Content Selection
Section 3.6 Pedagogy
Section 3.6
In any effective teaching-learning process, it is inevitable that the Teacher should employ im- pactful practices to ensure learning of the students. For this to happen, the Teacher should have the firm belief that all students have the potential to learn and do Mathematics. The Teacher should use culturally relevant practices and differentiated learning experiences to meet learning needs of the diverse students. The focus should be on the development of conceptual under- standing with procedural fluency, effective communication, creative problem solving, and other mathematical skills. Effective teaching practices in the mathematics classroom must be support- ed by an inclusive, positive, and safe learning environment, where students feel valued and en- gaged.
The teaching of Mathematics should be ground on this understanding of how children learn Mathematics. The rest of this section describes key instructional practices and methods that are useful in Mathematics teaching. It also describes the aspect of multi-level and remedial teaching that Teachers often encounter in Mathematics classrooms. Finally, it gives attention to how to cater to specific learning difficulties.
3.6.1 Instructional practices
a. Instruction should help students to understand a particular mathematical concept and encourage students to use various representations for deeper understanding of each concept, as each representation provides a different perspective.
b. The Teacher should focus on building understanding of the concept, encourage them to express their understanding in their own words using mathematical vocabulary and terms (including in their own home language when different from the medium of instruction).
c. The Teacher should provide opportunities to engage in meaningful discussions involving questions that require explanations (“How could you explain your thinking to someone just learning this?”, “How do you know?”).
d. Incorporate problem-solving tasks in classroom that encourage students to reason, communicate, represent, and connect, as well as justify their thinking.
e. Effective use of tools and representations (particularly pictorial or physical representations) can help students to think through a problem and devise strategies for solution. Tools and representations assist students in modelling situations concretely, pictorially, and abstractly.
f. Teachers should spend some time daily to support mental Mathematics and visualisation strategies, including solving questions involving computation that will help them build computational fluency, solving puzzles, answering riddles, and playing games.
g. Small group work can be effective for better learning and for promoting peer learning.
Group work may include problem solving, group discussion and reasoning, proving, etc.
However, it should be of small duration so as to manage the groups effectively.
h. Meaningful practice should be an integral part of the Mathematics classroom through the use of worksheets, puzzles, games, mental and oral Mathematics, group work, and homework involving paper and pencil. Practice should be meaningful and purposeful.
Teacher’s Voice B-3.6-i [to be edited]
Discovery-Based Method
My understanding of ‘Discovery-Based Method of Teaching’ is a teaching strategy in which teachers assist students in discovering mathematical facts and formulas through organized activities and observations. In this approach the teacher provides the neces- sary teaching materials and guides the students to carry out some activities which would lead the students to arrive at a new knowledge. Such discovery activities could be done individually or in small groups of students. This approach enables students to actively participate in the learning process and discover things for themselves. For instance, to teach the students that the sum of the angles of a triangle is 180˚, I asked students to draw their triangles, measure the three angles and add them together. The students would discover that the sum of the angles is 180˚.
Alternatively, I asked them to draw triangles on papers, cut out the three angles and arrange them together to form a straight line and the sum of angles on a straight line is 180˚. So instead of telling them the mathematical knowledge as just facts it is always better to apply discovery approach which enhances active learning in the mathematics classroom. Same exercise I repeat for sum of the angles of a quadrilateral is 360˚. Here, students are to draw any quadrilateral, measure the four angles and add to discover that it is 360˚. Then like they did for triangles I asked them to draw different quadrilateral and cut out the angles from the corners and join them to meet their all four vertices at a point without leaving any gap as shown below to form a complete angle i.e. 360˚.
Here, my emphasis is always on to design activities that help my students learn mathemati- cal concepts instead of just memorizing them as facts and formulas.
a. Play-way (activity based) method: Play-way or activity-based method helps in developing desirable attitudes and skills. It gives confidence to students. Many types of games and toys are now available to students which have their roots in mathematical concepts or ideas.
These games use patterns, quizzes, and puzzles. Many types of dominoes, number checkers, counting frames, patterns of magic squares, puzzle boards or blocks are now easily available or can be made locally. These may be effectively used for teaching in the classroom.
b. Discovery/Inquiry-based method: This method allows students to explore academic content by posing, investigating, and answering questions. It demands complete self-activity of self-learning on the part of the student. Through this method, the student learns to reason and that helps in the development of a scientific attitude. It also allows students to draw connections between academic content and their own lives, which can be particularly important for culturally and linguistically diverse students.
c. Problem solving method: Word and logic puzzles (including grid-process-of-elimination puzzles) are a fun way to teach deductive reasoning. Simple puzzles can help develop in students’ skills of logical and creative thinking in an enjoyable manner (DNEP 2020, Sec.
4.6.5 pg.93).
d. Inductive method: Inductive method is based on principle of induction. Induction means to establish a universal truth by showing that if it is true for a particular case and is further true for a reasonably adequate number of cases then it is true for all such cases. Thus, inductive method of teaching leads us from known to unknown, particular case to general rule and from concrete to abstract. When a number of concrete cases have been understood, the student is able to attempt for generalisation. Here only various facts and examples are presented to the students and from where they have to find out rules or establish a general formula.
e. Deductive method: Deduction is the process by which a particular fact is derived from some general known truths. Thus, in the deductive method of teaching student proceeds from general to particular, abstract to concrete and from formula to examples. Here a pre-established rule or formula is given to the student, and they are asked to solve the related problems by using that formula or to prove theorems using definitions, axioms and postulates.
All of the above methods are suggestive and have their appropriateness at different Stages and with students of different age groups. It is also true that one method does not work for all stu- dents and Teacher has to intelligently choose a combination of methods to ensure the learning of every individual. The matrix below has suggestive methods in rows and Stages in three columns.