Math: rote learning vs. conceptual learning

rote learning

It’s undeniable that mathematics is an important skill in everyday life. Everything from telling the time to shopping for groceries requires the ability to recognize numbers and mathematical principles. 

However, when it comes to children learning math, there are many ways to approach it. Is it necessary for children to practice reciting their multiplication tables until they know them off by heart or is it more beneficial for them to tackle word problems that approach math in a more conceptual way? 

In order to answer this question, it is important to understand what kinds of thinking both forms of practice utilize and develop, so that you gain a better understanding of what your child might respond more to as well as how you can best assist them. 

Read on for a more in-depth look at how we can train our kids to be proficient in mathematics. 

Rote learning 

Rote learning refers to the practice of using repetition to drill information into your child’s memory. One example in the realm of mathematics is having your child practice reciting their multiplication tables over and over again, until they have memorized them to the point that they can answer multiplications at random. 

How rote learning works 

As you may have guessed, rote learning relies on your child’s memorization ability. This is in contrast to conceptual learning, where your child learns to understand the math problem and puzzle it out to reach the answer. Rote learning requires your child to recognize the equation put in front of them and connect it to the answer stored in their mind. 

Since rote learning is dependent on your child’s memorization ability, your child’s memory is going to be instrumental in how much your child can gain from using this method. 

Improving memory 

Memory is like a muscle – the more you work it out the stronger it gets. The SHICHIDA Method employs various activities and techniques to help your child develop their memorization skills. With SHICHIDA your child can learn to use various memorization techniques such as eidetic (or photographic) memory, mnemonics, and auditory memorization. 

Check out how SHICHIDA at Home can help develop your child’s cognitive ability from the comfort of your home, all while facilitating that all-important bond between parent and child.

The benefits of rote learning 

Did you know that repeating information in your mind can have a profound impact on your brain’s plasticity and memory capacity? This is the power of rote learning. By practicing words, numbers, or patterns over and over again, you can enhance your brain’s ability to form and recall memories. Plus, rote learning can lead to longer retention of concepts – even for a lifetime! This is why we as adults are able to instinctively recall the Alphabet Song or our multiplication tables. 

Rote learning is great for learning fundamental skills, such as letters, phonics, sight words, numbers and even simple arithmetic. Without learning these building blocks, it will be difficult for children to apply them at a conceptual level. 

Rote learning is the cardio of education 

If we compare academic learning to learning to play a sport, we may gain a better understanding of how important the fundamentals are. If we wanted to become good at tennis for example, we need to practice our forehand, backhand, and serve. However, on a more fundamental level we need to condition our muscles to be able to perform these actions. We need to work on our cardio so that we have the stamina to continue playing until the completion of a game. And to enhance these fundamental abilities, we need to do repetitive strength training. 

This is essentially the same reason rote learning is important. In the same way that your tennis game will suffer if your muscles lack strength, if your child is unable to recognize numbers, the fundamental building blocks that form the basis of mathematics, then they will never be able to solve equations.  

Approaching rote learning the right way 

Just like running laps or lifting weights, rote learning is repetitive in its nature. If approached in the wrong way, it can become dull, tedious, and put your child off learning. Therefore, it is important to know how to approach rote learning the right way, so that your child can still have fun while applying this kind of repetitive practice. 

Use songs 

Songs and music are a great way to apply rote learning. Not only are songs fun to sing and dance to, but they also make information easier for your child to store and remember later. This is because they are applying their auditory memorization skills to memorize large amounts of information. By connecting the information to a musical tune – and in some cases dance moves – your child can memorize a lot of useful fundamental information. 

Songs can be used to memorize the alphabet, the colors in the rainbow, the multiplication tables – even something as complex as the constant Pi. 

SHICHIDA at Home utilizes many songs and animations to help your child memorize core concepts, while having a blast singing and dancing along! Check out how SHICHIDA at Home can help develop your child’s cognitive ability from the comfort of your home, all while facilitating that all-important bond between parent and child.

Add a tactile element 

Adding a tactile element to your child’s learning always helps reinforce learned knowledge. Using their hands helps children concentrate and also helps connect knowledge in their mind. Using tactile elements when you implement rote learning is no different. 

Try this when your child is learning how to write numbers. Point to the number and say the number with your child: “5”. Then help your child run their finger along the lines of the number to practice writing it, once again saying “5” as you do so. Finally let your child use their pencil to trace or write the number. Confirm their understanding by asking what number it is: “5”. 

As your child gets older, the level of the activities will become more advanced. However, having children use their hands to complete activities will always be beneficial. For example, if you are practicing multiplication tables, recitation is good, but it is important to also use worksheets every now and have them write the answers down to reinforce their knowledge. 

Mix it up! 

Rote learning is repetitive – that’s why it works. However, too much rote learning can have a negative effect on your child’s desire to practice. If they feel burnt out, bored, or unstimulated by these activities, they will lose the excitement of learning. 

That’s why it is important to use a variety of activities that help your child understand how they can apply the skills they are gaining through this rote learning. If your child is tired of solving addition equations on a piece of paper, give them a Story Problem to try to figure out. Tell them a story that involves addition and if you are able to, use something they can see and touch such as toys or real-world objects to reinforce your story. 

This is where conceptual learning becomes important. 

Conceptual learning 

Math is more than just crunching numbers in everyday situations. It’s about being able to think critically about problems and using what we know about numbers to solve them. Learning math gives us the power to solve problems, both simple and complex. Sometimes, creative solutions to problems must be explored in order to arrive at the correct answer. 

While rote learning can be quite effective in acquiring the building blocks of mathematics, conceptual learning is what is needed to apply math to everyday life. 

For example, your child may be able to tell you quite easily what the answer to 8 x 5 is. However, when faced with the same equation in the context of a more organic scenario, they may fail to understand the connection. 

“I am having a birthday party and I want to give each of my friends a bag of lollies. Each bag will have five lollies in it. How many lollies to do I need to buy to have enough to give each of my eight friends a bag?” 

Now, your child may have memorized their five times tables so they can give you the answer to 8 x 5 without hesitation. But without understanding what this equation actually means, they cannot solve the problem above. This is why conceptual learning is important. 

How conceptual learning works 

Mastering mathematics on a conceptual level is just like any form of problem solving – it requires thinking critically and creatively. 

Critical thinking 

Critical thinking goes beyond just memorizing facts and accepting everything you hear. It involves scrutinizing information and questioning its validity. By learning to ask questions such as: “How do we know?” and “Is this true in every case or just in this instance?” your child can joyfully explore beyond black-and-white thinking. 

This type of thinking can be developed at a young age. SHICHIDA at Home engages your child with hands-on activities that will build trust in intuition, navigate varied information, understand diverse perspectives, and even ask thought-provoking questions. 

Check out how SHICHIDA at Home can help develop your child’s cognitive ability from the comfort of your home, all while facilitating that all-important bond between parent and child.

Creative thinking 

Creativity is a valuable skill in today’s world. It means being able to see patterns and solutions that are not immediately apparent and finding new ways to tackle old problems. With lateral thinking as a tool, your child will be able to bring fresh perspectives and innovative ideas to their work.  

Creative thinking isn’t limited to artistic types. Creative thinking is a skill that anyone can nurture and develop. SHICHIDA at Home offers various Image Training activities that centre your child and allow them to practice creative visualization, as well as problem solving tasks that get them thinking of creative solutions to puzzles. 

Check out how SHICHIDA at Home can help develop your child’s cognitive ability from the comfort of your home, all while facilitating that all-important bond between parent and child.

How to practice conceptual math 

Understanding mathematical word problems can be challenging at first, particularly if your child has gotten used to thinking of mathematics in terms of just numbers and symbols. 

Here are some tips to ensure that your child can understand how to apply mathematical formulae to everyday problems: 

1. Start early

It is never too early to introduce your child to mathematical word problems. Start very basic and use real world objects to demonstrate the problem for your child. 

For example, “Mommy bought one apple and two bananas. How many pieces of fruit are there altogether? Let’s count them. One, two, three! There are three pieces of fruit altogether!” 

By seeing the fruit in front of them and counting the fruit with mom and dad’s help, your child can visualize and thereby understand the math problem as they hear it. 

This leads to our next tip: 

2. Visualize or model the problem

When your child is tackling word problems, get them thinking creatively by treating them like real-life stories or situations. Encourage them to act them out, sketch visual aides, and create models that bring the problems to life. For younger children, try using real world objects like toys or counters to model the problem. 

In certain situations, it may even be beneficial to remove the numbers from the scenario entirely, so that your child can understand the situation without focusing too much on the numbers. 

3. Practice identifying the question

As children get older, the word problems they are given to solve will become more complex. Just like in real life, they need to be able to identify the information that is relevant to solving their problem. This requires an understanding of what the question actually is. 

When your child is old enough, try giving them this problem: “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?” 

This problem is designed to get your child thinking about the problem, not in the sense of numbers and math but in a more critical sense. Giving your child these kinds of trick questions every now and then will allow them to practice identifying the question and figuring out that they do not have the information necessary to answer it. 

Combine rote learning and conceptual learning to succeed 

As you can see, in order for your child to succeed in math it is important to utilize BOTH rote learning and conceptual learning. Conceptual learning will teach your child what questions they need to ask to find the answer. Rote learning will give them the fundamental skills to arrive at the answer. 

References 

Attard, Catherine. “Promoting Creative and Critical Thinking in Mathematics and Numeracy.” Engaging Maths, Engaging Maths, 25 June 2017, engagingmaths.com/2017/06/25/promoting-creative-and-critical-thinking-in-mathematics-and-numeracy/. 

Doyle, Alison. “What Is Creative Thinking?” The Balance, 14 Apr. 2022, www.thebalancemoney.com/creative-thinking-definition-with-examples-2063744. 

Singh, Manpreet. “Advantages and Disadvantages of Rote Learning.” Number Dyslexia, 22 Sept. 2021, numberdyslexia.com/advantages-and-disadvantages-of-rote-learning/. 

“What Is Critical Thinking? | Math for Liberal Arts: Co-Requisite Course.” Courses.lumenlearning.com, courses.lumenlearning.com/cccs-coreq-mathforliberalarts/chapter/module-1-overview/. Accessed 8 June 2023. 

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