Conceptual Understanding - What is it?

[Tyleralp1]

Hey all,

As the title says, what exactly is conceptual understanding? I've heard many people on this forum is a really good way to learn the information in VCE. I've even thrown around the term myself, but actually have no idea what it means to be frank. So what really encompasses this term of "conceptual understanding"?

Thanks!

[lolalol]

From what I gather, conceptual understanding is basically understanding WHY things work/are the way they are. It's really understanding the reason behind what you're doing, as opposed to just rote learning an answer/a method of solving a problem/an equation (this is often referred to as procedural fluency).

For example (I see you're doing chem), you're given the mass of substance and the molar mass of a substance. You know that to find the number of moles of that substance you have to use the equation n=m/M (aka number of moles = mass divided by molar mass). That's procedural fluency. But conceptual understanding is understanding that molar mass = the mass of 1 mole of substance, therefore dividing the mass of a substance by its molar mass gives you the number of moles. As in, if you have 18g of substance which has a molar mass of 18g/mol, you've obviously got 1 mole of that substance.

Hope that makes sense hahah! Good luck for the rest of the year.

[keltingmeith]

Let me enlighten you with an example around maths - in particular, the derivative.

So, what is the derivative? Well, you multiply by the power and subtract one from the power, right? If the derivative equals zero, you have a stationary point! And if the derivative is negative, the graph goes down, and if the derivative is positive, the graph goes up!! Man, you could answer any question with this kind of knowledge!!!

... But, you've managed to define a bunch of different scenarios where knowing the derivative is useful, without actually TELLING ME what the derivative is. Honestly, it's a really simple idea - the derivative is the gradient of the tangent to the curve. We can mathematically define this as the gradient between two points, and then slowly make the distance between those two points (take the LIMIT to) 0. If you understand what that means, and can interpret it well, you have a conceptual understanding of the derivative.


But that's too easy, yeah? What about DNA.

In DNA, the four bases (A, T, G and C [lel for never learning their actual names~]) are only seen in one pair - G with C and A with T. So, if you're ever given a one sided strand, you can find the other! Why, though? Because the textbook told you!

Wrong. They bond that way because they're connected by powerful, polar bonds - hydrogen bonds, to be precise. As such, to create a more stable connection, they only bond in those pairs. The reason those pairs are the most stable is because of the number of polar ends - G and C have 3, A and T have 2.


Okay okay, that's sorta obvious - we can get trickier, though. Let's look at an electric cell. Electrons flow from negative, to positive. Because that's the way electrons move, durr. They don't like negative, so they go to positive!

... But then, why don't protons move around? I mean, we can see the compounds in the cells act as lewis acids or bases, so wouldn't that also imply in aqueous batteries that protons could go flying around? Well, that's because electrons are smaller and WANT to move around. Even in reaction mechanisms, we only consider the electrons forming and creating bonds, because protons are just so heavy. So, we see the electrons go from negative to positive because they're so much lighter than the protons, so they move first, and that lowers the net positive charge, so all of a sudden the protons can't move to balance it out, because they're hitting a net zero and becoming happy.


THIS is what we mean by conceptual understanding. Not just memorising random facts to answer questions - being able to rationalise those random facts with your theoretical knowledge.

[note: used entirely science/maths examples because I feel too much people don't think conceptual understanding can be obtained in these topics, but they totally can, and you really should venture to understand the conceptuals in STEM subjects as well!]

[brightsky]

From what I gather, conceptual understanding is basically understanding WHY things work/are the way they are. It's really understanding the reason behind what you're doing, as opposed to just rote learning an answer/a method of solving a problem/an equation (this is often referred to as procedural fluency).

For example (I see you're doing chem), you're given the mass of substance and the molar mass of a substance. You know that to find the number of moles of that substance you have to use the equation n=m/M (aka number of moles = mass divided by molar mass). That's procedural fluency. But conceptual understanding is understanding that molar mass = the mass of 1 mole of substance, therefore dividing the mass of a substance by its molar mass gives you the number of moles. As in, if you have 18g of substance which has a molar mass of 18g/mol, you've obviously got 1 mole of that substance.

Hope that makes sense hahah! Good luck for the rest of the year.

This is pretty much spot on. Here are a few examples in the realm of maths:

- We all know that two straight lines are perpendicular if and only if the product of their gradients equals to -1. Why is this the case?
- We all know Pythagoras' theorem: c^2 = a^2 + b^2, where c is the hypotenuse of a right-angled triangle, and a and b are the other two sides. Why does the theorem hold?
- We all know that d/dx (x^n) = nx^(n-1), where n is a rational number. Why is this true?
- We all know that antidifferentiation is the reverse process of differentiation, and that differentiation can help us find gradients. Why is it, then, that antidifferentiation can help us find areas? Is area, in some sense, the opposite of gradient?
- We all know that Newton's third law of motion states that every action has an equal and opposite reaction. Why doesn't this mean that all objects are in static equilibrium?

If you are able to answer all of the questions posed above, then you have conceptual understanding. If you are unsure of the answers, and are only able to apply the theorems to solve problems, then you've only got procedural fluency. It is possible to go through VCE with just procedural fluency, but I find that having a certain degree of conceptual understanding makes learning new things easier.

[Tyleralp1]

Thanks all so much for those explanations! Its good to see somewhat varying interpretations of "conceptual understanding". Thanks for all the examples, particularly yours EulerFan101.

So in a nutshell, it's basically understanding the full reasoning behind a process?

So like the Textbook tells me Lipids are not a polymers. But to conceptual understanding I would need to know that the reason is because a polymer is a chain of many repeating smaller units (monomers) and the limitations of the condensation reaction of the fatty acids (two for phospholipid and three for triglyceride) is the reason why it cant from polymers?

Though I'd have to say for some areas it's a bit half and half. Like if Brightsky is on point with those questions..Conceptual Understanding seems a bit more than neccessary, as well as extra learning as I'm sure a textbook wouldn't tell you those answers?