Notes: Community of Mathematics | Mathematics & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET PDF Download

This chapter emphasizes that by selecting a common mathematics task or problem, a classroom community is developed where students share their ideas and solutions, fostering a sense of coordination and cooperation. It also discusses various methods for facilitating student discussions and analyzing solutions.

The subject of Mathematics can be understood in an efficient way through the communication in the community of teachers and students. It is the mathematical communication through which the students reflect upon, clarify and expand their ideas and understanding of mathematical relationships and mathematical arguments. 

For example: Students of a particular class are divided into a number of small groups and then allowed to create different solutions to a lesson problem and after that present their solutions to their classmates. By this way a certain community develops in the class among the students through which they share their ideas and knowledge among the peers. Thus, by choosing Mathematics tasks and problems evoking significant Mathematics and prompts students to discuss their mathematical thinking, the student’s mathematical communication can be established. The establishment of student’s mathematical communication transforms in precision and sophistication throughout the primary, junior and intermediate grades.

The characteristics relevant to all the grades are as follow:

1. Precision: It shows the problem’s detail, relevant choice of method or strategy to solve the problem and its accurate calculations.
2. Assumptions: It shows that the details of the mathematical task or problem are addressed in what manner in the solution. 
3. Clarity: It shows the reader’s ease of comprehending the solution of the problem which requires the reader’s inference in the minute extent. 
4. Cohesive Argument: It shows the interplay of mathematical examples alongwith explanations, diagrams, graphs and tables or charts. 
5. Elaboration: It shows the justification of mathematical ideas and strategies with proper and significant mathematical details.

Categories of Mathematical Communication

• Expression and organisation of mathematical understanding and learning. 
• Different types communication for different audiences (e.g., Peers, teachers). 
• Using conventions, vocabulary and terminology of the subject in oral, visual and the written format. 
• The students can be evoked to organise, reorganise and strengthen their mathematical ideas and thinking by means of listening, talking and writing about Mathematics. 
• In this way, the students can analyse, evaluate and build on the mathematical thinking and strategies of others. In order to develop student’s mathematical understanding it is desired for the teachers to carry out various mathematically based pedagogical moves in parallel as given below Making students aware of how to take part in mathematical discussion. 
• Making mathematical visual records of the class discussion for all the students to see. 
• Using mathematical notations or symbols in order to record student’s mathematical thinking.

Coordinating Student Discussion and Analysing the Solution

1. Gallery Walk

• Gallery walk is an interesting discussion technique that takes students into a situation of more focused and active exchange with other student’s mathematical ideas and understanding.
• By means of analysis and response the gallery walk prompts students and teachers to mathematically engage with a range of solutions.

It is generally carried out after the solutions have been generated by the students either on computers or the pieces of paper. As there are a number of forms of gallery walk, some of them are as follow:

1. Small Group Problem Solving: In this form of gallery walk, the students in small groups develop one solution to the lesson problem on chart paper.
2. Small Group Discussion: In this form of gallery walk, the solutions are rotated among the groups and it continues until all the solutions are analysed and responded to by all groups. Comments are accumulated for each solution that are reviewed by the groups for any further comments.
3. Teacher Observation: While students are engaged in discussing their classmate’s solutions, the teachers moves around the classroom tapping student’s understanding and noting student’s use of Mathematics vocabulary and symbolic notation.
4. Whole Class Discussion: After coming back to their own solution, the groups formulates the comments, questions and suggestions for the development of an oral report that would be presented to the whole class. The small group oralreports furnish the significant details which the teacher can use to highlight and summarise key mathematical ideas and strategies related to the lesson learning goal.

2. Math Congress

• Math congress is a Mathematics instructional strategy developed by Fosnot and Dolk. The primary objective of the math congress is to develop the mathematicians in the classroom learning community.
• It enables the teacher to make students more focussed on reasoning about a few large mathematical ideas derived from the Mathematical thinking embeded in the student’s solutions. Thus, the math congress does not show each solution of the problem, on the contrary, it focuses whole class discussion on two or three, strategically selected, student solutions in order to develop every student’s mathematical learning.

3. Bansho (Board Writing)

• Bansho, in Japanese, literally means board writing. The purpose of Bansho is to organise and record mathematical thinking derived from and collectively produced by students on a large size chalkboard or dry erase board.
• The use of mathematical expressions, figures and diagrams of student’s solutions and strategies to a lesson problem are included in the board writing. This written record enables simultaneous comparison of multiple solution methods and the students can construct new mathematical ideas and strengthen their mathematical understanding. As the chalkboard is a written record of the entire lesson, the students and teacher can have a whole view of the class’s mathematical discussion throughout the lesson.

Values Related to Mathematics 

1. Moral Values: Morality is the important phase of life which is most effected by time, person, situation and place. Mathematical knowledge is helpful in character and personality development. It develops all those qualities which a person of strong character must possess. Child develops qualities of cleanliness, reality, punctuality, truthfulness, honesty, loyality, justice, dutifulness, self-control, self-reliance, self-confidence, patience. 
2. Social Values: Man is a social animal and human life depends upon the cooperation of each other. In order to live a social life, its knowledge is needed because the give and take process, business and industry depends upon the knowledge of Mathematics.
3. Cultural Values: The culture of every nation or society has its unique characteristics. The history of Mathematics presents the image of culture of different nations. The person becomes critical observer, logical thinker and proper knowledge of Mathematics changes the mind of the person. Thus the person becomes more cultured with the proper knowledge of Mathematics.
4. Disciplinary Values: Mathematics is not meant only for development of mental abilities but also to develop their personality with some qualities like concentration, truthfulness, seriousness etc. That is why the disciplinary value of Mathematics is also important. 
5. Psychological Values: Mathematics education is also useful from the point of view of psychological aspects. Mathematics fulfills the psychological needs of the children. The teaching of Mathematics follows the various laws and principles of psychology. For example, The child acquires knowledge on the various principles of psychology such as-learning by doing, learning through experiences and problem solving, etc.

Value Related to Scientific Attitude: The knowledge of mathematics trains the children in attempting the problems according to a definite and distinct procedure which may be called as the scientific method. Scientific attitude involves open mindedness, critical observation, suspended judgement, free from superstition and false belief etc. Thus, the training which a child receives in studying Mathematics can be applied to solve the problems arising in new situations.