Techniques of Teaching Mathematics

Mathematics teaching and learning have been a top priority in education. Several commissions and committees have underlined the importance of improving mathematics techniques of teaching. The National Education Policy (1986) emphasises the importance of mathematics as a tool for promoting creativity.

As a result, traditional methods of mathematics instruction that depended mainly on rote learning and drill have been replaced by methods that rely on exploration and problem-solving approaches. 

Mathematics Pedagogy is a significant topic in the Mathematics portion of CTET, UPTET, REET, HTET, and other TET examinations, which is worth 30 marks per paper. In this article, we have described the numerous approaches and techniques for teaching mathematics according to the syllabus, which will assist the teacher in most successfully planning instruction in the classroom.

Different Methods of Teaching Mathematics

• Induction & Deduction

Mathematics is experimental and inductive in nature. Induction is a type of reasoning in which a general law is formed from studying specific objects or processes. The child can utilise measurement, manipulative or constructive activities, patterns, and so on to find a relationship they will later symbolically represent as a law or rule. The law, the norm or definition devised by the child, is the sum of all specific or individual cases. The evolved generalisation is viewed as a tentative conclusion in every induction.  

• Analytic & Synthetic Methods

Analysis and synthesis are methods of discovering relationships between entities that use thinking and arguments. Synthetic Euclidean geometry is a good example of a framework that works by deduction. It helps people learn to think clearly and reason well. In every proposition, there is a hypothesis and a conclusion. The hypothesis can be the information in the statement or a set of axioms, definitions, principles, or relationships that have already been proven. The conclusion is the result to be proved or arrived at.

• Heuristic or Discovery Method  

The modern way of teaching maths focuses on meaning, understanding, and how it can be used. The “traditional” or “drill” idea is different from this.

Children should understand and care about what they are learning. Under the “drill” idea, they are told the facts, which they remember by doing them over and over again. In “meaningful” learning, the child helps find the answer. He thinks about it. He discovers how things are connected by doing, experimenting, and participating in events. 

All discovery methods are closely tied to real work or problem situations that show the child how inadequate his or her current schemas are. Second, teachers who use the discovery method should help the child have a good attitude and learn how to use controlled settings to test their ideas and find new connections.

Different Techniques in Teaching Mathematics

• Drill & Practice

Mathematically, the drill is one of the most important ways to learn. All tasks used to teach have one main goal: to make learning a habit. Getting good at something takes making it a habit, so drill practice is an important part of getting good at something. Most practice lessons fall into three categories. The first type of lessons for success is those that teach basic skills, such as multiplication tables, addition combinations, fractional equivalents of decimals and percentages, factorization, construction in geometry, etc. These include the subject matter, which must be learned well in order to learn quickly and correctly in the future. 

For a drill lesson to be effective, the following things should be taken into account: 

1. Drills should come after students learn and understand the basics. It shouldn’t make people think that they should memorise things without understanding them. 
2. Drills should be different. Some boring and regular tasks can make learning uninteresting.
3. Each student should be able to do drills in a way that is useful to them. Every child should understand why and how it works. 
4. There should be short practice sessions, and the learner’s progress should be checked often. 
5. Drills shouldn’t be set up just to keep students “busy.” It should be based on events that make you think, so that you don’t just do the same thing over and over. 
6. Drill can also help teachers figure out what’s wrong with a student. 

• Oral & Written work

Oral work helps each child work at the best speed for him so that he can be as accurate as possible. Work should be done orally and in writing in any lesson, especially if modern practice or worksheets are used. Oral work is a quick drill that helps you get used to a basic process, way of thinking, or set of facts. It helps get more work done in the same amount of time.

But written work is needed when a teacher needs to check each child’s work or when she wants the kids to practise working on their own. Throughout written work, accuracy in computation, legibility of figures and symbols, speed, the right algorithm, which is the logical and sequential order of steps in the answer, neatness of work, and correctness of results should be kept in mind. Written work can also be saved as a group record, which can be used to see how far a student has come over time. 

• Play way technique

The Play Way method, also called teaching through games, is the most modern way to teach maths. A game is a planned action that the students do under the teacher’s supervision. Even though games can only teach certain math ideas, the most important thing that games like quizzes, puzzles, guessing games, etc. are good for is drilling or practising different math ideas out loud.  

• Assignment & Homework

Planned assignments, which are based on each child’s growth and encourage each one to learn independently, have replaced the idea of homework in recent years. One of the most important parts of teaching is planning the task. It is part of a learning activity that involves setting up a task and finding the best way to do it. Teachers think that the best way for students to learn is to do things on their own.

Here are a few aspects of a good assignment: 

1. The task should be clear and unambiguous. It should be short but clear enough for each child to understand what they are supposed to do. 
2. It should predict problems with the work that needs to be done and offer ways to solve them. 
3. It should compare the new lesson to things you’ve learned in the past and link the topic to everything else related to it. 
4. It should be interesting, let the student want to do something and let them think as well.  

• Unit Planning & Lesson Planning

A unit is a chapter segment that helps guide the lesson plan. A unit ensures that the subject matter makes sense and that the learner’s wants, interests, and ability to learn are considered. 

The way information is grouped into units has many benefits: 

1. a) The teacher is in charge of the lesson plan, and the students carry it out with the help of teachers and other students.
2. b) Units cover more than one subject, which makes it easier to see how different parts of maths and other subjects are related. So, learning is more integrated and less scattered. 
3. c) Different tasks and experiences are offered to meet the different ways people learn. The child is not forced to learn. d) Practice is more useful, and problem-solving skills are better when they are learned in real-world settings. 

So, this encourages students to think critically. 

A unit usually has three parts: (1) the goals or objectives, (2) learning situations to help meet these goals, and (3) tests to see how well the goals have been met.

Planning a lesson means setting up a forty-minute time period for teaching. Since maths is a topic that builds on itself, each day’s lesson is needed to understand the next lesson. A well-planned lesson gives the teacher a sense of comfort, keeps them on track, stops time from being wasted, and makes it easy to move from one part of the topic to the next. It is best for the teacher to plan the lessons they want to teach beforehand, ideally at the start of each week. 

The lesson plan should have the six parts below: 

(1) Goals or goals, (2) background information or what you already know, (3) introductory or motivational activities, (4) growth activities, (5) a summary, and (6) a way to use what you’ve learned.

• Materials & Teaching aids

The textbook has been the main source of explanations, directions for processes and procedures, solved model examples, diagrams of quantitative relationships, practice tasks and sample test papers. A good textbook saves teachers time and effort. It also eliminates the need for the teacher to write down tasks and problems. The value of a textbook goes up if it has good pictures and diagrams.

Today, teachers use many learning tools to help students understand ideas and how they can be used. These include a) Materials made of concrete or semi-concrete, such as measurement tools. Some of these things are easy to find in the community, and others, can be bought. 

1. b) Field trips and displays. Through tours and trips, students can see how maths is used in the real world. Children find collecting pictures, newspaper articles, posters, and charts fun and useful. 
2. c) Construction work. Activities related to building can be a significant example to see how maths is used in it 
3. d) Moving pictures, film strips, and slides are all types of multisensory tools. 

Audiovisual aids help both the teacher and the learner interact in an interesting, quick, fun, and useful way. 

• Laboratory approach to teaching mathematics

We know that a lab is mostly used to teach science. Recently, this idea has been used to teach maths for the first time. People think it’s hard to learn maths it’s verbally taught.

Students learn by doing things in a classroom. They do projects, play with materials and models, and use different tools, which helps them understand what this math terminology means. In a lab, a child can see how much of what they learn in maths comes to life. The lab is a place where problems can be solved in settings that are like real life. In the lab, there should be wall charts, models, math tools, film slides and video tapes, and many things that can be touched and moved. 

In a lab situation: a) Learning is child-centred, not teacher-dominated. The practice is done by the students. The teacher guides or helps the students. 

1. b) The work is relevant to the learner’s life and important to them. 
2. c) The students are more interested because they work with real problems instead of just ideas. 
3. d) Many community resources are utilized as the subject matter is organized into functional activities.  

CTET Mathematics Preparation Tips

Follow these CTET Preparation tips if you want to be ready for the basic questions that are asked in the CTET exam, Paper 1 and Paper 2.

Sample Papers: Before the test, the CBSE will give out sample papers that you should work on to fully understand the type of exam, how it is set up, and how the questions are asked.

Pedagogical Concerns: Students should be well-versed in these topics because the mathematics exam will include pedagogy-related questions. It is critical to understand practical methods and their potential for teaching. You should learn about both formative and non-formative evaluation here.

Examine NCERT Books: Depending on the paper code, students taking paper I or paper II need to review NCERT math books from classes I through 5 or 6 through 8.

Practise Mock Tests: To do well on the CTET exam, you must know the previous year’s questions. There are mock tests on several websites. Sign up online for a CTET course or coaching.

How to crack CTET without Coaching?

Is it possible to pass CTET without support? This is a question that all CTET candidates have in mind. Candidates can prepare for the CTET Exam without attending any coaching sessions by developing an effective Preparation Strategy. CTET Preparation Tips might help candidates who desire to excel their exams. Students can appropriately prepare for their exams by following these study strategies. Students can use the following preparation techniques.

• Check the CTET Exam Pattern to see how many marks are awarded to each section and how many questions are covered in each area. Candidates can prepare successfully for the CTET Exam by understanding the exam format.
• Knowing the CTET Syllabus makes it simpler to prepare for the exam. The syllabus may include information on the most significant subjects of each subject covered in the exam. 
• Identifying your strengths and shortcomings is vital when preparing for the CTET. This helps you determine which topics demand more attention.
• Incorporating essential books in your CTET Exam Preparation is crucial to comprehend each exam topic properly. Only the CTET Books recommended by subject experts for each subject should be used for optimum preparation.
• Short notes and one-liners can help with CTET exam preparation. Always take short notes on each topic so that revising is simple throughout the exam.
• Collect appropriate study materials from past years, such as textbooks, reference books, and exam papers. Make sure you have reliable and up-to-date study materials.
• Make a study schedule and schedule time for each course and topic. Set attainable objectives and prioritise your study method accordingly. Take regular pauses to avoid burnout.
• Strong foundation: Depending on your exam, focus on creating a strong foundation in CTET essential topics such as Child Development and Pedagogy, Mathematics, Environmental Studies, Language (English/Hindi), and Science/Social Science.

Books for CTET exam preparation

The important mathematics books for CTET exam preparation are

• Mathematics & Pedagogy for Class I-V – Arihant Publication
• A Complete Resources for CTET: Mathematics and Pedagogy – Haneet Gandhi, Pearson Publication
• CTET & TETs for Class VI-VIII Mathematics & Pedagogy – Arihant Publication
• Mathematics and Science for CTET 2021 Paper II – Hankeet Gandhi and Yukti Sharma, Pearson Publication
• Mathematics Exam Goalpost (Class 1 to 5) – Wiley Publication
• Mathematics & Pedagogy (Class 6 to 8) – Disha Publication

Candidates can check the syllabus for other competitive exams at the links given below: