By Braden Weaver
When it comes to school, there is always those questions that absolutely stump you, whether it be a test or a homework problem. In my almost 18 year career as a student, it has got to be one of the worst feelings to be completely blank and have no clue where to begin. My previous mindset was “well its either I know it or I don’t”. Please DO NOT try this it could result in bad grades. The better way to come up with the answer is to try and remember past lessons that have similar concepts to the problem at hand, then start breaking down that problem in order to solve it. This is where conceptual knowledge comes into play. Conceptual knowledge refers to the knowledge of, or understanding of concepts, principles, theories, models, and classifications. Now you’re probably thinking “how on earth am I going to be able to do this in a limited time?”. The process of connecting a lesson to another lesson is a lot quicker than you think. There are actually a few ways you can boost your conceptual knowledge to make you a better student guaranteed! One of the first ways is to be able to group things just by looking at them. For example, look at the picture below. Just by looking at it you can already tell what those objects are. That’s right, they’re vegetables! The second way you can better improve your concept skills is to be able to make connections between things. If I had a list of broccoli, zucchini, and celery, it would be easy to put all of them in a Venn diagram to find out differences and similarities between the three vegetables. Lastly, students like yourself can transfer the ideas that you can get from vegetables and use it to find something more important. For example, which vegetable is considered the healthiest? Just something that is a little more complex.
Moving on from vegetables, math is very important when it comes to conceptual learning. It is known that many kids in upper level math classes are only satisfied with using algorithms and finding the answer without actually knowing how they got the answer. I don’t know about anyone else, but once I got to college, I didn’t care about how I got the answer as long as it was right. Math is really a struggle for most students as it is quite hard to understand the concepts. Conceptual knowledge can come in handy whether it be simple addition and subtraction, or even something a little more complex like square roots and square of a number. To start off all of your tired little brains, lets do an easy subtraction problem. What is 72-69? Students in lower grades would have to take away from the 7, so you have 12-9 and 6-6, which leaves you with 3. It’s the right answer, but that’s what’s called procedural math. Conceptual math would be to have (60 +12) – (60 + 9). Here you can cancel out the 60s and you’re left with 12-9 which is easy enough. It may not mean like much, but at a younger grade level, it is helpful to understand that large numbers can be composed into smaller numbers to make problems easier.
Let’s take it a step further into something closer to college level speed. Learning the concepts for square roots can be a little tricky, but once you step back and break down the numbers it becomes easy. An example problem could be “what is the square root of 48?” Now I know you’re thinking, “that isn’t exactly an answer” and you’re right it’s not. There are many answers, but the best way is to figure out what two numbers equal 48. Off the top of my head I think square root 16 x square root 3 = square root 48. To break it down even further the square root of 16 is 4. It can also be easy to realize that no two somethings multiply to equal three, so it will remain as square root 3. The final answer will be 4 square root of 3. This is really one of many answers and what is unique in math is that there can be many different approaches, which exactly fit into conceptual thinking.
It can be told that once students reach high school they have acquired their own preference of learning, and at the pace they want. They also tend to lean towards a certain kind of instruction. The whole point of conceptual knowledge is to bring a different kind of approach to a problem, not following some sort of algorithm or equation to answer. Use previous knowledge and your own experiences to help you. If you’re a younger college student reading this just remember, it is always helpful to relax, take a deep breath, and have confidence in your academic ability. I promise that it will help you with any assignment or test that you do.
References:
Bauer, Susan Wise. “Conceptual & Procedural Math: What’s the Difference? – Well-Trained Mind.” Well, 8 Aug. 2016, welltrainedmind.com/a/conceptural-procedural-math-whats-the-difference/?v=7516fd43adaa.
“Conceptual Knowledge in the Workplace.” Training Industry, 30 July 2020, trainingindustry.com/glossary/conceptual-knowledge/.
Marschall, Carla. “3 Ways to Boost Students’ Conceptual Thinking.” Edutopia, George Lucas Educational Foundation, 10 Sept. 2019, www.edutopia.org/article/3-ways-boost-students-conceptual-thinking.
“Read ‘Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools’ at NAP.edu.” National Academies Press: OpenBook, www.nap.edu/read/10129/chapter/8.
“Teaching Square Roots Conceptually.” The Bearded Math Man, 19 Oct. 2019, onteachingmath.com/teaching-square-roots-conceptually/.