In this short blog, we discuss conceptual understanding in math. We also try to learn conceptual understanding with simple tips. Educators continuously talk about conceptual math. And why conceptual understanding in mathematics is essential?

Moreover, the “Common Core Standards” in math stress conceptual understanding in math. Educators feel it offers better ways of understanding math concepts. At the same time, many math teachers neglect its importance. They think if students learn all the definitions and rules, they can solve math problems.

In simple terms, conceptual understanding in math definition is knowing the core subject concepts. That helps students solve mathematical questions more efficiently.  
 

What is Conceptual Understanding In Math?

What is Conceptual Understanding In Math?
Conceptual understanding is an integrated and functional knowledge of math. Students with conceptual understanding know more than just rules and problem-solving methods. That means students are not only taught how to solve the problem. But they learn the way behind it.

Students understand the ideas behind math concepts and their contexts. They can organize their knowledge in a big framework. That means they can learn new ideas by connecting them with ideas they already know.

Conceptual understanding in math also supports retention. Because students learn math rules and facts by understanding them. That helps them to use and remember easily whenever required. In the meantime get the best My Math Lab Answers for top grades. 
 

Why is Conceptual Understanding Important In Math?

Why is Conceptual Understanding Important In Math?

When students are passionate about something, they tend to explore it in multiple ways. The same is true while solving math questions with conceptual understanding. Here is why conceptual understanding is important in math:

Focus on Foundational (Conceptual) Knowledge: 

Conceptual understanding helps students apply higher-order thinking. That means students learn to solve complex math problems with abstract understanding.

Students Learn To Visualize: 

If students learn through visualizing math, it will significantly affect the learning process. With this strategy, students properly understand what the problem is asking.

Moreover, you can learn more about the math major in this blog.

Develop Strategies Instead of Methods: 

It’s easy to lose interest in math solving math problems with rules and formulas. However, by step-by-step process and providing real-world applications, students learn more. They start making the strategies for solving math problems. 

Explore Multiple Ways For Solutions: 

There are always many ways to solve math questions. With conceptual understanding, students develop their own processes while solving math problems. This way, they build a strong mathematical foundation. 

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What Is an Example of Conceptual Understanding In Math?

Here are some conceptual understanding in math examples:

1. A three-digit number is always bigger than two digits number.

Some primary students will always be sure that 4.34 is bigger than 5.4. Because it has got more digits. As in the first few years of learning, they have learned only whole numbers. And, here they are applying the concept of the “digits” rule. 

2. While multiplying two numbers, the answer is always bigger than the original two numbers.

This rule again applies to the whole numbers. But when students come across numbers like 1/2 and 1/2. The result will be half of a quarter.

3. Just add 0 while multiplying any number with 10.

However, that is not true. When you multiply 0.25 x 10 or 0.34 x 10, that means we should try to stop this rule. And instead, offer concepts behind multiplications.

The examples given above are examples of conceptual understanding. But, knowledge of rules and process is not exactly a conceptual understanding.

However, it is much more than that. The students must learn which rule or idea to apply in a specific situation. The students must demonstrate understanding of:

  • Which math concepts or ideas are essential. And why are they important?
  •  Which concept is helpful in a particular context for problem-solving?
  • Why and how do concepts help in problem-solving?
  • How an idea or procedure is mathematically defensible? Why it is justified while using.
  •  How to flexibly adapt previous knowledge to transfer to new problems.

 

How To Develop Conceptual Understanding In Math

How To Develop Conceptual Understanding In Math

Conceptual understanding is all about How To Overcome Math Anxiety? Here are some simple tips for developing a conceptual understanding in math:

Belief

Educators need to develop self-belief in students. It will help them implement a conceptual understanding in math questions. Besides, students must develop math ideas. Moreover, they know how to apply ideas and rules to a specific problem.  

Sense-Making

The students should evaluate how their solution makes sense. Here the educators play a major role in developing sense-making in students. It’s always better to teach them to construct viable arguments and reasoning. Rather than making them learn the easy math tricks to solve problems. This way, students will conclude their own. It will also improve their creativity, visualization, and problem-solving skills.

Scaffolding

The learning process should start with easy numbers, equations, and concepts. If the numbers become more difficult, students can easily lose interest. The easier numbers are the best starting point, and we can include the bigger numbers with time. Also, maintain challenging thinking. Here, students will learn to connect earlier concepts with later ones.

Time

Students can develop conceptual ideas in a day or two. It results from repeated exposure to specific math ideas in various contexts. Students need to struggle, and that struggle will gain them the math concept. This process requires time, regular practice, and dedication. The learning objective should remain consistent for a week or two. Till students internalize a specific concept.

Multiple Representations

Educators should engage students in mathematical ideas through graphs, lists, or math notations. Developing conceptual understanding means providing students a chance to select the representation. Narrowing to one representation can sometimes make things challenging for students. Moreover, it won’t encourage students to expand their thinking. Conceptual understanding makes you learn How To Be Good At Math!  

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Conclusion

Developing conceptual understanding in math is not a single-day task. The teachers and students need to work together to get better results. Educators need to apply innovative learning techniques. So that students can expand their thinking and critical abilities. Students must allow using their math knowledge to come to the solutions. This will bring mathematics more close to them.

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What is conceptual understanding in a general context?

Conceptual understanding means an integrated and functional knowledge of math ideas. Students applying conceptual understanding know more than isolated math facts and procedures. They understand why a mathematical idea is essential. And apply them in the kinds of contexts in which it is useful.

How do students demonstrate conceptual understanding?

When students provide evidence, they can recognize, label, and generate examples of concepts. It is the use and interrelating models, diagrams, and manipulative and varied representations of ideas. Moreover, identify and apply principles. Know and apply facts and definitions.

What is an example of conceptual understanding?

Students learn a “borrow and regroup” routine for multi-digit subtraction problems. Conceptual knowledge means an understanding of meaning. That means knowledge that multiplying two negative numbers yields a positive result is not the same thing as understanding why it is true.

What is the difference between procedural understanding and conceptual understanding?

Procedural knowledge involves understanding the rules and methods of math. At the same time, conceptual knowledge consists of understanding mathematical relationships. Procedural knowledge is a series of steps that must be followed to solve mathematical problems.

Alice Walker
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