Mathematical achievement is the best predictor of mathematics ability (Margaret et al). This means, that if you’ve succeeded in math before, you should continue to flourish. Furthermore, I believe the mental aptitude (general intelligence, g of IQ) necessary to understand “university calculus (The Fundamental Theorem of Calculus)” and “The Algebra (The Fundamental Theorem of Algebra)” is the same.
The Litmus Test
If you can read well, then, chances are, that you can do calculus. Research done by Klieme et al. in 2001, shows a strong correlation of r=.91 between mathematical ability in a literacy test vs a curricular test. This leaves the door open to the possibility of a connection between those two mental abilities.
Many people can do algebra and read well. The reason algebra is so easy is because it doesn’t have as many operators as calculus so it takes less time to master. Algebra asks us to imagine that there are mathematical objects, called variables, that can represent numbers and be used in formulas and equations.
Calculus is inherently more complex because it is a class of mathematics that includes all the mathematics that precedes it. Namely, algebra, trigonometry, and geometry. These courses are covered or introduced in the teenage years of a scholar’s life.
Many people believe a pre-requisite grade in these classes is necessary as proof of mathematical ability but that’s not true because latent ability exists (Walton, Spencer, 2009). Maintaining GPA is only necessary for university admission and to satisfy prerequisites.
If I Can Do It You Can Too
Take me as an example, I took trigonometry and pre-calculus in high school and got D’s. This was because I was crippled by a common self-destructive idea “D’s get degrees.” By the end of high school, my grasp of algebra was weak – namely, in the rules of logarithms.
Also – I completely missed the point on the fundamental theory of algebra. Trigonometry: the unit circle? Never heard of her. If you didn’t personally know me, then it would probably be a good bet that I couldn’t succeed in university calculus.
But I did. I passed university calculus. I even went all the way to calculus 3, multivariable calculus. Something I didn’t believe was possible before it happened.
The main ingredient to my success? My weak schoolboy axioms were destroyed and replaced with a new basic philosophy:
Service before self.
Excellence in all we do.
Yes, these are the Air Force core values, but the Air Force gave them to me and told me they were now mine too. I thought about them a lot over my 4-year term. Thinking this way made me stop doing the bare minimum.
I signed up for online school and had a long road ahead of me… I started with college algebra 1 and 2 in 2016 and didn’t regain the confidence to retry trigonometry and precalculus until 2020 (another story). Which I passed with a B and C respectively.
Then, in Spring 2021, in the office of my new home, I began a rigorous study of university Calculus/Analytic Geometry I at San Diego Mesa College with the famous professor Michael Brown. The book we studied was Single Variable Calculus: Early Transcendentals by Soo T. Tan. It was a rollercoaster and I was teetering on passing/failing the entire time. Sitting pretty with a C on final exam day, I took it, and it solidified my final grade as a B!
But how did I do it? How did I pass calculus I, arguably the hardest of the calculus series to pass?! I even went on and passed multivariable calculus (calculus III), and linear algebra; next on my list is differential equations.
How Did I Pass University Calculus?
I had a very powerful value system that acted as my foundation and helped improve my resiliency. Feel free to share your mindset and philosophy advice in the comment section below. Many people find that calculus is a barrier to their future. My system went as follows:
That is, do what is right when no one is looking. I never cheated myself out of learning by depending on calculators to solve my problems. This is a big mistake people make and many don’t realize it’s a short-term solution to a long-term problem. You should only use calculators and tutors to help your understanding of the subject. If you think “I’ll cheat now and learn it later” you probably won’t and it takes integrity to hold yourself accountable.
Service Before Self
This core value is personal to me, as it’s difficult to embody outside of the Air Force. The way I used it to succeed in mathematics was to realize that comprehension in mathematics was something larger and brighter than me. That striving to understand mathematics, even if painful, would make me better and stronger. That it is a noble and worthwhile endeavor, no matter what the pessimists or haters say.
Excellence In All We Do
Where A’s are our minimums. Ever heard someone say “no one cares about your grade”? This is an example of a pessimist and hater, and they have no place around excellency. Realize that striving for excellence is the only way to it and it’s a private endeavor. There will always be those who fail to embody a value of excellence in exchange for mediocrity and comfort.
In the Air Force, being excellent is not inherent to being an Airman. It’s an individual endeavor that shows in the character of the Airman. In their workmanship and sharpness. They have pride in the way they present themselves.
In mathematics, that means truly understanding the theorems, rules, laws, and definitions. Never questioning the utility of any foundational knowledge to calculus. To have an undying trust that every page you read is a building block to your future self. To develop a personal mathematical aesthetic appreciation, style, and taste. Learn the history and development of ideas and where you stand in your throwness.
In the university, there are “C” students. The grownup version of the “D” student in high school, a shadow of my former self, I must admit. Where the new mantra for them is “C’s get degrees.” They will have you believe that they’re so brilliant that they’ve concocted a plan to beat the system and get the same “job” as the A students. Maybe they believe the idea that “C students manage B students who manage A students.”
This is because there is currently a romanticism of the misunderstood average class of scholars who never tried. After all, the system wasn’t built for the real world. That A students are under a silly spell that convinces them to desperately cling to their books, words, and numbers – unprepared for reality. Not like this hero – the anti-mathematician.
Let us agree that those who strive to destroy or shun an individual’s pursuit of enlightenment is enemy of the enlightenment. That they may partake in pursuit of the higher goal at our side but never bring us down to their level. Whatever virus has extinguished their flame, let it stay with them.
If you’ve shown a minimum mental and technical aptitude, be confident that you can pass university calculus. It will take work and sacrifice. Succeed by having a good value system like is taught in the Air Force; have integrity, a sacrificial attitude, and always strive for excellence. If it’s good enough for the world’s greatest Airmen, then it’s good enough for a young scholar. Don’t listen to the pessimists and haters, they will drag you down and make you feel terrible for being drawn to the light. Persist forward and never give up and you will pass university calculus.
Margaret M. Gullick, Lisa A. Sprute, Elise Temple, Individual differences in working memory, nonverbal IQ, and mathematics achievement and brain mechanisms associated with symbolic and nonsymbolic number processing, Learning and Individual Differences, Volume 21, Issue 6, 2011, Pages 644-654, ISSN 1041-6080, https://doi.org/10.1016/j.lindif.2010.10.003.
Walton GM, Spencer SJ. Latent ability: grades and test scores systematically underestimate the intellectual ability of negatively stereotyped students. Psychol Sci. 2009 Sep;20(9):1132-9. DOI: 10.1111/j.1467-9280.2009.02417.x. Epub 2009 Jul 29. PMID: 19656335.