The Importance Of Conceptual Understanding For Math & Science
Many people have the misconception that just memorising facts can help in exams. While memorising can aid in language subjects, such as History or English, the main disadvantage is that it does not allow for a deeper understanding of the subject, which is what Math and Science require.
Math and Science often need the students to apply concepts and formulas to solve questions. A case in point: one of the teachers mentioned in the magazine The Atlantic that he asked his first trigonometry class, “What is the sine of π/2?" The class promptly told him it was one.
While the class answered it correctly because they memorised the standard formula, he later discovered that they did not understand what “sine” even meant.
Without conceptual understanding, which is what Math and Science need, is like learning that “Brutus killed Caesar” without knowing who either party was, or what “kill” even means.
What is conceptual knowledge?
Conceptual knowledge is understanding the fundamental principles and the relationships among them. This highlights two crucial factors that can help students develop conceptual understanding in class: allowing students to “struggle” with problems and discussing the relationships among the concepts taught.
These approaches aid students in developing the ability to apply their skills and knowledge in new contexts. Conceptual knowledge development is dependent on the teacher’s approaches since they are the ones that provide the students with explanations and problem-solving strategies.
Conceptual understanding will help the student choose and apply the right process for a situation and to incorporate new information correctly, adding to what they already know.
To grasp Math and Science concepts, students should learn with understanding, actively build new knowledge from experience and past knowledge, and reflect on their thought processes. That is why conceptual understanding is considered inseparable from Math and Science, and is considered an essential competency.
How conceptual knowledge helps in Mathematics (E-Maths, A-Maths)
Conceptual understanding in Mathematics will mean an integrated functional grasp of mathematical concepts. Students will know more than just the formulas and methods, why the concepts they are learning are essential, and how they can be of use. Organising their knowledge into a coherent whole helps students learn new topics quickly by connecting them to the topics they have already learned.
One thing about conceptual understanding is that students can represent mathematical situations in various ways and how it can be used for different purposes. If students figure out the relationships between multiple facts and methods learned, the formulas will be easier to retain and use. Moreover, they can be reconstructed if forgotten, so they are unlikely to remember the formulas wrong.
Let’s take a simple example of students having to solve simultaneous equations. They may try to draw up something that will allow them to figure out the values of x and y or use other concrete materials to show their working.
In attempting to convert x into y or y into x, the students may be able to arrive at a standard measure for both x and y and determine the value. However, the representations they draw up can differ.
By comparing the different representations, students are likely to use different solutions, allowing them to discuss the similarities and differences, the advantages, and how they are connected if they can come up with the same answer.
This helps them to extend the known concepts and procedures to learning new topics, such as when learning substitution and elimination for Additional Math’s simultaneous equations.
For example, students who have learned the ins and outs of sine, cosine and tangent and how they work are likelier than students without that understanding to come up with their procedures to be able to work backwards and prove that one equation is equal to another when the question calls for it.
How conceptual knowledge helps in Science (Physics, Chemistry, Biology)
One interesting thing to note for Science is that students are not blank slates when they first learn that subject. On the contrary, they already have an intuitive understanding of the physical world, even though it can contradict the scientific concepts and theories taught in class.
Nevertheless, evidence supports the claim that students' intuitive concepts are relatively stable and deeply held. A researcher named McCloskey proved that when it comes to Physics, people have systematic beliefs regarding the motion of objects that affect their interactions with real-world objects.
However, not all intuitive theories the students hold can be considered unitary and systematic. Should that intuitive theory be false, they may also have false beliefs and mental models, constraining the students’ logical skills and the nature of simple explanations, increasing misinterpretations of scientific information.
As a result, students may rely on generalised versions of what they already know to produce misconceived simple explanations for specific scientific processes, such as heart transfer and diffusion, for which a simple answer will not be enough.
In this case, conceptual understanding is needed for the students to organise facts and ideas they learned or already have into meaningful concepts. This can assist students in aligning their intuitive thoughts with scientific ones to make meaningful connections. Therefore, students can apply their conceptual knowledge to multiple scenarios.
After all, their initial understandings are “knowledge in pieces”, so it is up to the students to put the pieces together to solve the puzzle. This allows students to grasp the knowledge and explain theories while backing up their claims.
Conclusion
In Math and Science, conceptual understanding is better than memorising to remember the concepts. During exams, it is likely that questions would be slightly modified to throw students off.
If students can grasp how to apply the concepts rather than remember what it is at face value, they have a higher chance to adapt and figure out the solutions to these questions.
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Our O Level online tuition in Singapore provides personalised and interactive teaching that can suit your child’s pace. What sets us apart is that we make learning enjoyable, so students can grasp concepts better and apply what they have learned to new challenges. For more details, check our website or contact our number.