Michio Kaku explained Conceptual Understanding in his keynote speech at ISTE 2016 that educational development and teaching methods frequently follow technological breakthroughs and waves. As new waves of technology emerge, teaching and learning expand in breadth and depth across grade levels to meet the wave’s need for skills.
As the fourth wave of technology approaches—the quantum era—Kaku calls for a revolution in education, arguing that the way students are taught must change. So, how can we educate future generations to prepare them for careers and life in a technologically advanced world?
We agree with Kaku that shifting the focus and teaching for conceptual understanding is critical.
What is Conceptual Understanding
Conceptual understanding, or the ability of children to grasp ideas in a transferable manner, can assist students in applying what they learn in class across domains. It’s a hot topic in the classroom these days, as rote memorization and traditional methods of teaching math are seen as inadequate for real-world learning and application.
While teaching to the test is common for state accountability and measurement, it does not always provide students with the skills they need to complete tasks outside of the classroom.
Brown and Kane found that when preschool children were encouraged to use previously taught and demonstrated solutions, they were more likely to transfer skills across situations. Rather than being given an explicit rule, they learned best when they saw examples of solutions.
In a similar vein, when it comes to math or another academic subject, children should be able to make decisions based on an emerging understanding gained through witnessing example solutions, rather than an explicit rule that only covers one problem or one way of answering a problem.
Conceptual Understanding in Math
Math is highly regarded, and learning math is highly valued all across the world. Most of us have certainly heard of conceptual programs and conceptually oriented issues when it comes to studying arithmetic. Furthermore, the significance of conceptual thinking as a major component of arithmetic learning has been highlighted over time. Before we get into why conceptual knowledge is vital, let’s first define it.
What is Conceptual Understanding in Math?
The word “conceptual understanding” refers to a thorough and practical understanding of mathematical principles. Conceptually aware children are aware of more than isolated facts and procedures. They understand why a mathematical topic is important and how it may be used in a variety of contexts. They form their knowledge into a logical framework that enables them to acquire new concepts by relating them to what they already know. Comprehension the ideas also aids retention since facts and procedures learned via understanding are easier to recall and use, and may be recreated if lost.
Teaching students not only how to do something, but also why they should do it, is what conceptual thinking includes. Children can perceive the wider picture that underpins all arithmetic themes and activities through conceptual knowledge, helping them to think more fluidly, apply their math abilities in a variety of circumstances, and employ higher-order thinking skills.
This was demonstrated by the findings of Gao and Bao’s investigation, which revealed:
Students enrolled in concept-based learning environments outperformed those enrolled in traditional learning settings. In fact, pupils who learned conceptually like the learning methods more, with a higher comprehension and transferability resulting from a better grasp of concepts.
The Importance of Conceptual Understanding in Math for Children
While most people believe that conceptual learning is central to higher education and is necessary in later grades, this is not the case. Conceptual learning is a novel method to conceptual thinking that focuses on the “why” and “how.”
Many conventional learning contexts, for example, require youngsters to remember multiplication tables. When youngsters learn multiplication tables by repetition and can only retain them by memory, they are certain to become stuck, repeat them again, or even panic since they have no resources to assist them locate the solution.
However, if they are taught multiplication through a conceptual framework, they will understand that multiplication involves repeated addition. So they realize that 8 x 4 is 8 multiplied by three. Children might then use the skills they learned for repetitive addition and counting to multiplication, division, and a variety of other tasks. The solution to the multiplication table would eventually occur to them naturally, without the need for any memorizing techniques or supporting procedures.
Conceptual comprehension can also help students overcome arithmetic anxiety and gain confidence in their math ability. This is true even for youngsters who are not normally apprehensive but become concerned when faced with particular circumstances. Consider math word problems. When they face a complex word problem, many youngsters may become anxious. However, via conceptual knowledge, students may use the notion to discern what the word problem means, reason rationally, and effectively use what they have learned to solve any difficult challenges they may confront.
When youngsters solve issues using memory, they may become stopped when confronted with a complicated equation or while demonstrating a hypothesis. When children comprehend concepts, they see that solution techniques may not be as important as they think because they understand how equations operate and the minor things that may be brought together to generate the greater notion. With this insight, individuals can devise alternative approaches or approach a hard problem in a new way to find a solution. As such, conceptual knowledge entails knowing both concepts and how to link to them in an integrated and ordered manner.
According to studies, concept-based learning based on an inductive and inquiry-led method improves mathematical ability and comprehension.
Children can benefit from developing conceptual knowledge in arithmetic in a variety of ways. This will help youngsters acquire confidence in their abilities to solve arithmetic problems and enhance their computational skills, which will assist them as concepts and problems get more complicated throughout their academic careers. Children with a strong conceptual basis learn to think and reason for themselves rather than depending simply on memory aids.
When people perform in the workplace, they frequently act based on prior knowledge, assumptions, and understandings about a specific situation. They make intelligent decisions about what to do, which often has to be done in an exploratory, innovative manner, especially if the situation is novel. Most of the time, people will lack all of the necessary information and will need to be explicitly told how to make the correct decision. This is where conceptual understanding and associations come into play.
If students are not exposed to this type of exploratory learning as young learners, they will lack the necessary skills to apply situations to everyday problems. We can teach our students everything they need to know, but unless they are building on, analyzing, evaluating, or having the opportunity to be creative with this knowledge in a relevant way and making associations, they will not develop the ability to deeply understand and transfer knowledge to make educated assumptions about new situations.
When information is unavailable, people must rely on conceptual understandings and associations formed about similar concepts to make decisions. As Kaku predicted, the fourth wave of technology is on its way, and it will be completely new, so we must prepare our students to make decisions and use deeper understanding to process new information.
How is Conceptual Understanding Attained?
It does not have to be difficult to combine academic learning, assessment, and soft skills. As Kaku mentioned in his keynote speech, information can be taught in a variety of ways, including MOOCs and robots, as well as the Internet, people, and more. Robots can replace the way information is taught or basic tasks are performed, but creativity, experience, and underlying structures may be more difficult to replace.
What needs to be taught that hasn’t previously been emphasized is the common thread that runs through concepts, the underlying structure of information, and how ideas are related. To accomplish this, we must expose our students to real-world examples of professions and embed the learning within them.
Effective teaching activities must incorporate real strategies that students will use in the real world, just as an effective learning game incorporates learning into the core mechanics of the game. Instead of simply teaching memorization and facts, we must prepare students to form thoughtful opinions and decisions based on abstract ideas, just as they would in a future profession.
One method for getting people to understand something is to take what they’re interested in and have them investigate it as if they were professionals in that field. Project-based learning and exploratory units are excellent ways to approach conceptual understanding, especially in a school district that may not have the resources to pursue personalized learning.
Instead of giving your students facts and dates in social studies, ask them to approach history as an anthropologist — read books as a historian seeking to understand why an event occurred, and identify people groups, traditions, and customs as an anthropologist. When students can put these ideas together, they are learning to recognize underlying patterns and cause and effect.
As author Warren Berger discovered, children enjoy having their questions answered, which fuels their desire to learn more. We can address this in the classroom by encouraging curiosity. In a science unit, have your students investigate a hypothesis as if they were scientists. Inquire about how scientists approach new ideas, and whether they are tested. What do they study? What information do they require? Develop an understanding of how cells work in addition to knowing about cells and what they do. Making these connections early on will provide them with the critical thinking and investigative tools they need to make sound assumptions.
They generate curiosity and more questions when they ask great questions. They gain a deeper understanding as they ask more questions. We must present students with situations that have common threads so that they can begin to learn patterns and underlying structures by asking questions on their own.
Promoting Equity by Improving Conceptual Understanding
While knowledge and facts are important for a student’s success, the ability to make connections is even more important—but often underdeveloped because testing does not typically assess it. Traditionally, standardized testing has measured a student’s ability to memorize information and quickly plug in formulas, and when students are unable to perform in this manner, they are placed lower than others and given special attention. In the real world, however, skill memorization and the specific score a student receives may not be indicative of his ability to perform or use prior knowledge to make an informed decision.
When we teach for comprehension rather than memorization, we level the playing field and provide students with the skills they need to succeed in the future. The ability to transfer skills and knowledge will be far more valuable than memorizing information that may become irrelevant, and making this the primary focus will relieve students of the burden of memorizing information apart from how it can be applied in a project or real-world setting.
Although biotechnology, nanotechnology, and artificial intelligence are all new concepts, there may be underlying patterns and existing ideas that can be applied to how we approach new developments. We teach students to find patterns and think like professionals by teaching for exploratory, conceptual understanding. When we do this, we are preparing students to succeed beyond a standardized test and to face the fourth wave head on.