Teaching Math

TEACHING MATHEMATICS

David Ali

February 2012

1David Ali February 2012

Objectives

• Identify major approaches to teaching and learning

• Discuss basic strategies used in the teaching / learning process in primary and secondary schools.

• Identify the strengths and limitations of the strategies discussed.


Deductive Approach

• Teacher – directed

• Teacher gives basic ideas, concepts at the start.

• Teacher gives examples to illustrate concept.

• Involves students at the end.


Inductive Approach

• Student – centred

• Students engage in activities to develop concept / ideas / formulae principles.

• Students derive the rules, definitions etc. out of the activities they did.


Lecture/Presentation/ Expository Teaching

• Teacher – directed• Teacher gives and explains information• Much of classroom time is devoted to

presenting and explaining information.• Exists to a lesser extent in lower classes. Why?


Lecture/ Presentation/Expository Teaching (continued)

Strengths:• A lot of information can be given, In a short

space of time.• Teacher can control pace, content, sequencing

and organization of material.• Same information is given to all – common

frame of reference.


Lecture/ Presentation/Expository Teaching (continued)

Limitations:• Individual differences not considered• Little or no student participation• Difficult to determine amount of student

learning • Rarely involves the affective and psychomotor

domains.


Demonstration/ Direct Instruction

• Teacher – directed• Teacher demonstrates skills to students• Students observe and imitate teacher• Linked to social learning theory • Effective way to acquire basic information and

skills.• Practical subjects are best taught through

demonstrations.


Demonstration/ Direct Instruction (continued)

Concerns:• Emphasis on teacher talk • Does not cater to higher level objectives e.g.

originality and creativity


Cooperative Learning

• Student – centred• Work together to complete common task• Each student has a specific responsibility• Responsible for own learning as well as others• Social skills – communication, respect for

others• Group score


Cooperative learning (continued)

Concerns:• Requires careful monitoring to ensure

objectives are met.• Be aware of group dynamics


Problem Based Instruction (continued)

• Student – centred• Focus on an authentic / real life problems• Investigation and inquiry skills• Fosters self – regulated learning• Social and intellectual benefits.



• Rests heavily on the concepts of constructivism

• Students explore, investigate and construct their own knowledge and meaning

• Piaget, Vygotsky and Bruner – theories linked to constructivist approach.



• Concerns:• Most schools lack organizational structures for

Problem Based Instruction (UTT?)• Adequate library and technological resources

for research and inquiry?• Standard 30/40 min. period does not support

Problem Based Instruction


Discovery Learning J.Bruner

• Student - centred • Students discover rules, formulae, principles –

guided by teacher.• Deeper understanding by students• Meaningful learning


Eclectic Approach

• Use a variety of strategies in classroom• A judicious mix depending on learning goals

and objectives• Both teacher – directed and student –

centered strategies can be used effectively.


References

1. Arends, R.I. (1998) Learning to Teach.

Boston. McGraw-Hill

2. Burden, P. Byrd, D. (1999) Methods for Effective Teaching. 2nd Ed.

Boston, Allyn and Bacon

3. Orlich, D. Harder, R. (1998). Teaching Strategies: A Guide to Better Instruction.

NY. Houghton Mifflin Co.17David Ali February 2012

Teachers and Attitudes

By their personality and character they are able to command the respect of their pupils Show respect for studentsShow genuine interest in students and what they think and sayDevelop a quiet calm relaxed attitude combined with firmness and a sense of purposeHave knowledge of the pupils individuallySensitive to the needs and differences of studentsRespecting contributions from all students


Instructional Strategies

Deductive

Starts with a known principle and moves to the unknown

Inductive Starts with an unknown principle and moves to a known


Instructional StrategiesChild-Centered

Acknowledges that children needs should determine what they learn at school Recognize and respond to the changing charactereristics that distinguish children of different age.Train children in skills that are written the capabilities of their stage of development.Select what is taught and the methods used so that they are appropriate to the comprehension and experience of the children.Utilized the strong motivational forces that control so much of children’s national learning.Apply knowledge of child psychology and child development to the content and methods of learning.


Teacher Centered EducationTeacher’s act as essential links between the child and what he is learning.Teacher’s select what the children learn, the methods by which they learn and the pace at which they learn.Teacher’s see their role as communicating, knowledge to their pupils efficiently as possible.Teacher’s spend most of their time actually teaching.Pupils get the impression they can learn only when their teacher is present and teaching.Pupils tend to be regarded as more or less uniform groups of learners rather than as individuals with different gifts and needs.


ProjectsGains practical knowledge and sense of cooperation that exists among peopleTeacher guides the children as they find need for help Children identify problem and solutionResponsibility is placed on the pupils and give scope for their initiativeLeadership qualities emerge from childrenSustain motivation through the natural enthusiasm they generate


Co-operative Learning

Allowing students to work on tasks that require co-operation


Resource Based Learning

A system of learning that depends on resources rather than teachersIndividual pupils progress at there own pace and learn independently Resources as applied to education include any media or materials that help learningBooks audio visual aids software and hardware of educational technology people and materials


References

1. Burden,P. & Byrd,D. (1999) Methods for Effective Teaching-2nd Ed. Boston, Allyn and Bacon

2. Evertson, C., Emmer, E.T. & Worsham, M. (2000) Classroom Management For Elementary Teachers-5th Ed. Boston, Allyn and Bacon

3. Kellough, R. & Roberts,P (1991) A Resource Guide for Elementary School Teaching: Planning for Competence 2nd Ed. NY. Macmillan Publishing Company

4. Orlich, D. Harder, R. Callahan, R. & Gibson, H. (1998) Teaching Strategies: A Guide to Better Instruction NY. Houghton Mifflin Company

5. Sotto, E. (1994) When Teaching Becomes Learning A Theory and Practice of Teaching NY. Continuum


Teaching Math

Education

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