HOW TO ENHANCE PEDAGOGICAL CONTENT KNOWLEDGE

THROUGH CELEBERATION OF NATIONAL YEAR OF MATHEMATICS 2012

Narayananunni MP, Lecturer in Mathematics education

DIET Palakkad, Kerala.

Librarian's doubt

To present the topic ' Interest', one mathematics teacher ask to 'Iteehyamala' , a

collection of stories, written by Kottarathil Sankunni, one of the famous ancient

malayalam writer to refer. What is the role of 'Itheeyamala' in mathematics learning ?

Pedagogical content knowledge

The pedagogical content knowledge include the knowledge of learner and their characteristics, knowledge of educational contexts,knowledge of educational ends, purpose and values and their philosophical and historical bases.

Shulman (1987)

Fenna and Frank (1992)

It is the knowledge of subject matter with its nature and mental organization of teacher's version, knowledge of representations of the content,knowledge of student's cognitions and knowledge of teaching and decision making are the main components of the special type of teacher knowledge with pedagogically powerful.

Pith and attraction of

MESH(Mathematical intervention to Enhance Student's Happiness in learning) [National maths year programme of District Institute of Education and Training (DIET),

Palakkad, Kerala ] 1. Seminars on mathematics conducted at sub district and district level that proclaims the strength and beauty of the subject. 2. Workshops on mathematics laboratories which provided opportunity for teachers and students to interact and work together. 3. Co living camps that offer chances for problem solving through construction and Visualisation ( Elements of theatre in education) 4. Two day study camp to children - high achievers – which unveils unending possibilities of mathematical thinking and problem solving.

Objectives 1. To identify strategies for effective interpretation of

mathematical concepts for the purpose of presentation.

2. To know how mathematics laboratories help

to work together and to get involved in healthy dialogues.

3. To explore the effectiveness of theatre elements

in understanding and explaining concepts and principles.

4. To know the way and extend that the specific experiences

paused in problem solving influence the performance of children.

1 district seminar, 12 sub district seminar, 100s of school seminars (Funded by DIET and SSA)

Hepatia - logical thinking , the strong resistance against the orthodox leadership , dedication evolved out of personal loss etc. are some of the values discussed and shared. After her demise her friend Orastrus who had to leave for Mali. Thimbooku university made Hypetian mathematical thoughts as a part of their curriculum. And later Arabians propagated the thoughts, that reached Kerala through Christian business men, were developed by the scholars (as Parameswran,Achuthan and Neelakanta somayaji...)of kerala school of mathematics and handed over it back to the world of mathematics. This episode highlights and establish the universal nature of the subject,

Fermat's last theorem.

The investigations and evidences in this connection evoked interest among all. Long search for knowledge reaches a satisfying answer through Andrew wails, shares and highlights the need of dedication for learning mathematics.(from the first half of 17 Th century, to the end of 20 Th century)

An + bn = cn where n < or = 3

This episode highlights the need of dedication for learning mathematics.

Mathematics and Literature

C.Radhakrishnan, an eminent figure in malayalam literary field analysed the essence and meaning of democracy in the background of triangle in his novel 'Munpe parakkunna pakshikal'. It is really an attempt to unveil mathematical possibilities even in literature. His observation is that democracy becomes perfect as the three components viz. people, political parties and power becomes 3 points in a straight line instead of 3 vertices of a triangle is highly relishing.

People

Political party

Power

This is an attempt to unveil mathematical possibilities even in literature.

Folk Mathematics 'Vattatharai kondu vittatharai thakkil sattanai

thiriyum kuzhi'

This means the product of the half of 'vattom' and 'vittom' will give the base area of a well . This is the strategy proposed by local carpenters of Kerala and Tamilnadu nearby Kanyakumari, to assess the area of a circle.

This is the same of our pie x r2

is an enjoyable craft of mathematics.

Carpenter's style to find 'Vattom' (circumference) of well

Measure the 'vittam' (diameter) of well

Divide the vittam into 7 small equal parts

22 times of the length of small piece is the

vattom of well

Maths in Physics

Maths teacher's version

Average = Sum of terms divided by No of terms

science teacher's version

Average velocity = (u + v) / 2

Here consider first and last term only.

Why ?

In a uniform motion velocities are in AP.

36

Find the length of diagonal of the square ?

One Folk style. 36 divided by 12 = 3.

Then 3 x 10 = 30. Again half of 30 is 15. And last 36 +15 = 51.

Here 36 + 5/12 of 36 = 36 ( 1 + 5/12) = 36 ( 1 + 0.41667) is near to 36 root2

MATHS LAB

It is the explorations to seek how the subject could be utilised to equip one to work among a social group. More than 500 teachers were incorporated in the programme of workshops and laboratory setting. The spirit and enthusiasm shown by the teachers to equip laboratories in a classroom or varantha or even in a box was a matter of pedagogic attraction.

Vision of Maths Lab

Place to know and experience mathematics.

Decorated by TLMs and mathematical wall paintings.

Suitable place to constructions and experiments.

Availability of enough working tables with tools and equipments

within the reach of student's hands.

Bulletin boards and Math magazines to share their findings.

Availability of essential reference books.

Use available space effectively.

Length = 6 units = 6 ones =6(1) = 6

Length = Eleven ½ s = 11( ½ ) = 11/2 = 5 ½

Length = twenty one ¼ s = 21( ¼ ) = 21/4 = 5 ¼

Concept of Fraction

Addition of fraction

5 + 3 = 5 ones + 3 ones = 8 ones = 8 ½ + ¼ = two ¼ s + one ¼ = three ¼ s = ¾ ½ + 1/3 = three 1/6 s + two 1/6 s = five 1/6 s = 5/6

Mathematics Residential creative camps

(organized in more than 400 schools by inter relating the possibilities of construction and elements of

theater in education.)

Prerequisites for visualizing a mathematics concept 1.How the content need to be re manifested in the transition from abstractness to practical level ? 2.Which is the most suitable moment for the presentation ? 3.Which are the latest techniques to be used for visualizing the content.?

Process of class room theater – 3 stages

1.First one is preparation for performance. In this session of pre-discussion, there is a need of minute level analysis of the selected concept and presentation strategy in the group with the help of teacher. 2.Next is the stage of performance. 3.The last one is the zone of post discussion to review the whole presentation and make clarity in the level of concept and practice. (here it is must to ensure the active participation of students and teacher in the discussion.)

Theatre in Education

TIE do not focus on performance It is the process leading to performance Teacher should explore the scope to transact the text using theatre Teacher should be vibrant , alert and inspiring It is a prominent tool to enhance creativity.

Here Child identifies learning as his own need Scope of free interpretation Promote critical and creative thinking

The study camps with special focus on problem

solving

To think differently To visualize beautifuly To interpret logically To relate the observations to the numerical terms skillfully

Ability to make geometrical construction, that is what demand by the situation of the problem Competency to identify the sequences among the data in connection with the problem Identify different types of the relationship among the data given and establish new relationships between the data we have Arrange given datas systematically Use suitable eauations and tables Solve the problem by solution of similler problem. .............................................................

Problem solving ability

Findings and inferences.

1.It is highly effective to analyse mathematical concepts for common

presentations

2.various interpretations of one and the same mathematical concepts are

highly comprehensible.

3.The application situation such as literature, culture, vocation, science etc.,

are highly conducive for communicating mathematical ideas.

4.It is possible to utilise maths labs as platform to work together and to

share effectively.

5.Theatre elements help in the learning of mathematics for leading to

interesting activities, for sharing ideas and observations with others.

6.Learning experiences based on problem solving help children to confront

with higher level mathematical issues.

THANKS

Narayananunni MP, Lecturer in Mathematics education

DIET Palakkad, Kerala.