Why is Algebra Easy but Calculus is Hard
Math can be challenging. You may have noticed that it's harder for some people than it is for others. This is especially true of Calculus and other advanced mathematics classes. Before I ever took Calculus, it sounded like the hardest thing I had yet to do. However, Calculus doesn't have to be the monster that we make it out to be in our heads. In fact, I asked over 200 calculus students: Is calculus hard to learn? Here's what they said.
"Depends on who is teaching it and how interested the student is."
-Liam Slivka
"It is when you don't know algebra."
-Jon C. Whelpley
Is Calculus Hard?
In a poll of 222 Calculus students, most of them, about 68.9% said that Calculus is not hard to learn. However, as Liam Slivka states: "[it] Depends on who is teaching and how interested the student is." According to the Calculus Survival Guide, students should spend 12 hours per week studying. The students who fail Calculus are the ones who don't put in the time to learn it.
Many students, including myself, have struggled with Calculus because they're lacking in the fundamentals. However, if your Algebra and Trigonometry skills are lacking, you shouldn't be discouraged. Most students have gaps in their knowledge that they must fill. You may have to work at it, but you can improve on your weak points. Ideally, before you take Calculus.
Math is sequential, which means that the stuff you learned in the last class is used to help you learn the stuff in the next class. You wouldn't learn to multiply before you could add, would you? If you decided to attempt it, you would probably feel like half the students in my class who don't have the fundamentals down.
If this sounds like you or sounds like it could be you once you take Calculus, don't worry . There's plenty you can do to prepare yourself for what's to come. If you want to know how to prepare for Calculus, scroll to the bottom of this article .
Is Calculus Harder Than Algebra?
Calculus is harder than algebra. They're about the same in terms of difficulty but calculus is more complex, requiring you to draw on everything you learned in geometry, trigonometry, and algebra. Calculus is built on top of these previous courses so without the solid foundation all around, you're doomed to fail Calculus.
If you did well in algebra and trigonometry, you will do well in calculus. These concepts are used and expanded on in Calculus. Everything from graphing, to factoring, to solving for a variable will be used. The challenges faced in earlier courses will be equal to the challenges you faced in previous courses because you've since grown and expanded your mathematical ability.
Think of it as climbing a staircase. If you want to climb 100 steps, you wouldn't try to go from the ground straight to the hundredth step. Instead, you climb each step, step-by-step, making each equally as challenging as the last.
How Many Students Fail Calculus?
According to the Mathematical Association of America, 25% of students on average in America don't earn a high enough grade in Calculus 1 to move on to the next course. One 2015 study from Western Michigan University showed a failure rate of up to 40% for Calculus 1 in the Spring semester of the same year. To read up more on the WMU study or to learn more about the MAA, check below.
Joshua Ayerdi: Relative Rates of Success of Students in Calculus I
Mathematical Association of America: About
From this information, you could easily make the presumption that Calculus is certainly not easy, but it's really not that simple. These numbers don't necessarily speak to the difficulties or ease of Calculus. They speak to the countless other reason why students fail Calculus.
Why Do Students Fail Calculus?
The reasons students fail calculus are numerous. However, I don't want anyone to be discouraged by looking at this list. My intention is to prevent you from making any of these mistakes or at least minimizing them. I've already talked about how a lack of fundamental math education can be detrimental. It's the primary reason students fail. Aside from that, here are the other reasons:
– Not putting enough time into studying.
– Not doing enough practice and homework problems.
– Not paying attention in class and taking quality notes.
– Thinking they don't need it, so there's no point to learn it.
– Thinking that Calculus is not important.
As you can see from the list, the reasons people fail Calculus stems not only from people not doing the work or not knowing their fundamentals. It also boils down to having the right mindset going in. If you knew that Calculus was important to your future, you would have no problem paying attention in class, taking notes, and doing practice problems.
If you want to pass, you'll be willing to work for it. And if you work for it, you will pass.
Why Is Calculus Important?
Calculus is important because of all the real-world applications that it has. Calculus makes many things possible, and many more things easier. For example, in business, Calculus is used to maximize revenue and minimize production costs.
If you'd like to know more about the uses of Calculus, check out my article:
What Is Calculus Used For? (Real-Life Applications)
If you think you don't need to learn Calculus because you'll never actually use it, you might be right. At least about the part where you never use it. However, there's actually a good chance you will use if you plan on working in any science field. Besides, why would you want to put any limitations on yourself or your potential? What if you change your mind about your future plans? It happens… All the time.
Derivative Vs. Integral
The difference between the two is that the derivative shows the instantaneous rate of change of a function while the integral shows the area under the function with respect to the x-axis. These are somewhat opposites, as the integral of a function is also known as the 'anti-derivative.' Differentiation is learned in Calculus 1 and Integration is learned in Calculus 2.
For the record, if you only have to take Calculus 1, consider yourself blessed. Calculus 2 has many more new concepts than the former, making it a notoriously difficult class. This is the class where math boys and girls become math men and women.
If you think you need to have a solid foundation with the former, you will certainly need it with the latter. When you don't master the skills in one class and move on to the next class, you get 'holes' or 'gaps' in your knowledge. These gaps accumulate and with each consecutive class.
How To Prepare For Calculus
First, fill any gaps in your math knowledge that may be essential to learning Calculus. This means Algebra and Trigonometry. Do this before your Calculus course begins. Once you've started class, read the syllabus. Do your best to learn the assignment list for the list so you can start getting ahead on your homework.
Yes, you heard that right. It's not enough to simply do your homework on time. At least not if you want to really excel. Not to mention, if you're a week ahead on all your assignments, what's stopping you from taking a week vacation right in the middle of the semester? Not much. More importantly, you have some room just in case of some sort of emergency. Stuff does happen.
Calculus Resources And Tools (Top 10 List)
If you like to brush up on Algebra and Trig, there are some great resources in my article above. After you brush up on the basics, it would also give you a serious competitive advantage to read #4 the list below. The good news is it's a quick and fun read.
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