Achievement test/Unit test in Mathematics

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: …………………………………………………………………..

………………………………………………………………………………………………..

Sl. No.	Topics/Concepts	Number of lessons required	Time/Period	Scope of subject/Content	Method of Teaching	Teaching Aids

Proforma-II

Sl. No.	Sub title	Behavioural Objectives	Teacher’s Activity (Method)	Pupil’s Activity (Method)	Pupil’s Assignment	Evaluation

Differences between Unit plan and Lesson plan

Unit Plan	Lesson Plan
1.       Content is grouped in terms of facts, principles, concepts, laws, generalization etc.	1.       Content is presented in the form of teaching point in logical and psychological order.
2.       Learning activities are mentioned only.	2. It deals with the learning activities in details.
3.       It is made up of several lesson plan.	3. It is the part of the whole.
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.	4. It is daily auction plan.
5.       In Unit plan evaluation tools and techniques are mentioned only.	5.In lesson plan actual test items are given.

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.

Sl.No	Objective	Marks	Percentage
1	Remembering	5	10%
2	Understanding	15	30%
3	Applying	20	40%
4	Skill	10	20%
	Total	50	100%

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.

Sl.No	Sub Units	Marks	Percentage
1	Concept of sets	5	10%
2	Set notation	5	10%
3	Types of sets	15	30%
4	Sub sets	5	10%
5	Union set	5	10%
6	intersection of set	5	10%
7	Venn diagram	10	20%
	Total	50	100%

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.

Sl.No	Type of Questions	No. of Questions	Marks	Percentage of marks
01	Objective	25	9	18%
02	Short answer Type	8	16	32%
03	Essay type	3	25	50%
	Total	36	50	100%

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.

Difficulty level	Marks	Percentage
Easy	15	30%
Average	25	50%
Difficult	10	20%
Total	50	100%

 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

Content

Knowledge

Understanding

Application

Skill

Total

Sub Unit I

Sub Unit II

Sub Unit III

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.

Sl No.	Sub Unit	Objectives	Specification	Type of Q.	Marks	Time Limit	Difficulty Level

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.