IMPACT OF ACTIVITY IN MATHEMATICS CLASSROOM (Higher Secondary Stage )

BY :

AJAY TYAGI and PANKAJ ROHILLA

Amity International School, Saket, New Delhi.

INTRODUCTION • Mathematics is the exact science that requires high level of

accuracy. It is one of the most interesting , systematic and logical subject. Mathematics lays the foundation for the study of most of the subjects. Even if a person is not educated he is using mathematics in some form or other .For example, a vegetable seller can quickly do the calculations for the quantity of vegetables we have purchased from him without use of any paper .This calculation skill he develops not by studying books but by the concrete day to day activities that he does in his daily life .Real teaching of mathematics can be done by allowing a child to use his nature and intuitive ways of thinking. Mathematics learning always proceeds from simple to complex and from concrete to abstract. It is the subject which involves step by step development like algebra requires the knowledge of arithmetic , calculus depends on algebra, dynamics depend on calculus and so on.

OBJECTIVE

• According to the vision of NCF-2005 the life of child at school must be linked to his life outside the school. Textbook should not be the sole basis of examination, other resources and sites of learning should be an integral part of learning process. Given space, time and freedom children generate new knowledge by engaging with the information passed onto them, if we perceive and treat a child as a participant in learning process not as receiver of fixed body of knowledge.

Teaching of mathematics can be made effective by applying activity based method. Teaching should be done so as to reach every child sitting in the class. A proper guidance and well directed process should be used for the teaching purpose so as to make the learning of mathematics more effective and easily caputurable by the student. The aim of teaching mathematics should be based on the concrete understanding of the subject and its various form and then use these concept for problem solving purpose. Mathematics is abstract and deductive in nature and that is why it is considered as difficult. Teaching is the help, the guidance provided by teacher to the students. Whenever this guidance is not in tune with student, teaching becomes difficult. Here our aim is to minimize this difficulty level to the least. By combining demonstration and activity method along with use of audio visual aids, abstract concepts can be made concrete.

METHODOLOGY

METHODOLOGY

• The traditional and innovative methods were used and students were examined , evaluated for the successful delivery of the lesson .The two homogenous sections of class XI were taught using the above two methods .In one section traditional method of teaching was used which was named as Section A and the Section B was the one in which we have used innovative method .

TRADITIONAL TEACHING METHOD

• In the class room, generally, a teacher transmits the knowledge to the students. It is his ability of delivering the knowledge that can transform the life of various students .He is responsible for the motivation and directing the students to capture the knowledge transferred by him . Traditional method of teaching generally involve the lecture method with the help of chalk and talk. It is the most commonly used method adopted by the teacher in delivering his lesson. We have taught the topic

• “CONIC SECTION” to the section XI A by lecture method using chalk and talk .

PERIOD 1:

• After drawing the diagram of doubled napped cone on the black board, students were told how we obtain various curves of parabola , circle , ellipse and hyperbola by cutting the cone with a plane at different angles .

• At the end of the lesson students were asked to redraw the diagrams of the curves obtained and to find out some applications of these curves in day to day life .

PERIOD 2:

• The concept was introduced algebraically using the general quadratic equation in two variables.

• Students were explained that various curves can be obtained using the concept of locus. Concept of eccentricity was also introduced.

PERIOD 3:

• In this period general equation of the circle with center (h , k) and radius ‘r’ was explained to the student .

• Students were explained how to form the equation of the circle under given conditions.

• After some illustrations students were allowed to complete the exercise given in NCERT book .

PERIOD 4:

• Doubts of the students from the topic circles were taken.

• Topic parabola was introduced in general form . • Various properties of all four types of standard

parabolas were explained using the diagrams . • Examples were explained to the students for

finding the focus , equation of axis , equation of directrix etc. related to the parabolas .

• Then the students were asked to complete the exercise and find out some applications of parabolas from their surrounding .

PERIOD 5:

• Concept of parabola was revised with the students and their doubts were cleared.

• The concept of ellipse was introduced and all properties of ellipse were explained to the student using the diagram .

• Some questions related to standard equations of ellipse were discussed with the students .

• Then the students were called on the blackboard to do few questions and some assignments were given to the students .They were also asked to find out the significance of planets having elliptical path .

PERIOD 6:

• The doubts related to the ellipse were discussed and the concept of Hyperbola was introduced .

• The properties of Hyperbola were discussed using the diagram and questions related to hyperbola were discussed .

• Students were called on blackboard to solve some question .

• Assignment from NCERT textbook was given to the students .

INNOVATIVE TEACHING METHOD

PERIOD 1:

• After drawing the diagram of doubled napped cone on black board , students were told how we obtain various curves of parabola , circle , ellipse and hyperbola by cutting the cone with a plane at different angles.

• Then students were shown the power point presentation and animation of obtaining the various curves by cutting the double cone by a plane at various angles using KYAN in the class room.

• At the end of the activity students were asked to redraw the diagrams of the curves obtained and to find out some applications of these curves in day to day life .

PERIOD 2:

• The students were taken to Maths lab and were given first hand experience of cutting the cone. Teacher demonstrated that different conic section can be obtained from a circular cone by a plane .The shapes of these sections depends on the position of cutting plane .Students faced great difficulty in imagining these shapes and attaching themselves with these topics .To overcome the problem, we have demonstrated how to obtain the shapes of various curves by using a concrete right circular cone.

• A cone model made up of dough and a cutter used to work as plane .First the teacher demonstrated the cutting of cone at various angle and then students were asked to follow it .Students were divided in a group of two and each group provided with a cone made up of dough and a cutter .They were asked to perform the activity and repeat the same at different angles to obtain different curves. One of the student was doing the activity while the second student was noting down the observations. Students were asked to perform the same at home using fruits and vegetables which are in conic shape naturally like carrot and beet root.

PERIOD 3:

• In this period general equation of the circle with center (h , k) and radius ‘r’ was explained to the student .

• Students were explained how to form the equation of the circle under given condition .

• After some illustrations students were allowed to complete the exercise given in NCERT textbook .

Circle

• The Standard Form of a circle with a center at (0,0) and a

radius, r, is……..

222 ryx

center (0,0)

radius = 2

Circles • The Standard Form of a circle with a center at (h,k) and

a radius, r, is……..

222 )()( rkyhx

center (3,3)

radius = 2

PERIOD 4:

•Doubts of the students from the topic circles were taken and the next topic parabola was introduced in general forms . •Various properties of all four types of standard parabolas were explained using the diagrams . •Then some examples were explained to the students for finding the focus , equation of axis , equation of directrix , etc related to the parabolas . •Then students were asked to complete the exercise and find out some applications of parabolas from their surrounding .

PERIOD 5: Concept of parabola was revised with the students and their doubts were cleared. Then the concept of ellipse was introduced and all properties of ellipse were explained to the student using the diagram .Some questions related to standard equations of ellipse were discussed with the students .Then students were called on blackboard to do few questions and some assignments were given to the students .They were also asked to find out the significance of planets having elliptical path.

Why are the foci of the ellipse

important? • St. Paul's Cathedral in London. If a person whispers near

one focus, he can be heard at the other focus, although he cannot be heard at many places in between.

Ellipse

• The ellipse with a center at (0,0) and a horizontal axis

has the following characteristics…

• Vertices ( a,0)

• Co-Vertices (0, b)

• Foci ( c,0)

1916

22 yx

PERIOD 6:

• The doubts related to the ellipse were discussed and the concept of Hyperbola was introduced .

• The properties of Hyperbola were discussed using the diagram and questions related to hyperbola were discussed .

• Then students were called on blackboard to solve some question .Home assignment was given to the students .

PERIOD 7:

• The students were taken to interactive room and explained the concept using the software GeoGebra. Then the students were asked to draw the graph of various curves on computer using the software to verify and note down their observations. To makes the study of the concepts more clear and easy concept of locus and eccentricity was explained to students using the software Geogebra.

• After the completion of lesson students were given assessment test to evaluate their achievement and understanding of concept.

GEOGEBRA IMAGES

• ..\geogebra\circle.ggb

• ..\geogebra\ellipse.ggb

• ..\geogebra\hyperbola.ggb

ASSESSMENT TEST MAX. MARKS-30

Fill in the blanks : 1. The eccentricity is defined as the ratio of distance of a variable point from a fixed point called

focus to its distance from a fixed straight line called _____________________. 2. Focal distance of a point on a parabola is given by the expression ____________________. 3. A chord passing through the focus and perpendicular to the axis of the ellipse is called the __________________. 4. If the centre of the hyperbola is (h, k) and the direction of the axis are parallel to the coordinate

axes its equation in standard form is_________. 5. The position of the point (2,3 ) with respect to the circle is ______________________. ( Interior /exterior ) True/false 6. Parabolic mirrors are used as reflector in cars : True/false 7. The projection of the artificial satellite is hyperbolic in trajectory . True /false 8. The cable of a uniformly loaded suspension bridge hangs in the form of a parabola True/False 9. Circle is the special case of ellipse . True /False. 10. The eccentricity of the hyperbola is less than 1. True /False.

Answer The Following Questions:

11. Find the distance between the centre of the ellipse given by the equations:

12. Give two uses of parabola in day to day life . 13. Give the length of the latus rectum of the parabola

given by the equation . 14. Find the relation between the length of transverse

axis , conjugate axis and the eccentricity of a hyperbola . 15. Find the area of the triangle formed by joining the

vertex of the parabola with the end point of its latus rectum.

Class Activity:

• Students of both the sections are divided in the group of four and were given activity to make rangoli using atleast four curves obtained from conic sections.

11TH - A

11TH -B

OBSERVATIONS

• Success in learning mathematics depends to a great extent on the power of attention and concentration. By making a child learn by doing and relating abstract concept of mathematics to daily life we can make a concept interesting and child gets attached to it. In turn self motivating him to explore it further and deeper.

• When students were involved in hands on activity in mathematics laboratory it was observed that they were easily connected to the concept and realize its significance in daily life .While they were watching the animation of the conic section the properties of conic sections were easily understood by them. After completing the activity when concept was explained mathematically to them in the class it was observed that students were very keen to know more about these curves, their applications and came up with many queries.

• Through the body posture like upright position , blinking of eyes and shifting of body posture it was evident that students were keen and eager to know and were attentive to the lecture .They were able paraphrase their understanding of the concept. We saw congruency between their verbal and non verbal communications .

• When Math lab activity was going on there were some students who did not have high spatial ability were very excited when they observed different curves obtained by cutting the cones themselves. Those who were high in spatial ability were enriched by the animation of cutting the cone shown in the class .

• After the assessment test its was observed that section taught through activity method could understand and apply the concept more efficiently then those who were taught by traditional method . Same observation was noticed when two sections were engaged in class activity of making rangoli .

CONCLUSION

• In chalk and talk method a child is a mere recipient of information. It’s a unidirectional flow of information. To make a child active participant in the process of learning mathematics, he needs to be involved .Today is an era of information technology , new school and curriculum being introduced that require no books and bags. To make pace with time we need to use the handy tools of IT like GEOGEBRA in the class room. Geogebra is the wonderful tool which can help in explaining various concepts of mathematics .Though activity based teaching is time consuming but rewarding in the sense that we could engaged whole class in understanding the concept and make them understand its real life significance.

REFLECTION OF THE STUDENTS

Reflections of the students after the activity class

RESULT OF THE ASSESSMENT TEST Name of students

Section A

Test score

(Max Marks 30)

Name of the student

Section B

Test score

(max marks 30)

ABHASS NAYAR 8 ADITI KHANNA 12

ACHANTIYA SHARMA 7 ANKITA MUNJAL 21

AAKASH GOEL 29 ARUSHI MEHRA 29

AKSHAT JAIN 10 DEEPIKA SINGH 16

ANMOL LAL 21 HARSH KINHA 12

BIPSHA MANDAL 12 MANOJ V P 19

DHRUV 26 NAMAN ANAND 22

DHWANIT 15 NIKITA WALIA 21

ISHAAN 12 SIDDHANT KHANNA 29

KUNAL 15 TANULEENA 24

KESHAV 11 VIDHUR NARANG 29

MANNAT 27 USTAV SEN 30

PRANAV ARORA 19 YASH GUPTA 10

RAGHAV GUPTA 14 YASH VARDHAN 20

RIJUL CHOPRA 10 YASHANK 9

REFERENCE

1. NCERT text book class XI.

2. Handbook for designing mathematic Lab in school by PROF.HUKUM SINGH.

3. Lesson plan conic section by VIRGINIA LAIRD ,Rockwell High School ,Richardson , Texas.

4. Geogebra workshop given by DR P.K CHAURASIA (Professor NCERT).

SUBMITTED BY

1. Ajay Tyagi (09810486036)

2. Pankaj Rohilla (09811344299)

Amity International School

M- Block

Saket

New Delhi-17.