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Teaching Strategies

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Teaching Strategies
Objectives give us a guide on what is to be achieved in the classroom. But even after stating the objectives clearly, we have to deal with the next step on how to achieve our stated objectives. The ability to engage students into purposeful or reflective thought about the ideas that we want them to develop is the single most important key to effective teaching. Without thinking about the important concepts of the lesson, learning will not happen. The following are some suggestions which the teacher can use alongside the strategy/method that they intend to adopt.

Create a mathematical environment - students need to feel comfortable trying out ideas, sharing insights, challenging others, seeking advise, from other students and from the teacher.
Pose worthwhile mathematical tasks - posing questions that create curiosity among the students, making mathematics problematic so that students get involved in seeking solutions, finding out which methods work, challenging the thought of others and generally engaging in reflective thought about ideas.
Use cooperative learning groups – working in groups is helpful in encouraging the discourse and interaction envisioned in a mathematical community.
Use calculators and models as thinking tools – models help students to explore ideas and make sense of them. Manipulatives and calculators should be part of the classroom environment to be accesesed by students who may need them.
Encourage discourse and writing – to explain ideas clarifies and enhances ownership as students search for connections to use to justify an explation in an argument.
Require justification of students responses – requiring students to justify their responses develops confidence and self-worth and a positive effect on how students view mathematics.
Listen actively – when teaching is made child-centred and not teacher-centred then attention must shift towards the way students think for the purpose of strengthening more internal connections. It helps in developing understanding. 

Definition; A strategy for teaching mathematics is therefore a combination of decisions a mathematics teacher makes in order to achieve a stated instructional objective.

Components of a strategy for teaching ;
Methods of teaching
Methods or techniques of teaching need to be considered when a plan is being devised . Methods of teaching are techniques or acts intended to achieve a certain end. These acts range from teacher-centred expository approach to discovery method which is mainly leaner centred. The choice of suitable method depends on the nature of the objective and on the kind of students we have to teach.
             2, Background of the learners 
                 The teacher will have to consider when preparing for a strategy
The age of the learners – the age of the learner will influence the kind of strategy a teacher wants to utilise. A yonger leaner e,g 14 yr old will require less listening but more participation. That is, they are best taught by using strategies where leaner participation is high. On the other hand more mature leaners e.g 18 yr old are likely to withstand expository teaching longer than the younger ones. 
The ability of the learner- a class of less able mathematics students will demand a teaching strategydifferent from one used with a more able class.
The learners knowledge of the content – where learners possess adequate previous mathematical knowledge necessary for successfully teaching of that topic the strategy adopted will be different from that of the leaners with very little background knowledge.
For example if the students are being taught “solution of simultaneous equations by the use of inverse matrix method” the learners who have little background knowledge of i) identity matrix
                          ii)determinant of a matrix and
                         iii)inverse matrix
will require different strategy for successful teaching of this topic compared with learners who already posses this knowledge.
Deductive and inductive approach – inductive approach is where in the process of teaching we begin from known to unknown. That is, begi by giving examples which are familiar to the students then lead them to a generalization. On the other hand deductive approach the rule is stated first then examples based on that rule are given. (See the hand out) 
Teaching Strategies and Methods
It is important for teachers to be aware of the available strategies and methods for purposes of making a suitable choice when it comes to instruction.
A strategy can be defined as the overall way in which the process of instruction is organized and executed. The two main strategies include expository and heuristic strategy to teaching. The two strategies can be considered to form extremes of the major forms of classroom. This picture is represented on a line often referred to as continuum as shown below.

The line below represents various methods that run from expository on one hand to heuristic on the other end with intermediary methods in between.
Strategy: expository----------------------------intermediary-------------------------------------heuristic
Method: lecture      dictation                  demonstration               discussion        field    project/problem
                                 of notes                                                                                 work          solving                                             
Expository is teacher-centered while Heuristic is leaner-centered.
Table: Strategies and some of the characteristics

Expository; ”talk and chalk”
Heuristic (discover) dialogue and inquiry

Transfer of information
Development of individual potential

Nature of learning
Surface learning/Rote learning/Memorization
Deep learning/ self direct learning

Teacher’s role
Authoritative: “All knowing expert”
Facilitator, developer

Teacher activity
Telling, asking questions, correcting, etc
Guiding, providing resourses, etc

Student activity
Listening, note taking, asking questions etc
Exploring, reflecting,questioning, etc


Lecture, dictation, demonstration, etc

Discissions, self directed projects, problem-solving, etc

Expository constitutes a high proportion of our teaching strategy.
Expository by the teacher also becomes an indispensable strategy especially when a topic is being introduced or some difficulty area is to be explained.
Expository is efficientin covering a wide area of content- an advantage of expository teaching.
It has certain draw backs which if not checked can result in ineffective teaching.

A brief summary of the commonly used methods
Lecture method
In lecture method the teachers exposition is central in classroom communication. It is most appropriate when a teacher is introducing a topic or a new idea which necessitates learners principally listening to the teacher’s exposition. It by no means implies that learners should only play the role of the listener. However, by involving the leaners such as through questioning or doing something, lecturing can be made much more interesting. Utilization of teaching aids can make the use of this method even more interesting.
Example; Derivation of quadratic formular.
As the teacher goes from one step to the other it is important that they explain slowly and obtain continual feedback from the learners because it is through questioning that we can know whether or not the students are following
  e.g   ax2  + bx + c = 0……………………step I
          x2 +  x +  =     …………………step II        etc
Discuss some of the advantages and disadvantages of lecture method in teaching and learning of mathematics.
Discovery method
      3.   Discussion method--- quite helpful in mathematics
       4. Field trip
How would a mathematics teacher use field trip in the teaching and learning of mathematics.

 Resources in teaching mathematics
The use of instructional aid or instructional materials or resources is an indispensable component in the teaching learning process. This lesson will focus on the importance of resources and their role in providing an image or representation of concepts in mathematics. During the lesson various types of resources will be discussed.
  Definition: A resource is something relied on for support, help or consolation. Resources in education are used to support and/or facilitate learning. They establish learning conditions.
Role of resource in mathematics lesson
 The role of resource in mathematics is very critical. Every topic in mathematics can be physically explained by use of appropriate resources. In using a formal lecture method, where students have to listen throughout the lesson, there is very low retentivity. However where teaching incorporates some aspects of seeing or doing as well, the students are likely to remember more of what they are taught. When learners are involved in some activities in the classroom the learning becomes an unforgatable experience. Not forgetting that mathematics is an abstract subjectwhich presents relatively more problems to our students compared with the other subjects. Resources are crical in mathematics teaching for they bridge the gap between abstract and the concrete. 
Range of instructional aids
These include;-
Commercially produced material
 Materials locally available within the environment
Materials which we could make ourselves with or without the help of the students
Materials borrowed from other institutions
   So an “aid” or resource does not have to be commercially sophisticated material. A discarded bottle tops or tincan effectively aid in the learning of mathematics. Many student-teacher take the chalk board for granted such that they hardly ever think of it as an aid. As a matter of fact the chalk board is the most important teaching aid at the disposal of the classroom teacher. The chalk board is particularly important to the mathematics teacher because relatively, we teachers of mathematics ues the chalkboard far more than other teachers.
Types of teaching and learning resources for mathematics classrooms
Manipulative objects such as manila cut-outs, geometrical instruments, graph-papers, models of solids etc
Own bodies such as figures
Environmental such as urban structures, trees, field trips etc
Print media such as mathematics textbooks, newspapers, magazines, journals etc
Audiovisual instructional aid: helps the learner to learn by utilizing senses of sight and hearing. These include resourses such as textbook, television, computer videos, computer graphics, calculators, charts etc
The teacher or a visiting professional. 

Role of resources in mathematics classroom
The following are some opportunities that students will experience as a result of interacting with relevant resources.
Higher retention of learned concepts: by verbalising their thoughts through discussions and reporting.
Creativity: intellectual and imaginative
Equity: activities which involve all learners.
Interest and motivation: inquiry / analytical mind
A positive attitude towards mathematics

All these are possible  i) if opportunities are possible and
                                  ii) if the resources are effectively used

Effective use of resources
To effectively use resources, it is important that the teachers;
Use the resource for specific instructional objectives.
Be familiar with the material or device prior to using it with the students.
Prepare the students
Use the material correctly. The activities should be simple enough to encourage slow learners and be able to challenge fast learners.
Conduct a follow up to:- clarify confusing points, dicuss interesting points, point out subtle points that may have been missed and correct misconceptions.

When planning to use the resource it is important to consider the following utilization factors;
Level of sophistication
Technical quality
Cost factors
Time and storage

Some of the commonly used teaching aid
Chalk board- this is by far the the most popular and readily available teaching aid. In some cases it is the only teaching aid available to the teacher. Om the whole mathematics teachers use chalkboards more than any other subject teachers. A mathematics teacher cannot do without a chalk board. Hence the need to utilize it effectively.
The chalkboard is the kind of mirror which reflects what kind of teacher we are. In fact, the manner we use the chalk board can either enhance or depress learning. If we use it poorly the students in the class will perceive us as confused, lazy, disorganised and unprepared. If we make careless scribbling on the chalkboard we should similarly expect careless scribbling by students in their mathematics exercise books and we should not complain later that they are careless. On the other hand a well organised teacher will be reflected through his chalkboard work and students work is likely to be neat too. When a teacher logically presents a worked out problem on the chalkboard, the students will equally acquire the habit of logical presentation of work in their exercise books.
Therefore, when using the chalkboard the 
Writing should be clear and large (cos classrooms are already large)
Coloured chalk should be used to provide contrast-it is appealing and catches learners attention
Chalkboard should be printed where applicable
Textbooks- is the most common instructional aid in teachind and learning mathematics. Today mathematics books are a major factor in determining what topics are taught and how they are taught. At times the text book together with the chalkboard might constitute the only teaching aids at our disposal. Therefore how can we ensure that we make the text book an effective teaching aid? The following is the list of the role of the text book in class or attributes or quality which a useful textbook should posses.
The textbook should contain most of the content for the course since like in any other subject the textbook is used a great deal in classroom. Therefore it should contain most of the topics that are intended to be covered. A book which contain only part of the content to be covered is unlikely to be useful.
Topics should be well presented in a logical manner, so that it can be used to build up students understanding. The textbook should present the content clearly and logically.
The textbook should contain ample exercises to help in mastery of the skills since learning mathematics depends on mastery of concepts and skills which are established through practice.
Useful for independent study—a textbook which is well written and is to serve as an aid in teaching should have the topics well sequenced and simplified to enable the students to work independently of the teacher.
Useful as reference book—visual aids and classroom instruction cannot provide all instruction necessary. There is need for reference to cover some of the instructions from the textbook. Hence a good and useful textbook should contain the entire content for the particular class and even more for it to serve as  reference book.
Useful for planning –textbooks assist teachers in writing their daily lesson plans and schemes of work.
A good textbook provides a sequential approach to teaching.
The teacher-made teaching aids
These include ;
The chart—this should only be made if its usefulness will exceed what we could do on a chalkboard or if it supplements what we are doing using the chalkboard. It serves very little purpose to draw a graph on a manila sheet or even that of threedimensional object if the chalkboard is available or if it’s already drawn on the chalkboard.
However on those occasions when the chart has to be made the following points should be noted when making a chart;
It should be of suitable size. This is because  a large chat, clearly visible to all students sitting at different places in the classroom is suitable.
ii) It should be appealing to the students. A well made chart besides its usefulness as an aid in learning should be attractively done and appealing to the students so that it catches their attention. So whether a graph or a bar chart etc variation of colours should be taken into consideration to make it nice and attractive.
Much writing should not be allowed on the chart. Too much writing distracts student’s  attention and they end up concentrating on what is written on a chart instead of focusing on the important features. 
A chart should be used so as to motivate the students as they observe the features on the chart.
One of the reasons for making teaching aid is to bridge the gap between what is abstract and a concrete situation which resembles it. The degree of abstractness varies from topic to topic in subject like mathematics. For example a topic such as “three dimensional geometry” is a typical kind of subject which usually gives learners problems unless appropriate aids are used. This is because visualizing planes, intersection of lines, intersection of plane with a line, angles etc present students with awful difficulties in imagining what goes on without concrete objects physically before them to help in visualization. So in such a topic there is need to prepare solid objects which will be helpful in enhancing student’s learning.
Motion projectors 
Developing countries face serious financial constraits to the extent that modern technological products such as a movie projectors and television are rare to come byexcept in a few high cost schools. However when these products are available they can contribute a lot in making learning interesting and enjoyable. The very presence of these gadgets produces a lot of enthusiasm and excitement. Whenever they are available they should be utilized in order to motivate students and facilitate learning.    
The environment- as a source of teaching aid
   There is need to accept the fact that it is impossible for a teacher to expect conditions where many teaching aids will be constantly available. Financial constraints as well as heavy teaching loads makes it difficult for a teacher to fully meet their objective of obtaining self-sufficiency teaching aids. However a conscientious teacher must be aware of the richness of environment in terms of availability of teaching aids.
For instance, one can collect discarded tins, empty boxes, bottle tops etc which may turn out to be useful aids when teaching. For example in teaching probability one can use bottle tops, marbles etc.
It is our inventiveness as well as our enthusiasm which will make us utilise the surrounding environment properly.
Printed materials as teaching aid
A part from the text book there are other printed materials whose collection may turn out to be of invaluable help. News papers and other periodicals contain diagrams and charts which are relevant in teaching mathematics.
For example in teaching statistics-news paper are full of bar charts, circle graphs etc about daily life information concerning our population. The bar chart may illustrate export and import of various items. This kind of aids bring mathematics closer to the real life experiences of the learners
When students see for themselves annual government expenditure illustrated in form of circle graph they will not only see the relevance of such methods of representing statistical information, their understanding of mathematics will also be broadened. This too will motivate the students.
Use of calculators in mathematics classroom
the use of calculators in slass eases the computation. However students who are exposed to the use of calculators sometimes end up demonstrating very low competence in calculation. They may end up pressing buttons without the slightest idea of the mathematical process involved (i.e they let the calculators think for them).

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