Some Ideas on Effective Strategies to Teach Math

Math is the most debated subject with almost everyone giving their opinion on how it needs to be taught. Most people believe that mathematics is about computation. You find them arguing not only for its place in the school curriculum but also emphasizing on the use of traditional methods of instruction in computation.

Teachers goals for instruction are interdependent on the beliefs and knowledge about pedagogy and subject matter. It is to a large extent, a reflection of what they think is important and how they think students learn.

If you teach elementary classes, then you find the responsibility of developing the interest in the subject as well as the burden of building fundamental concepts in young minds quite overwhelming.  Children move away from anything where they do not experience success.

From my perspective “Making Math Fun and interesting brings the child close to Math but what sustains the child’s interest is success in Math.” 

To achieve the goal of continued interest and success in Math, effective instructional strategies is important. So how do we make the teaching of Math effective?

Balance ‘Conceptual understanding and computational skills/procedural knowledge.

It is about balancing the “how?” and “why?”. The belief is that computation, the how of Math if the teacher can make the child understand the battle is won.  However, the fact remains that without understanding the “why?”, the “how?” is often forgotten.

The time taken to understand concepts differs in different individuals. For some, it would be immediate, while for some it may take days, weeks or even months and years. For example, we start teaching place value of numbers very early, right from preschool, but children understand this only partially first.  You might have seen them struggling to remember ones and tens place.  However, this understanding deepens over the years and by the time they finish elementary school, the concept of place value bothers them the least. 

This explains why the spiral approach is used in Math curriculum design.  The concepts keep coming back. This approach has its own merits however; it is not without pitfalls.  If a child doesn’t understand a concept, trusting the spiral approach and assuming that the concept will appear next year when the book comes back with the same concept is highly detrimental. The next year’s coursebook might not present the concept at the same level making it a little difficult for the child to grasp. 

The relationship between the “how” and the “why” – or computational skill and conceptual understanding is complex. We often have come across situations where the “how?” is learnt mechanically without understanding “why?”. This varies from child to child. Thus, conceptual understanding and computational skill often actually help each other.

Try often alternating the instructions.  For example, teach how to add fractions, and let the student practice. Then explain why it works. Give some practice again. Do a back and forth.  It might work or may not or may require more time. As a rule of thumb, don’t leave a topic until the student knows “how” and understands the “why”. Ensure success in the end.

Try checking for understanding through drawing

Pose a question like “State/Write an example of the addition of two 3-digit numbers and draw a picture of it”. With this, you test the student’s understanding of a concept by asking him/her to produce an example, preferably with a picture.  Whatever the student produces can tell the teacher a lot about what the child has understood.

Always define clear learning goals and student outcomes and remember them

We often come across these two types of learning goals. 

The learner should be able to:

{No} -complete the contents of the coursebook by the end of the academic year.

{No} – pass the annual tests.

{Yes} perform basic arithmetic operations

{Yes} add proper fractions.

{Yes} write multiples of 3, 4, and 5.

Specific short term learning goals help in setting up a proper progression for learning. 

For example, concepts of addition, subtraction, multiplication and division of fractions all connect with the goal of understanding part-and-whole relationships. The concept of fractions is important to master topics like ratios, proportions, per cent, etc.

Always remember the ultimate goal of school mathematics education, i.e., the students should be able to use math effectively in their lives. Young children need to be taught to be able to handle money wisely. They should be able to deal with credit cards, shopping, budgeting, etc.  For this understanding basic arithmetic operations, understanding fractions, proportions, percentages and interpreting data are very important.  

There are quite a few students who need to be prepared for further studies in Math and Science. Though not everyone will need Math, many professions do require Math skills.  It is very unlikely that young teenagers would always know what profession they might choose so they must master the required Math skills.

Finally, I would like to add an important goal that is to provide scope for students to appreciate the beauty of mathematics. For example, begin with appreciating the beauty of symmetrical structures. Don’t beauty and symmetry go hand in hand?

Keeping the ultimate goals in mind will help form a better connect with the learning goals you decide for your classes and the better teacher you will be.

Know the tools of both learning and assessment

The most important tool that one should not forget to use is the classroom board, the readily available teaching aids, and the book that is being used. The internet is a storehouse of resources: software, interactivities, animated lessons, worksheets, tutorials and games.

The quantity won’t equal quality. Knowing a few “math tools” inside out is more beneficial than a mindless collection and use of the activities to enhance the lessons.

Using manipulatives

“Should manipulatives be used or is it ok to not to?”

Use of manipulatives is often stressed these days. They are highly recommended as they provide hands-on experience to the child.  It should by no means be over-emphasized. The ultimate goal is to learn to do math without them. Manipulatives have to be used as an aid to building concepts.   

Use of Games

Games are useful for eliminating the boredom associated with rigour in Math. Games can be used to reinforce just any topic in Math. Card games, easy to make, help in paired work as well as group work.  The scope of developing social skills is a bonus here. At times a game is what’s worth a thousand worksheets.  Explore the online games on the internet and start using them during class or assign as homework.

Include sessions of guided discussion

It is often observed there is a strong connection between the teacher’s content knowledge and pedagogical content knowledge in planning and teaching math concepts. The success of a class highly depends on the teachers understanding of children as learners.

Let us discuss guided discussion in elementary classrooms.

Let problem-solving form the basis of most instructions in the classroom. Look for the scope of instructions around the activities that students do such as sharing snacks, water bottles placed on the stand, several students opting for lunch in the school canteen, celebrating birthdays and attendance for the problem-solving task. Allow students to spend time discussing strategies in pairs, in groups and then as a whole class. Participate in the discussion as a facilitator, but do not demonstrate the solution to the problem. A task, for example, write word problems and present to the class or design and play a math game can be given. 

During discussions, observe mentally and make notes of what the students know and think and be ready to modify your instructional decisions. Select a solution that is incorrect and present, so that a discussion can be initiated around common misconceptions.

These discussions should be enough for the teacher to gauge what her students know, what problems should be given to the next, based on what is important for the students’ progress.

Look for scope for Model-Based Reasoning

Modelling has been largely missing from school curriculum instruction. This is because concepts like spatial visualization and geometry, data analysis, measurement, and probability do not find enough representation. Scope of modelling ranges from kindergarten through twelfth grade (K–12). For example, most concepts in Geometry can be taught through modelling and provides large scope for deductive reasoning.  Model and teach Geometry as much as possible.

Exhibit a positive attitude towards Math, show your love for the subject

Your attitude as a Math educator matters. Do you like math? Do you practise mathematical reasoning? Are you happy to teach Maths and enthusiastic about it? This often shows up in how you teach Math.

Don’t limit Mathematics to just Math lessons based on the contents of the coursebook. Always keep handy some fun math books, puzzle books, etc. To be precise explore some interesting topics in Math beyond the school curriculum. Don’t forget the storybooks revolving around Math concepts. Readout to the children some history of Mathematics and mathematicians. Share often examples of how you use Math in your daily life. Keep throwing up situations that require mathematical problem-solving.

Reference and citations

“7 Effective Teaching: Examples in History, Mathematics, and Science.” National Research Council. 2000.

How People Learn: Brain, Mind, Experience, and School

The national academies of sciences, engineering and medicine.


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