Planning for
teaching-learning and evaluation in mathematics
UNIT PLAN
A Unit plan represents a careful
organization of large block of selected and outlined subject matter and planned
learning experiences.
Planning a Unit is similar to lesson
planning, a unit may have various lessons. Therefore, it may not be completed
in one class period. Unit plans are very helpful for the new teachers because
it helps him to know exactly how much subject matter in certain topic suits the
varying age-levels of the students.
A Unit is related learning segment made up
of a few lessons along with an outline of its actual execution in the
class-room. Thus a unit will consists of both the subject matter and
methodology of its delivery to students. After having divided the prescribed
syllabus into a number of teaching units the teacher will decide the time that
could be allotted to each unit. After that he can break up each unit in a
number of lessons and each lesson should be complete in itself. After this the
teacher will enter in his dairy the scheme of work under various headings.
Definitions of a Unit:
1.
“A
Unit is a large a block of related subject matter as can be over viewed by
learner”.
----Preston.
2.
“A
Unit is an outline of carefully selected subject matter, which has been
isolated because of its relationships to pupil’s needs and interests”. ----Samford
3.
“A
Unit consists of a comprehensive set of related and meaningful activities, so
as to achieve pupils’ purpose, provide significant educational experiences and
results in appropriate behavioural changes.”
----Bossing.
Characteristics of a Good Unit:
1. The aim should be clear and well
defined.
2. The aids to be used should be
appropriate and very clear.
3. It should be based on principle
of psychology.
4. It should be complete integrated
whole in organization.
5. It provides for individual
differences.
6. In good unit there is provision
of evaluation and follow up.
7. It should be correlated with
other subjects and daily life experience.
8. A good unit provides activities
for students.
9. A good unit leaves pupil for to
work. They have chance to plan, organize and execute.
10. A good unit is always
comprehensible within the access of pupils.
11. It should permit some place for
trips, execution projects and demonstrations.
12. A unit can broken up into
interrelated sub-units or topics.
13. A unit should not be too lengthy
or too short.
14. The length of the unit should be
such as to retain the interest of the students.
Importance of Unit Plan
1.
Unit
plan helps in the systematic instruction of knowledge, understanding and skill
of the subject meaningfully.
2.
On
the basis of Unit plan it is easy to make preparations for daily lesson.
3.
It
makes a teacher compulsory to get into the mastery over the content, teaching
method, and design.
4.
In
the process of instruction of the Unit, it will be possible for the teacher to
do with enhanced confidence.
5.
There
is provision for, simplifying complex matter, concepts, repeated integration,
novelty assessment of individual learning, learning differences, remedial
teaching to fill in the gaps of differences.
6.
In
the Unit plan there is scope for motivation, insight, learning
experiences, revision, reinforcement, suitable feedback, total comprehensive
evaluation which make instruction effective.
How to plan a Unit?
The following points should be kept in
mind while planning a teaching unit.
1.
It
should be according to the needs, abilities and interest of the student.
2.
It
should be start with previous knowledge and experiences.
3.
It
should permit various experiments demonstration and projects etc.
4.
It
should be based on social and physical environments of the pupils.
5.
It
should satisfy some of the future needs of the students.
6.
It
should also provide new experiences to the students.
7.
It
should be of appropriate length so as to retain interest of the students up to
the last.
8.
It
should be result a co-operative planning of teacher and student.
Steps of Unit Plan:
1.
Subject:…………(Mathematics)
2.
Topic:
…………. (Heading of the unit)
3.
Class:
…………. (To whom the unit is to be taught.)
4.
Time:
………….. ( No. of periods)
5.
Aids:
…………. (What are aids to be used during the entire unit.)
6.
Content:
……….. (Syllabus to be covered)
7.
Sub-Unit:
…….. (Listing the name of the sub-units)
8.
Objectives:
……. (To be achieved after completing of unit)
For each Sub-units:
9.
Sub-unit
number and along with heading of title.
10.
Time:
(number of periods)
11.
Teacher’s
activities.
12.
Student’s
activities.
13.
Combined
activities (students and teacher’s)
14.
Assignments
15.
Follow-up
work.
Steps Involved in Developing a Unit:
1. Preparation
or motivation: It
is to motivate the students for learning. Motivation is provided by the teacher
from outside in natural and self-directed manner. It is not only required in
the beginning but throughout the lesson.
2. Previous
knowledge test: A
unit should be start from the ladder where the students are standing at
present. The background of students should be questioned. The teacher should
start with students where they are.
3. Presentation:
In this
step new experiences are given to the student. The subject matter is presented
to students with the help of aids or direct or indirect experiences which they
easily digested assimilate.
4. Summarisation:
At the end
of the unit the whole content is summarized sectional summaries can also be
provided.
5. Review
and Drill: During
the whole process of teaching unit, there is probability that some part of
teaching unit is forgotten and some has not been completely comprehended. So
some learning experiences require repetition which is called drill. Hence
review and drill may be required at a number of places during the lesson.
6. Evaluation:
This is
very essential part of unit. It only informs the teacher how much students have
gained and what discrepancies are left in a unit and how to remove them.
Proforma of a unit-1:
Subject: ...............................
Class: ……………
Name of the Unit:
………………………………………….
Major objectives of
the Unit: …………………………………………………………………..
………………………………………………………………………………………………..
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Sl. No.
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Topics/Concepts
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Number of lessons required
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Time/Period
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Scope of subject/Content
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Method of Teaching
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Teaching Aids
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Proforma-II
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Sl. No.
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Sub title
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Behavioural Objectives
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Teacher’s Activity
(Method)
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Pupil’s Activity
(Method)
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Pupil’s Assignment
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Evaluation
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Differences between
Unit plan and Lesson plan
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Unit
Plan
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Lesson
Plan
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1.
Content
is grouped in terms of facts, principles, concepts, laws, generalization etc.
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1.
Content
is presented in the form of teaching point in logical and psychological
order.
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2.
Learning
activities are mentioned only.
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2. It deals with the learning
activities in details.
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3.
It
is made up of several lesson plan.
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3. It is the part of the whole.
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4.
It
can be extended over more than 8-10 periods depending upon the subject matter
the objectives to be achieved and the learning activities.
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4. It is daily auction plan.
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5.
In
Unit plan evaluation tools and techniques are mentioned only.
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5.In lesson plan actual test items are
given.
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Advantages of content analysis
The teacher should have content in hand to
answer for the questions like what to teach? How to teach? And how much to
teach?
It is only the content which makes
provision for the teacher to select appropriate learning experiences that are
to be taken up in the classroom.
Advantages
of Unit plan:
1. It provides a basic course
structure around which general as well as specific class activities be or
teaching can be organized.
2. It clears the general aims as
well as specific aims of teachings.
3. It helps to develop the
democratic atmosphere in the class where teacher and students works in
co-operative manner.
4. It develops certain skills among
the students and sharpens their insight.
5. It gives authority to the
teacher to integrate the basic course concepts and those of related areas into
various teaching experiences.
6. It saves time as well as
develops interest of students towards learning.
7. Teacher can cater to the needs,
aptitude and attitudes according to the individual difference of students.
8. Students can apply the knowledge
gained in other life situations also.
9. As students learn independently
they develop self-confidence, resourcefulness and reliance.
10. It provides an opportunity to
the teacher to keep a balance between various dimensions of the prescribed
course.
11. Unit plan breaks up a lengthy
unit in to smaller sub-units or topics so that pupils can easily grasp the
scope of these during a brief over view.
12. It helps the teacher to present
to various principles and concepts constituting the unit in and orderly and systematic
manner without losing their continuity.
13. It provides frequent
opportunities for the students to review and reorganize their learning.
14. It helps the teacher to plan
definite outcomes of learning. So that they are clear not only to the teacher,
but also to the students.
15. It helps the teacher to plan a
variety of learning experiences, keeping in mind the individual differences,
the nature of content and objectives to be achieved.
16. It enables the pupils to see
clearly the relationship between the various facts process and principles that
make up the unit.
17. The study outline of the unit
plan provides the students with directions as to what to study and how to do it
most effectively.
4.2:
Evaluation in mathematics:
Unit
Test/Achievement test
Teaching and testing are the
integral part of educational system. Testing is implicit in teaching some of
the stages, which may be properly marked for testing procedures.
1.
During
teaching.
2.
At
the end of teaching a daily lesson.
3.
At
the end of teaching a unit.
4.
At
the end of the term.
5.
At
the end of the year/curriculum.
A test at the end of a teaching unit is
known as the unit test.
Usually the test / Examinations
are held based on the entire syllabus. A unit test is not a random assessment
of questions. It is preplanned, systematic and scientific test.
A unit test is a test which is
constructed, administered and assessed by a teacher after teaching a particular
unit to the students.
Characteristics of Achievement
test:
1.
Unit
test is an Evaluation tool for measurement of pupils and knowledge achievement
and to improve by giving feedback.
2.
It
is based on a single unit.
3.
It
is administered at the completions of the unit.
4.
It
is clear from the above evidence that a unit testing is an integral part of
teaching process. Unit testing makes instruction a dynamic process through
continuous evaluation and regular feedback.
Steps for setting up a
Achievement test:
The steps for setting up a good and meaningful unit test
are,
A) Planning (Design) of the test:
1.
Unit
Analysis
2.
Content
Analysis
3.
Weightage
to content.
4.
Weightage
to type of questions.
5.
Weightage
to objectives.
6.
Weightage
to difficulty level.
7.
Preparation
of Blue print.
B) Editing the Achievement test:
1.
Construction
of items
2.
Selection
of items
3.
Grouping
of test items.
4.
Instructions
of Examinee.
5.
Sections
in the question paper.
6.
Preparing
a marking scheme and scoring key.
C) Reviewing the Question Paper:
1.
Question-wise
analysis.
2.
Critical
evaluation of the test.
D) Administering the Test:
E) Interpret the test results:
1.
Score
the answer scripts.
2.
Item
analysis (After the test)
F) Statistical Treatment:
1.
Based
on measures of central tendency values.
2.
Based
on quartile points.
3.
Based
on frequency polygon & histogram.
A)
Planning (Design) of a unit test:
As it is obvious that, a
planning made carefully to begin with, the design of the test is prepared so
that it may be used as an effective instrument of evaluation. A proper design
would increase the validity, reliability, objectivity and suitability of the
test.
The following aspects
have to be looked up on while planning for a unit test and they are.
1. Unit analysis:
Here the teacher must analysis the whole
unit into its sub-units, sub-units may be listed under sub headings and must be
organized logically.
2. Content analysis:
The content analysis must be done for
each one of the sub unit separately by listing the important facts, concepts,
principles, generalizations etc.
3. Weightage to objectives:
The relative
importance of each objective is to be considered. For informative subject
Mathematics the objectives are knowledge understanding, application and skill.
The main task here is to decide the weightage to be given to the different
objectives include in the unit plan. This weightage should be decided by a
committee of experts, including the classroom teacher.
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Sl.No
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Objective
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Marks
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Percentage
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1
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Remembering
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5
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10%
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2
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Understanding
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15
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30%
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3
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Applying
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20
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40%
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4
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Skill
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10
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20%
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Total
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50
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100%
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4. Weightage to
content:
The content of a unit is taught
in the classroom by providing suitable learning experiences. All the subject
matter will not have equal importance. Therefore in order to test the
understanding of the content, a proper weightage must be given looking into the
nature, scope & importance of the content. The content weightage must be
given in such unit wise and teacher must see no content/sub unit should left
out.
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Sl.No
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Sub Units
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Marks
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Percentage
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1
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Concept of sets
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5
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10%
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2
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Set notation
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5
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10%
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3
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Types of sets
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15
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30%
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4
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Sub sets
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5
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10%
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5
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Union set
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5
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10%
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6
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intersection of set
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5
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10%
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7
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Venn diagram
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10
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20%
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Total
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50
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100%
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5. Weightage to
type of questions:
For testing different abilities
and subunits, different forms of using traditional form the essay questions.
In order
to test various learning out comes we have to use objective type, very short
answer type, short answer type and easy type questions. We have to use these
types of questions must given weightages on the basis of their adequacy etc. So
that they can achieve our Instructional objectives.
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Sl.No
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Type of Questions
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No. of Questions
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Marks
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Percentage of marks
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01
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Objective
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25
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9
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18%
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02
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Short answer Type
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8
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16
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32%
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03
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Essay type
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3
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25
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50%
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Total
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36
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50
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100%
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6. Weightage to
difficulty level:
It is an accepted fact that in a
class room there are 3 types of pupil’s average above, below average;
accordingly the test should not be difficult not too easy. The test should
provide suitable opportunity to the bright, medium and weak students in class.
The teacher expected to classify the items in three levels-difficult average
and easy.
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Difficulty level
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Marks
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Percentage
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Easy
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15
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30%
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Average
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25
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50%
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Difficult
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10
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20%
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Total
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50
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100%
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7. The Blue-Print:
The blue print is a 3 dimensional chart showing the
weightage given to objectives, content and types of questions in terms of
marks.
The blue print serves many useful purposes.
1.
It
helps to improve the content validity of teacher made tests.
2.
It
defines as clearly as possible the scope and emphasis of the test.
3.
It
relates objectives to content.
4.
It
acts as a guide to construct the unit test.
Blue print
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Content
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Knowledge
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Understanding
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Application
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Skill
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Total
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Sub Unit I
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Sub Unit II
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Sub Unit III
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B) Editing the unit test:
Once the design is thoroughly
prepared. The next step is to edit the test in the form at question paper. In
editing the test the following points to be keep in the mind.
1. Construction of items:
A teacher must
construct or prepare number of questions on the unit. The items must be of
variety. Like essay type, very short answer type, short answer type and
objective type etc. The construction of test items it is necessary to identify
the objectives and its specification that the item intends to measure. The
items should over all sub units.
2. Selection of test items:
The teacher must select the relevant item according to blue
print, based on objectives content coverage, type of question required. They
should have scoring key and marking scheme for better clarify.
3. Grouping of Test items:
We have to group the selected
test items into different categories depending on the type of items.
4. Instructions to Examinee:
There are two types of instruction in the question paper
1. General instruction
2. Specific instruction
The general
instruction must be given in the beginning of question paper.
a)
This
paper has two/three sections (A, B, C)
b)
All
questions in the section is compulsory
c)
About
time, medium of answering.
The specific instructions enable
the examinee to understand how to respond to a question.
5. Sections in the Question Paper:
Generally, the objective type items grouped under section a
short answer in section B, Essay type in Section C.
6. Preparing marking scheme and
scoring key:
The
marking scheme should be prepared for the essay and short answer type of
questions only the important points to be written in the expected answer in
scheme. The expected answer must be allotted with certain amount of time.
The scoring key must be prepared for the
objective type items.
C) Reviewing the question paper:
1) Question wise analysis:
Each Question must be considered separately and analyzed in
terms of its sub unit, objective and specifications type of question marks
allotted, time limit for answering.
The purpose of Question wise
analysis also to know the strength and weaknesses of question paper, To tally
the question paper with blue print, to determine the content validity and for
the satisfaction of paper setter.
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Sl No.
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Sub Unit
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Objectives
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Specification
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Type of Q.
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Marks
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Time Limit
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Difficulty Level
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2)
Critical Evaluation of the Test:
It is done to ensure the
correctness, relevancy working and distracter of the item. All the Questions
must be free from grammatical errors and relevant to the unit taught, age level
of examinee and the distracter are homogenously given in objective questions.
The question paper must cover the whole content. The test
paper must be graded according to their difficulty level.
No guess work should be encouraged.
D) Administer the test:
The revised question paper
should be administered to the students. The teacher gives instruction to
students and he should see teacher should supervise the unit test.
E) Interpret the test results:
Score the answer script: Each student’s answer is numerically
quantified and a list of individual students score in prepared.
The item wise analysis is done
to know the validity of the each test item separately and then the item
difficulty index is calculated.
F) Statistical Analysis:
The raw scores obtained from the
scoring of the test papers. After that construct a table of frequency
distribution. In this table, the teacher takes appropriate class intervals and
relevant frequencies. After preparing the table the teacher calculates central
tendency i.e., Mean, Median and Mode. By the calculation of central tendency,
we interpret that if Mean < Median
the test is negatively skewed and
easy if mean > median the test is
positively skewed and difficult, if
mean = median then the test is average.
After the teacher calculates Quartile division, i.e., Q1,
Q2, Q3 on the basis of QD’s we can interpret that if Q3-Q2 < Q2-Q1, the test is negatively
skewed and easy, if Q3-Q2 > Q2-Q1,
the test is positively skewed if Q3-Q2 = Q2-Q1 the given test in average.
On the basis of these
calculations, the teacher can draw the graphs of frequency polygon and
histogram.
Use of an Achievement Test:
1.
They
help in knowing the learner’s achievement.
2.
They
are useful to know the weaknesses and strengths of students.
3.
They
are helpful in classifying the students.
4.
They
help in deciding the effectiveness of teaching.
5.
They
help in knowing the objectives are achieved (or) not.
6.
They
become the part of continuous evaluation.
7.
They
help to teacher to improve his teaching effectively.
8.
They
help in development of self-confidence in facing the examinations.
