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Methods/ Mathematics

Northern Caribbean University

College of Education and Religion

Department of Education

MTED 201: Primary Mathematics Methods

Factors that influence how children learn

Psychological influences

Professional influences

Technological influences

Language influences

Societal influences

Research influences

Psychological influences:

The essence of this theory is students construct their own understanding of math ideas (by interacting with physical models of these ideas).

Professional influences:

Its emphasis is back to the basics, the 3 R’s were emphasized (reading, writing, and arithmetic).

Technological Influences:

In the math class there should be at least a calculator.

Language influences:

Language is a part of the whole thinking process. Students verbalize, it is used in problem solving, and relationships are formed.

Societal influences:

A number of societal factors influence decisions made by the government in classes, telling what is to be taught.

Research influences:

Research is very important, because it can help us understand what to teach, when, and how to teach. Teachers should keep abreast with journals and visit seminars.

How do students learn mathematics?

Cognitivist/constructivist approach (Mental discipline theory of the 19th century)

Behaviourist

Learning Theories

Research on learning theories impacted how math was (and is) taught. Predominant in the 19th century was mental discipline. (Math is an area where mental discipline can be very effective).

Two theories (in recent times)

Behaviorist

Cognitivist/ Constructivist

Behaviorist

Came to existence in the early part of the 20th century where what was done in the classroom was influenced by Behaviorist psychology.

E.L. Thorndike

Theory of stimulus response replaced mental discipline.

Stimulus response states that learning (only) takes place when a bond is established between some stimulus and a person’s response to the stimulus.

Drills and practices became a major component prominent during the early 20th century.

In the 1960’s a behaviorist named Robert Gagne’s published materials on conditions of learning. For any student there are a variety of learning situations that can be ordered according to the principle of pre-requisite learning. He outlined 7 learning situations students had to go through. They are:

Stimulus response

Simple chaining

Verbal sequences

Multiple discrimination

Concept learning and

Problem solving

(Students should verbalize math concepts promptly and properly.)

One of the major contributions to curriculum development was analyzing the structure of a task or concept to be learnt. What Gagne emphasized was a curriculum-centered approach to learning. Curriculum view, looked at, and then broken down into small stages. He organized a curriculum-centered approach.

Cognitive Theory

Constructivist theory is an addition to the cognitive theory. They consist of 2 major hypothesis.

1. Knowledge is actively constructed by the individual and is not passively received from an outside force.

2. Knowledge is an adoptive process that organized ones world, not the discovery of some independent, pre-existing world outside the mind of the individual.

Characteristics of constructivist/cognitivist Classroom

1. The emphasis would be on students’ autonomy, responsibility and group work.

2. Students spend much time interacting with materials representing math ideas and processes in different ways.

3. Students interact with the teacher. Teacher encourages, nurtures, and provides help.

4. A teacher is responsible for creating an environment where students are motivated to learn.

Jean Piaget

Learning is a change in behavior.

Key concepts:

Schema

Adaptation

Operation

Schema: A cognitive structure that one constructs by putting pieces of knowledge together to make sense.

Adaptation: The process by which the schemas are developed.

Adaptation can take two forms: assimilation and accommodation.

Assimilation occurs when one’s existing cognitive structure requires little modification to include a new idea.

Accommodation occurs when no relevant schema exists and learning occurs or new behavior is developed through experimentation, instruction or both.

Operation: This is the mechanism by which a schema is assimilated or accommodated-internalized action that modifies knowledge.

Developmental stages mentioned by Piaget, (occurs while learning is taking place).

Sensorimotor

Pro operational

Concrete operational

Formal operational

Four factors that affect/influence how rapidly one moves through the developmental stages

The four factors are:

Maturation – organic growth

Experience – physical and psychological experiences an individual has

Social transmission – teaching or the imparting of knowledge

Equilibration – process of bringing conflicting ideas into balance

Implications for teachers

Since most primary students are at concrete operational stage, teacher must provide the kind of concrete operational experiences that will enhance learning.

Piaget’s conservation task provides us with some ingenious methods for assessing readiness for certain concepts.

Piaget’s work can also provide direction for sequencing the curriculum. Children conceive numbers earlier in the concrete operational stage while mass and volume are not conserved until the end of that stage.

Zoltan Dienes

He developed a theory of math learning with the following four steps:

Dynamic

Perceptual variability

Mathematical variability

Constructivity principle

Dynamic is a 3-phase process and the first phase is what Dienes refereed to as preliminary or unstructured play. The activities that the children are involved in are relatively unstructured (first phase).

Structured play or games (second phase)

Explicit representation (third phase)

Perceptual variability: the principal says that learning is facilitated when the children see the concept in a variety of forms.

Mathematical variability: Like the perceptual variability principle mathematical variability principle suggests children be exposed to a variety of variables so that essential ones become evident by there presence in all examples, non examples as well should be used.

Constructivist: This principle suggests that children be allowed to build up or construct their own experiences.

Implications

Dienes' theory, like Piaget’s emphasized the importance of an active learning environment where children are actively involved or engaged with concrete mathematical representations.

Dienes' work makes somewhat more explicit the need for teachers to be aware of individual learning rates and styles.

Van Hieles

Dutch educators who taught math for a number of years and discovered students had difficulty understanding geometry. They saw there are five levels a student must past through.

5 levels

Visualization

Their global appearance and not their property recognize shapes.

Analysis

Here students observe the component parts of figures but are unable to explain relationships.

Informal dedication

Here they are able to deduce the properties of figures and express inter relationships, both within and between figures.

Formal deduction

At this level formal deductive proofs can be created.

Rigor

Different axiomatic systems can be compared rigorously

Expository Method

1. Good expository teaching involves a clear or orderly sequencing of information to be taught.

2. There is usually some teacher-pupil questioning with this approach so that he broad development of the lesson depends on the pupil’s responses.

3. Exposition in the Primary classroom seems most effective when the pupils are organized into interest groups.

4. Careful planning is required. Each stage should be understood before moving on to another.

5. Concrete teaching aids are often used in the initial stages. All teachers’ can find useful ideas.

6. It is essential that questions and answers constitute a dialogue; a pupil’s answer should be carefully analyzed.

7. Even when the answers appear incorrect, exploration initiated by the teacher can lead to decision and proves fruitful to both teacher and student.

An example of this is the addition of sing digit numbers.

Step1

Teacher presents problem of 3 + 4 after suitable motivation introduction.

Step 2

Show how two sets of items can be combined or added.

Step 3

Teacher counts items (, bottle caps) to find the answer 7.

Presentation should deliberately exploit many modes of representation. Verbalize, mode, visual...

Implications

It is a fast and efficient way of giving information.

It is relatively easy to organize and often requires little teacher preparation.

It is possible for the teacher to motivate the class with enthusiastic and lively discussion.

The lesson can be regulated according to pupils responses.

Limitations

Poor expository teaching leads to passive learners.

Retention and transfer of learning may be curtailed.

It doesn’t adequately cater to individual differences.

It can be and is generally teacher dominated rather than child centered approach.

Games

These are procedures that employ skill and chance and usually have a winner. They are usually played between at least two people and instructors made clear. Games are usually played to practice and re-inforce basic skills. They can also be used to introduce new concepts to develop logical thinking and also for problem solving.

Dominos for example can be made from cardboard, dots, fractions, percentages, decimals can be used on. It is very effective for re-inforcing number recognition an association.

Implications

Games are highly motivating.

Pupils enjoy playing games.

They are more likely to generate greater understanding and retention.

They are an active approach to the learner.

Good attitudes to math are fostered through games.

Limitations

Collecting and constructing the materials for the game are time consuming.

Classes encouraged in playing games are likely to be noisy.

A game approach is not suited to all areas of the syllabus.

Guided Discovery

It is defined as a methodology of teaching where the teacher usually presents a series of structured situation(s) to the pupils. The students will try and study to see if they understand the concept. As oppose to exposition students are not told the rules, instead the pupils are more likely to be presented with examples an asked to figure out the generalization. Not all pupils find it easy to discover under all circumstances. It may lead to frustration and lack of interest in activity. To avoid frustration lack of interest you can have cards available with additional cues, this will cause students to discover through the guidelines given by the teacher.

Example:

Square numbers (1, 4, 9, 16, 25, 36, 49...)

Step 1

Give the children squares and ask them how may squares they can make with the pieces they have, this will be equivalent to square numbers.

1st square number = 1 = 1x1

2nd square number = 4 = 2x2

3rd square number = 9 = 3x3

4th square number=16 = 4x4

and so on...

The type of guidance given to students is very important; too much guidance may result in the discovery lesson becoming a teacher exposition lesson.

Implications

It encourages active pupil participation in learning mathematics.

Discovery seems intrinsically satisfying to pupils.

There seem to be more retention and transfer than in exposition.

It can cater to a wide range of abilities.

Limitations

It is time consuming for teacher to organize and for pupils to participate.

Some students may never discover the concept.

It demands a fear amount of expertise from the teacher, it requieres technical expertise (from teacher) to organize and to be able to guide students.

Investigations

Investigation is a form of discovery.

Pupils need to define their own problems set down their procedures and try to solve.

It is critical for pupils to discuss not only the outcomes of the investigation but also the processes (in the investigation).

As oppose to guided discovery where the objectives are clear an investigation often covers a broad area and involve activities that may have more than one correct answer.

Example

Open-ended investigation to note number patterns on a hundred board

Structured investigation e.g., which numbers can or cannot be written as the sum of two consecutive numbers?

9 = 4 and 5can

9 = 2 and 3cannot

10 = 6 and 6 cannot

Short open-ended exercises e.g. write 3 subtraction problems, which have 182 as their answers.

200 – 12 = 182

Features of an investigation

1. initial problem

2. collection of data

3. tabulation and organization of the data

4. making and testing conjectures

5. trying new concepts if first conjectures are wrong

6. attempting to justify

7. generalizing the rule

8. suggesting new or related problems

Implications

Suitable for mixed ability groups.

Promotes creatively.

Can be intrinsically satisfying to pupils.

Limitations

It requires a high degree of teacher confidence in the subject.

Can be difficult to fit into the conventional mathematics syllabus.

Can be time consuming.

Assessment

Projects

Discussion

Laboratory approach

Children play with and or manipulate concrete objects in structured situations.

Its purpose is to build readiness for the development of more abstract concepts quite apart from building practicing skills and problem solving. It is usually combined with the guided discovery approach.

Example

A teacher gives out cardboard cut out of geometric concepts and let students make pattern with shapes.

Activity and experimentation leads to thinking and communication that then leads to acquisation of skills and reinforcement.

This approach is supported by a number of math educators and theorists (Piaget).

Implications

It has the support of theorists.

In an organized situation pupils are able to proceed at their own rate.

Pupils develop their own spirit of inquiry.

It is especially used for younger children and slow learners

Limitations

Requires a good supply of materials and suitably designed classrooms

Demands a fare amount of teacher preparation and creativity.

Simulations

Simulation is a reconstruction of a situation or series of events, which may happen in any community. Usually the reconstruction of a situation is modified to fit the needs and abilities of the situation. Simulations require each student to make decisions, which are based on previous training and available information. In some ways simulations are really sophisticated games, e.g. monopoly

Example

Having a bank in the class, the skills of budgeting, computation and much more are learned from something like this.

Implications

Related to pupils own experiences and thus motivating.

An active approach to learning.

It develops new news functions for both teachers and students

It fosters co-operation amongst students

It relates math to real life situations

Limitations

The simulations are similar to games so they are time consuming to construct, not applicable to all topics and liable to create a lot of noise.

The Math Text book

The Math textbook is a major factor in determining what topics are taught and how they are taught. The textbook is a powerful means of determining whether new topics are brought into the school or whether the old mathematics is maintained. The Math curriculum should not be determined by the text; rather the test should be determined by prior decision making.

Contributions of a good math test:

1: It provides most but not all of the content for a course.

2. It presents topics in a manner that builds understanding of concepts, structure problem solving and computation.

3. It provides the exercises, the experiences, the directions for attaining mastery to practice review and application.

4. It provides a means for independent study.

5. It provides a means for making provision for individual differences.

6. It provides a compact reference book

7. It provides a basis for achievement testing.

8. It forms a basis for classroom instruction.

9. It brings directly to the student the exposition of the writer(s).

Qualities of a good math textbook

A good math textbook will have topics that:

Obtain the objectives

Allow selections to fit the sequence

Are in appropriate terms of interests, difficulty, and usefulness

Are in harmony wit h current curriculum interest

Mathematics

Structure of each topic is clear an concise

Level of rigor and precision is appropriate for the course

Use of symbols is correct but reasonable, accurate, and not overly cumbersome

Language

Narrative is readable and comprehensible

Abstractions and symbols are made meaningful

Language is interesting and thought provoking

Definitions and explanation are those that the students could understand

Pedagodgy

Material is included to create interest and motivate learning

To make it possible to meet the needs of different levels of ability

Strategies used are based on sound learning principles

Concepts are introduced by providing an opportunity for the student to discover ideas through reflective thinking, problem solving, experimentation analogies and generalization

Test for the evaluation of achievement by students and teacher(s) are included.

Mastery

Exercise emphasize reflective thinking and problem solving as well as straight toward manipulation

Adequate exercises of different difficulty levels are included

Review and remedial materials are included

Some exercise require the student to generalize

Enrichment-additional work

Enrichment topics are included

Suggestions are given for independent study

Research topics, projects, and independent experiment are suggested

References for enrichment reading are included.

Aids to learning

A teacher’s manual with suggestions for teaching

An answer key with worked solutions

Achievement test s

Overhead projectors

Accompanying workbook, laboratory manuals, audio tapes, and impute supplements.

Variability is important

Mastery is or should be exercised and emphasized reflective thinking and problem solving as well.

The following suggestions are given for the proper use of a textbook for a typical math class:

1. A selection of topics to be taught should be made from the test.

2. The text should be used as a resource and reference book (rather than repeating the text to the class).

3. Students as well as teachers use the text.

Dangers of textbook teaching

Many teachers are strictly textbook teachers; they are more concerned to "cover" the text than to "uncover" ideas. Their focus is on the text rather than on the learner. The content of the test becomes the content of the course. With the textbook there is the tendency to emphasise given rules and procedures defeats the possibilities for discovery, independent thought, and intelligent curiosity. The constant use of the textbooks kills interest by its monotonous, formal treatment. Learning needs a variety of meaningful, interesting experiences. The blind regimentation of textbook teaching loses the slow learner and bores the rapid learner. The narrow emphasis on the text ignores the importance of objectives such as attitudes and values.

Remedial Math

This is course prescribed for low achievers.

It is unlikely a student will learn in one year what he or she has not been able to learn in 6-8 years.

Frustration will continue, hostility will increase, and improvement will be degile.

Puzzles, contents, games and outdoor activity can improve computation skills of the slow learner.

A child needs enrichment and remediation when:

He or she returns to school after absence

He or she has faulty work ha bits

He or she developed ineffective math skills.

Problem solving

Students must be made aware of the different strategies of problem solving. According to Charles and Lester in 1982 problem solving of mathematical problem is a task to which the person confronting the problem wants or needs to find a solution. The person has no readily available procedure. The person must make an attempt to find the solution.

The problem should be made interesting thus motivating the student to solve it.

Problem solving begins with a task, which the pupils understand and are willing to encourage in, but which they have no immediate solution for. Problem solving is associated with development and learning ways to tackle and solve problems. It makes use of mathematical processes, which enables pupils to develop insight and sometimes new procedures. It involves exploration discovery and analysis. Problem solving therefore refers to the process of tackling a problem to try solving it.

Two kinds of mathematical problem solving are:

Applied mathematical problem solving

Purely mathematical problem solving

Applied mathematical problem solving is the process of attempting to solve problems in which the situation and questions defining the problem relate closely to some phenomenon in the real world and which may be solved by application of certain mathematical concepts and results.

Example

What is the geometric shape, which best describes the shape of the school garden?

Purely mathematical problem solving involves the process of attempting to solve problems in which the defining situation is entirely embedded in mathematical terminologies and operation.

Example

A rectangle is 15m long and has a perimeter of 54m find the width of the perimeter.

2L +2W = P

2W = P – 2LW = P-L

2

Problem Solving Situations

To define problem solving we need to classify the various types of problems that are encountered in the elementary curriculum. Problem solving is a process of how we are going to tackle a problem.

There are 6 basic types of problems:

1. Computational or drill problems

2. Simple translation problems

3. Complex translation problems

4. Applied problems

5. Process problems

6. Puzzle problems

Computational or drill

In this situation both speed and accuracy are important. Often the purpose of this type of exercise is to reinforce and practice procedures.

Simple translation

These are problems that usually include one step routine, verbal problems found in textbooks.

Complex

After Susan finished packing 10 books into each of 5 boxes, she weighed one of the boxes to determine postal weight. She determined it would cost her $2.35 per package, how much change would she get from a $20.00 bill.

Applied

These are much more complexed than the one step or multi-step verbal problems and have some type of application.

Example

How much water is used in your school over a period of a year? Could some of this be conserved how much money would be saved.

Some skills that would come out of such a problem are statistics, graphing, scale drawing, observation, measurement, estimation, and computation.

Process

In a process problem the students have no previously learnt procedure that can be applied for a quick solution.

Example

Finding the number of squares on a checker board.

Puzzle

The solution of these problems often involves looking at a problem in an unusual way. These are not always math problems. Solving one may not necessarily help you to solve others.

The Problem Solving Process

George Po’ly

There are four-phases to his process of solving a problem. The phases are as follows:

1. Be knowledgeable of the problem, understand the problem or get to know the problem.

Possible questions you may w ant to ask students are: Do you know what the goal of the problem is? Is enough information given in the problem? Can you restate the problem?

2. Devise some type of plan.

Things you would do when devising a plan: guest, trial and error, use a variable, look for a plan, make a list, solve a simpler problem etc.

3. Carry out the plan.

Implement the strategies you have chosen until the problem is solved or until a new course of action is suggested. Give yourself a reasonable amount of time in which to solve the problem. Do not be afraid of starting over.

4. Looking backward

Does your answer satisfy the statement of the problem? Can you see an easier solution?

Problem solving strategies

Dramatise or model the situation.

Example

Class reunion problem, 12 people came to celebrate the 10th university after their graduation each person shake hands with all the other persons how many handshakes were exchanged? 66 handshakes were exchanged.

Draw a picture

Construct a table or chart

Find a pattern

Solving a simpler problem

Guess and Check

Working backwards

Consider all the possibilities

Logical reasoning

Change your point of view

Write an open sentence

Problem Posing

The whole matter of problem posing is different from problem writing. Problem posing usually refers to the process of changing an existent problem into a new one by modifying the knowns, unknowns or the restrictions placed on the answer. There are four principles for guiding to engage in problem posing. They are:

1. Have students learn to focus their attention on known, unknown and restrictions. They could ask questions to themselves what I different things wee know and unknown? What if the restrictions were changed?

2. Begin in comfortable mathematical territory.

3. Encourage students to use ambiguity to create new questions and problems.

4. Teach the idea of domain from the earliest grades encouraging children "to play the same mathematical game with a different set of pieces".

Assessment

Assessment is a broad term defined as a process for obtaining information that is used for making decisions about student’s curriculum or programs and educational policies. According to Nitko, to assess a student’s competence implies collecting information to help decide the degree to which the student has achieved the clearing targets.

According to Payne, assessment concerns itself with the totality of the educational setting and is a more inclusive term that is it subsumes measurement and evaluation.

According to Cronback assessment has 3 principle features:

1. It uses a variety of techniques

2. It relies on observation in structured and unstructured situations.

3. Assessment relies on the integration of information.

Evaluation

The process of making a valid judgement of a students performance or product of such. The data used to make evaluations may be qualitative or quantities or both.

There are two types of evaluation,

Summative and

Formative

Summative evaluation is the testing of the final product of learning, e.g. final examination.

Formative evaluation takes place before and during the learning process. It includes test on pre-requisite skills to determine if review work is necessary. It includes observation on students learning to note what success and failures they are experiencing. By noting students weakness and difficulties teaches can design relevant learning activities and ask pertinent guiding questions that will help students correct their errors.

Formative evaluation is more effective.

Evaluating the Mathematics Program

The evaluation of a math program should consider goals, objectives and content. Additionally an evaluation of the math program also needs to address the mode of instruction and the setting in which it occurs.

Assessing students progress

To assess a student the first thing to use is

1. Achievement test

2 categories of achievement test are:

a. Teacher made, to measure knowledge of specific objectives.

b. Standardised test, which measure students' level of performance compared with other students.

2. Performance test students can use their ability, skills they have learned. This may include an elaborate problem solving activity or a simple task.

3. Diagnostic test (observation and interview, effective way of using these test).

4. You can evaluate student’s daily work. Keep a sample of the student’s daily work

5. Observation of the student’s

6. Interviews with child and or parent or guardian. Can be planned at times but most times should be spontaneous.

Assessing attitudes towards mathematics

Success in math is often correlated positively with favourable attitudes to mathematics.

· You can have a like heart attitude scale.

Scale – In this scale the students' would respond to statements such as "I am happier in Math than in any other class."

· Semantic differential approach. This consists of devising pairs of antonyms. The student marks a point on a 7-point scale to indicate which word most closely represents his or her feeling towards mathematics.

EASY . . . . . . . HARD

· Sentence completion. Give them a beginning of a sentence and ask them to complete it. E.g. Math is important because...

· Daily routine observation. These skills yield important insights to the child’s attitude toward mathematics. E.g. Half muttered statements, level of enthusiasm and other behaviours are indications of students' likes and dislikes towards mathematics.

The evaluation process consists of:

Evaluation

Recording and

Reporting

Recording – Children’s Progress

During the evaluation process information gathered has to be organized, and then recorded and stored in a way of easy access to the teacher. The teacher could have a personal math folder for each student with anecdotal records, check sheets from diagnostic interviews, teacher’s observation, test results, samples of daily work etc. Have a notebook with a page for each student or standard grade book.

Reporting – Children’s Progress

Parents and teachers should communicate about children’s growth and progress. Parents should be invited to teach class, to observe daily routine or just for math class. Teaching math requires hard work. A teacher what you need to do is create and help students rate for themselves representation of mathematical roles that will enable them to build significant mathematical knowledge.

How to achieve this

1. You must be knowledgeable of how children learn mathematics.

2. You must be familiar of math included in the curriculum.

3. You must be able to design strategies and activities that would help students learn concepts meaningfully.

4. Be able to assess the level of development of concepts in children.

Managing the mathematics classroom

You should have a number of equipment. Facilities to assist the teacher should be present.

Math classroom of the present

The first requirement for a math department is a well-trained, balanced and dedicated staff (necessary condition for quality teacher).

Classroom facilities

The classroom should be stimulating, comfortable rooms in which teacher an students will enjoy working. It should be equipped and pleasant.

Adequate light, acoustics, comfortable temperature and ventilation, adequate space and furniture suitable for the activities in the mathematics classroom should be present as in an efficient lab or office. The equipment must be appropriate, adequate and properly located.

Materials and tools needed should be readily available so the teacher could put them to use with ease and convenience and with a minimum of distraction.

The math classroom is to meet the needs of a modern instructional classroom. Provisions should be made for carrying out activities such as group work, lab exercises, etc.

To meet the major problems of modern math instruction a mere rectangular space with black board and fixed desk is out of date. The modern classroom must have plenty of space that provides for a variety of seating arrangement, adequate instructional materials an the equipment and facilities necessary for a variety of activities.

Class equipment

After classroom space has been provided it should be properly equipped.

Sufficient desk, files and seating for the teacher. Proper tables and seating for student equipment for demonstration, facilities for displays, exhibits and books. Storage space for classroom materials and students and teachers materials, books, and miscellaneous equipment. Both student and teacher should be provided with a desk that has enough writing space. Every math classroom should be in possession of a screen for projection, walls, chalkboards, bulleting boards, books, pamphlets, models and charts which should be constantly on display.

In managing the math class we need to think about special rooms. Whenever possible provisions should be made for special rooms. An example of this is a room that is designated as the teachers work area, where materials and conferences with students are kept, papers are marked, and lessons are written, a room can be set aside as a work room.

Scheduling the day of the fixed time schedule is becoming as much a part of the past as the traditional curriculum of the last century. Mathematics teachers must asses their teaching programs in order to determine schedules that make their teaching programs in order to determine schedules that make optimum use of the facilities and best serve the students. A number of schools have adopted what we call ‘flexible scheduling', which provide for class periods of varying lengths.

Team Teaching

Team teaching is where two or more teachers who combine their talents and resources to develop a joint instructional programs.

Advantages are:

There is co-operation in planning and material development. A certain amount of freedom is present allowing more individual attention for students. The teacher’s time is saved. Interaction between teachers is evident.

Disadvantages are:

Some persons ‘goof off’ and it takes a bit of pre-planning.

Calculators

The use of calculators ensures that the experiences in math matches reality, development of reasoning skills, promote understanding and application of math. The calculator is an essential tool for all students in math. It extends understanding, enhances students learning in math. Cognitive gain in number sense, conceptual development and visualisation can empower and motivate students to engage in true mathematical problem solving. Math ideas and experiences that go beyond these levels limited by traditional paper-pencil computation. It develops and reinforces skills such as estimation, computation, graphing and analysing data. The N.C.T.M. suggests that calculators should be used at all grade levels despite of support and easy access, calculators are not being used efficiently in classrooms. They also have the fear that child will become dependent, however primary school research says this is not so.

It is used to check answers, test-teach estimation. Children enjoy them and they can be used effectively for instructor. They should be used in all elementary classrooms. Calculators have been used extensively in home and offices. Tests that are written now permit the use of the calculator.

(The math forum is an essential tool whose responsibility is to ensure students are able to use them effectively.)

The negative effects of calculators are largely due to inappropriate use of instruments (and more).

Planning

Planning i9s a basic requirement for success. Planning should always be done, it helps for the smooth running or things. The successful math teacher must take time to plan units, lessons, exams, etc. Having a written plan may not be necessary after a teacher is 'seasoned', but some planning is still needed. At the beginning of the year the teacher needs to organise the entire years work in order to examine learning. It has been found that teachers who plan for the entire year are more at a faster pace, include more content, produce higher student achievement in comparison to teachers who start at the beginning of the book and proceed throughout the year without planning.

Yearly plan

Factors to consider when making yearly plan are:

Content

Time

Pacing

Grouping

Activities

Schools will design their own courses, make their own plans to meet the needs of specific groups. Every teacher has a responsibility to think carefully about overall design of the courses he or she teaches. Planning should not allow you to exclude certain topics. A yearly plan has foundation, syllabus provided by Ministry of Education. A teacher should utilise book with good principles, and make careful selection of text. The most important variable accounting for student achievement is the opportunity to learn a particular topic. Another consideration of the yearly plan in the structure of the class; when you plan consideration should be taken for individual/whole class instruction.

Unit Plan

In addition to the yearly plan, the teacher will need to plan for individual topics.

Purpose- for unit plans (aims)

Pre-requisite skills

Developing a new topic

Practising mastery of new topic

Review of previously studied topic

Story problem/application

Problem solving

Enrichment

Evaluating students progress

No lesson in itself will ensure success. It is the way the lesson is carried out that is important. Responses to unexpected questions, sensitivity to students' reaction are keys to success. The lesson must be practical.

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