knowledge for oneself. pushing students to try out their hypotheses, methods, and strategies with processes similar to those that experts use to solve problems Through exploration, learners are encouraged to carry out expert problem-solving processes on their own. Learners become independent of the teacher and begin to apply what experts do regarding forming and testing hypotheses, formulating rules, and gathering information students are forced to make discoveries on their own

4 principles : 1. Understand the problem • What are you asked to find out or show? • Can you draw a picture or diagram to help you understand the problem?

Page |5 • Can you restate the problem in your own words? • Can you work out some numerical examples that would help make the problem more clear? 2. Devise a plan • A partial list of Problem Solving Strategies include: • Guess and check Solve a simpler problem • Make an organized list Experiment • Draw a picture or diagram Act it out • Look for a pattern Work backwards • Make a table Use deduction • Use a variable Change your point of view 3. Carry out the plan • Carrying out the plan is usually easier than devising the plan • Be patient – most problems are not solved quickly nor on the first attempt • If a plan does not work immediately, be persistent • Do not let yourself get discouraged • If one strategy isn’t working, try a different one 4. Look back (reflect) • Does your answer make sense? Did you answer all of the questions? • What did you learn by doing this? • Could you have done this problem another way – maybe even an easier way? Newman Model

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Mastery learning

Teaching students by stages From lower and easy stage to higher and difficult stage Student need to master each stage to continue to next stage. Teacher gives remedial activities to weak students and enrichment activities to the fast learners.

Direct learning

Nadiah binti Abu Bakar Topic 7 : component of teaching mathematics • • • • • • •

Maths content Maths acquisition Evaluation Mastery learning Problem solving Generalization/ conclusion Promoting positive attitude towards maths.

Topic 8 & 9: Assessment of Mathematical Skills

Types of assessment Formal • •

Explanation •

Norm references test Criteria references test

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Norm-referenced tests have standardized, formal procedures for administering, timing and scoring. They have been "normed" or administered to a representative sample of similar age or grade level students so that final test results can be compared to students of similar characteristics. Criterion-referenced tests (CRT) measure what the person is able to do and indicate what skills have been mastered. CRT compare a person's performance

Page |6 with his or her own past performance Informal • Observation • Check list & rating scales • interviews

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Observe while a child is playing usually in his/her natural environment. The observer is able to see the interactions between the child and peers as well as noting speech and language, and motor abilities.

Topic 10 & 11 : Teaching Aids for Mathematics

Teaching aids

Explanation

The importance

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It helps teacher to deliver the lesson in class. It helps students to understand more about the lesson. It makes lesson be more interesting. Encourage and motivated students to be more focus in the lesson It helps students to get engage more actively in class Could use for classroom activities. Easy way to introduce visualize concept Help students to relate real world situation to mathematics symbolism

Types

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Concrete Abstract Portable Visual Audio

Characteristics

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Attractive Colourful Not dangerous Effective Long-lasting Clear Suitable for any kind of students Suitable for the subject easy to handle

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Commercial material – beli Recycle material – buat sendiri guna bhn terbuang Teacher’s made-material

• Categories

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Nadiah binti Abu Bakar

Topic 12 & 13 : FUNCTIONAL MATHEMATICS FOR LD STUDENTS. FUNCTION

EXPLANATION

EXAMPLE

Communication

Use mathematics to communicate in daily life

Go to the market & buy things

Self awareness

Be able to know about basic info about their own self

I/c no, house number, family’s phone number

Page |7 Social

Get connected with other people using mathematics

Change hp number between friends, social interaction in the market/ school

Use of public facilities

Be able to use public facilities without any help

To use public phone, how to pay LRT ticket.

Wealth & health

Be able to learn the monetary skills & their own health

Use money, know body’s temperature, blood pressure, buy & eat medication

Self direction

Know the orientation and direction

Left, right, straight

Recreation

Be able to know what is the best time & place to go recreation

Career

Be able to get job and have their own life

Work at the bank, cashier, sales promoter or etc.

Topic 14 & 15 : Mathematics Syllabus Study OBJECTIVES OF MATHEMATICS CURRICULUM Enable students to: • Understand the concepts of number • Acquire and apply addition, subtraction, multiplication and division skills. • Recognize basic shapes in the surrounding area and their characteristic • Acquire problem solving which involve mathematical operations • Use mathematical knowledge and skills to manage every life effectively and responsibly • Acquire measuring skills and use basic mathematical instruments • Acquire monetary skills in real life • Understand the concept of time. Nadiah binti Abu Bakar