reducing the book load, learning load and subsequently the load of ... on their
own legs. SCERT has prepared Training Manuals on General Guidelines for
CCE.
CONTINUOUS AND COMPREHENSIVE EVALUATION
MATHEMATICS
TEACHER’S MANUAL
IX STANDARD
PREPARED BY STATE COUNCIL OF EDUCATIONAL RESEARCH AND TRAINING, CHENNAI – 600 006,
TAMIL NADU
Team Reviewer Mr.K.Ramanujam Joint Director (Schemes) SCERT, Chennai – 600 006. Coordinator
Mathematics Team Head
Dr.S.Vincent De Paul
Mrs.B.Tamil Selvi
Reader,
Assistant Professor,
SCERT, Chennai – 600 006.
SCERT, Chennai – 600 006.
Team Members Mr.D.Iyappan
Mr.D.Mohan
Assistant Professor,
Lecturer,
SCERT, Chennai – 600 006.
DIET, Krishnagiri
Tmt.K.Mangaiyar Karasi
Mr. P.Chinnagounder
Lecturer, DIET, Dharmapuri.
Lecturer, DIET, Namakkal.
Mr. Asaithambi
Mrs. D.Umamaheshwari
Post Graduate Teacher,
Graduate Teacher,
GGHSS, Palakodu, Dharmapuri.
GHSS, Ashok Nagar, Chennai.
Mrs. B.Malavizhi
Mr.S.Rajendran
Graduate Assistant,
Graduate Teacher,
SBOA Matric HSS, Chennai.
GHSS, K.Morur, Salem.
Translation Team Mr.D.Iyappan
Mrs. B.Malarvizhi
Assistant Professor,
Graduate Assistant,
SCERT, Chennai – 600 006.
SBOA Matric HSS, Chennai.
Mr.Rajesh
Mrs. S.K.Saradha
Lecturer
Graduate Assistant,
DIET, Namakkal
SBOA Matric HSS, Chennai.
Preface The Government of Tamil Nadu, in a pioneering initiative to reach the goal of quality in education, introduced Continuous and Comprehensive Evaluation (CCE) and Trimester Pattern in 2012-13 for class I to VIII. Subsequently, CCE is being introduced in Std IX from the year 2013-14 in all the High and Higher Secondary Schools of Tamil Nadu. This
strategic
combination
of
CCE
with
Trimester
has
been
implemented only in the State of Tamil Nadu in India with the intention of reducing the book load, learning load and subsequently the load of miscomprehension. This has impacted not only the learning styles of the students but also enthused the teachers to assess students for learning. Incidentally the teachers have become co-learners in the process of administering CCE to students. This transformation has inspired the teachers to become reflective practitioners and students enthusiastic constructors of knowledge from their own past experiences, peers, teachers, elders, community, library and digital resources. CCE has opened the avenues for student community to seek knowledge from diverse resources and learn to stand on their own legs. SCERT has prepared Training Manuals on General Guidelines for CCE and Subject-Specific Guidelines to help teachers implement the studentfriendly - CCE and Trimester system effectively. SCERT proposes to train all the teachers at the secondary level to assimilate the strategies involved in the implementation of both Formative and Summative Assessments. The assessment Activities have been designed so meticulously that teachers would naturally find it easy to use, adopt or create their own activities to witness and assess the miracle of learning happening in the class room in a fear-free, friendly and enabling environment. The manuals deal with Scholastic and Co-Scholastic activities and also assessment of values, attitudes and life skills in each subject including Physical Education which has now been brought under curricular subjects.
Formative and Summative Assessments are carried out while learning and after learning respectively. The former assesses for learning and remedial activities are given for ensuring relearning and the latter is of learning and it has no scope for remedial measures. In this radical method of assessment, Teachers assess not only the learning and achievement but also the students’ social graces, their knowledge and application of social skills through Co-Scholastic assessment activities. This assessment method facilitates the identification and nurturing of the innate potential of students. Teachers get to know the all-round development of students. Besides, the Training Manuals have included strategic suggestions to develop assessment activities for the differentlyabled learners appropriate to their level of understanding and learning capacity. Teachers are hereby requested to undergo the training earnestly and assimilate the ideas and strategies discussed in a positive way and implement CCE and Trimester effectively in their respective classrooms. Then only the teachers can ensure the transformation of the younger generation into well-rounded personalities and responsible citizens of this country capable of shaping the future destiny of this country. Teachers shall take into consideration the fact that destiny of a country is shaped inside the four walls of a class room. Hence SCERT and the manual development team expect the teachers to realize their precious responsibilities to the students and to the Society and implement CCE and Trimester in all academic seriousness and involvement in their Schools. SCERT Chennai
Content Sl. No 1.
Continuous and Comprehensive Evaluation
1
2.
Skills developed by learning Mathematics
1
3.
Guidelines for using Teacher’s Manual
2
4.
Formative Assessment (a)
3
5.
Some Activities for FA (a)
3
6.
Formative Assessment (b)
5
7.
Types of Questions for FA (b)
5
8.
Summative Assessment
5
9.
Classroom Activities
6
Particulars
Page Number
10. Suggestive Activities for Formative Assessment (a) (Set Theory, Real Numbers, Algebra, Geometry, Coordinate
8-47
Geometry and Practical Geometry) 11. Laboratory Activities
47-54
12. Model Questions for FA(b) (Unit-wise)
55-61
13. Blue Print 14. Summative Assessment – Model Question Paper
62 63-66
Continuous and Comprehensive Evaluation
Continuous
and
Comprehensive
Evaluation
(CCE)
enables
the
students to be evaluated throughout the year besides enabling them to develop their physical, mental, attitudinal skills by which they attain holistic personality and become responsible citizens. This includes Formative Assessment (a), Laboratory activities, Formative Assessment (b) and Summative Assessment. In this method of assessment, teachers need to design an evaluation activity by which individual talents of each student is expressed. Formative Assessment (a) is done by involving students in activities while teaching the concepts. Mathematics Laboratory Activities help students learn mathematical concepts easily and apply them in real life situations. Formative Assessment (b) helps to assess understanding of concepts by administering students small tests. Teachers can understand the extent of concept attainment of students and the lacunae in this process can be resolved by adopting remedial activities for enhancing concept attainment. Skills developed by learning Mathematics
Numerical Ability
Mathematical Problem Solving
Estimation of Quantities
Approximation
Visualisation & Representation
Identification of Pattern
Data Handling
Investigation
Thinking Skill
Mathematical Communication
Application of Mathematical concepts in real life situations.
1
Guidelines for using Teacher’s Manual Teacher has to keep the following in mind while implementing CCE in classroom.
The objective of CCE is to understand difficult areas with reference to students understanding and adopt remedial activities for enhancing concept attainment. This
guideline further helps
teachers and learners understand their status in the teachinglearning process.
The assessment activities given in the manual are only suggestive. The teachers can use them as such or they can modify based on the classroom/students/local needs without affecting the objective of CCE.
This manual has many evaluation strategies and activities for undertaking assessment activities. Based on learning objectives, expected learning outcomes, time duration, students’ strength and available resources the suggested activities may be implemented.
Teacher has to take special care in order that students are not stressed while Formative Assessment is used in classroom for assessment.
Continuous Comprehensive Evaluation
Formative Assessment (40 Marks) (Throughout the Term)
Formative Assessment (a)-two best out of four Activities (2 x 10 = 20Marks)
Summative Assessment (60 Marks) (End of the Term)
Laboratory ActivityAverage of four Activities (10Marks) 2
Formative Assessment (b)-one best out of two Tests (1 x 10 = 10Marks)
Formative Assessment (a) FA (a) is an assessment done based on activities, while teaching a concept for the formation of the concept as well as to strengthening the concept. Salient Features of Formative Assessment (a) Even though all the students are involved in the activities conducted to strengthen the learning process, the teacher has to assess only five students by closely monitoring them. It is a yardstick for students for self assessment. Guidelines for teachers to diagnose the problems and take remedial activities to resolve them. Development of life skills like decision making, problem solving, building relationship, critical thinking and effective communication through group activities. Designing activities according to the learning pace of the students. Each FA (a) model activity is supplemented with descriptors for assessment. Teachers can develop their own descriptive indicators for the additional activities designed by them. Each student has to be involved in at least 4 activities in a term out of which the best 2 activities are to be taken into consideration for recording. (2 activities x 10 marks) = 20 marks
Some Activities for FA (a) S.No.
Activity
S.No.
Activity
1.
Group Activity
2.
Learning by doing
3.
Investigation
4.
Assignments
5.
Group Game
6.
Games
7.
Quiz
8.
Scrap book
9.
Interpretation
10.
sequencing the concepts
11.
Puzzle
12.
Mathematical Communication
3
S.No.
Activity
S.No.
Activity
13.
Role play
14.
15.
Concept Mapping
16.
Project Work
17.
Problem Solving
18.
Visualization
19.
Graphical Representation
20.
Model Making
21.
Albums
22.
Group Discussion
23.
Home Assignments
24.
Cross Word Puzzle
25.
Presentation digital means through diagrams etc.,
27.
through or 26. Graphs.
Flow Chart
Compare and contrast
Debate
Laboratory Activities Mathematics
Laboratory
Activities
help
students
to
explore
mathematical concepts, theories and theorems, learn and verify them using various materials. Under Formative Assessment, 10 marks is allotted for this activity. Based on the first term portions, Mathematics Laboratory Activities have been designed. The students need to involve in these activities in groups after the steps of the activities are clearly explained by the teacher. Eight activities are prescribed in this manual for the first term. Among these activities a minimum of four activities are to be undertaken by allotting 10 marks for each activity as given below. The average of these four activities is to be recorded under lab activity. Sl. No. 1. 2. 3. 4. 5.
Description
Marks
Lab Ethics
2
Adopting proper procedure for the lab activity
2
Recording
2
Verifying the solution of the problem Clear explanation for the questions
2
4
2
Formative Assessment (b) Formative Assessment (b) is a small test conducted for all students for a short duration after completing a unit for assessing the understanding the concept attainment.
Salient Features 1. Ensuring learning attainment of each student through the individual activity. 2. It is a yard stick for students to understand concept attainment by themselves. 3. Guidelines for teachers to diagnose the problems and take remedial activities to resolve them. 4. Development of life skills like self awareness, critical thinking, creativity and problem solving skill as diagnosis is done through individual activity. 5. All the students should take at least 2 tests in a term and the teacher has to take the better performance for recording. (1 small test x 10 marks = 10 marks)
Types of Questions for FA (b) S.No.
Types of Questions
S.No.
Types of Questions
1.
Multiple Choice
2.
Sequencing
3.
Fill in the blanks
4.
Right / Wrong
5.
yes / No
6.
Very Short Answer Type
7.
Matrix type
8.
Short Answer Type
9.
Odd one out
10.
Paragraph Question
Summative Assessment The examination conducted for 60 marks at the end of each term is Summative Assessment. This test is conducted for a specific duration based on the given blue print for each term.
5
The pattern of question paper and model question papers are annexed in this manual
Summative Assessment is conducted based on the instructional objectives like knowledge, understanding, application and skills
Besides sums given in examples and exercises, other sums based on the content can also be asked in this test.
Classroom Activities: Individual Activity Individual Activity necessitates each student to involve
in activities
under CCE. While implementing these activities, teacher has to pay individual attention on each student and ensure learning happens without any hitches. The learning through individual activity takes the concept to students long term memory and makes learning meaningful. Paired Activity Student can be grouped in pairs and the group can be assessed by involving them in activities. Small Group Activity
Based on the nature of the assessment activity, teacher can design activities by dividing the students into groups of 5 or more.
Each group may be assigned a group activity of a selected content.
The supply of required materials is to be ensured before implementing the activity.
The participation of each and every student is to be ensured.
Whole Class Activity Based on the nature of the assessment activity, all students of the class may be involved in a single group and assessment may be undertaken. For example, for assessing ‘Real Numbers’ all the students can be divided into 5 groups and each group may be involved to perform a role play by depicting one type of number (Natural number, whole number, etc).
6
Remedial Teaching The students who are unable to involve totally in FA (a) and FA (b) or such students who require additional help, teacher may design new similar activity or involve them in the same activity with guidance. The teacher has to repeatedly undertake this process until students attain total concept clarity as expected out of the activity.
Remedial Teaching
Diagnostic Test
Total Concept Attainment
Content
Transaction Time Allotment for Content and Mark distribution for the Term- I
Real Number System
25 14
Marks ( including marks for choices) 22 16
3.
Algebra
18
18
4.
Geometry
13
5.
Coordinate Geometry
20
12 18
6.
Practical Geometry Total
09
10
99
96
S.No.
No. of periods
content
1. 2.
Theory of Sets
7
Suggestive Activities for Formative Assessment (a) Unit 1 : Theory of Sets
Activity 1
: Well defined, not well defined sets
Unit
: Theory of Sets
Content
: Definition of Set
Learning Objective
: To develop the skill of defining sets
Assessment
: Awarding marks based on the given descriptive indicators through group activity
Duration
: 30 mts.
Procedure: The entire class is to be divided into two groups. While one group gives a statement on a collection of objects,
the other group has to say
whether it is well defined or not. Besides, their answer has to be reasoned out. Sl. No.
Statement
Nature
1.
No. of students studying in our school
2.
No. of good students in our class
3.
No. of prime numbers less than 10
Well defined Not well defined Well defined
4.
No. of Districts in Tamil Nadu
5.
No. of bright stars seen in the sky
Well defined Not well defined
Similarly, the activity may be done vice-versa. The teacher has to give equal opportunity for all the students and assess based on the descriptive indicators. Students may be given chance to give more examples. Descriptive Indicators
Initiative
Expressing the Statement Correctly
Reflecting Upon the Answer
2
2
2 8
Giving Reasons for the Result
Adding 1 more example & Defining it
2
2
Activity 2
:
Group Activity
Unit
:
Theory of Sets
Content
:
Three ways of representing a set
Learning Objective
:
To represent the set in 3 different ways
Assessment
:
Awarding marks based on the give descriptive indicators through group activity
Duration
:
30 mts.
Procedure: The students of the class can be divided into 3 groups. One group may be named as ‘Descriptive Form’, the second group as, ‘Set Builder Form’ and the third as ‘Roster Form’, While one group states a set on his own according to the name of his / her group, the other two groups convert the given set into their respective forms. Instead of giving chance for the same team, all the three groups may be given equal chance to initiate the process. Sl. No.
Descriptive Form
1.
A set of even numbers less than 20
2.
A set of odd numbers less than 10
Set Builder Form A = {x:x 20, x even numbers} -
Roster Form A ={2, 4, 6, 8.... 18} -
3.
-
B= {x:x
