I used to be a rebellious kid who loved literature but despised math and science. It’s ironic that I now find myself immersed in complex mathematical concepts and working as a professor of engineering.
Changing my mindset and becoming proficient in math was no easy task, considering my struggles throughout school. I only started studying basic math after leaving the Army at the age of 26.
My personal journey exemplifies the potential for adult neural plasticity, the brain’s ability to change and adapt.
Learning math and science as an adult opened doors for me in the field of engineering.
This experience also gave me valuable insights into the neurocysticercosis underlying adult learning.
My background in systems engineering and subsequent research on human cognition helped me make sense of recent advancements in neuroscience and cognitive psychology related to learning.
Throughout my teaching career, I’ve encountered countless students who were taught to believe that explaining and discussing their knowledge is the key to understanding math
Consequently, despite the intention to give equal importance to procedural skills, fluency, and application, they often receive less attention.
This overemphasis on understanding can be problematic since students may grasp the basics of an important idea but lack consolidation through practice and repetition.
Furthermore, students may mistakenly believe they understand a concept when they actually don’t, leading them to fail due to illusions of competence.
Learning math and science shares similarities with learning a sport. Just as a golfer perfects their swing through repetitive practice, understanding the “why” behind mathematical and scientific concepts frees us from having to repeatedly explain the “how” to ourselves.
We don’t need to keep counting marbles or recalling complex steps when multiplication becomes intuitive.
With enough practice, procedures and formulas become ingrained in our memory. By engaging in diverse problem-solving, we develop a deep understanding of both the rationale and execution of mathematical procedures.
Paradoxically, constantly focusing on understanding alone can hinder this process.
I gradually built neural “chunks” or subroutines that I could easily recall from long-term memory. This process of practice, repetition, and memorization formed the foundation for true understanding and fluency.
Experts in various fields, including mathematics and science, have emphasized the importance of building expertise through repetition and practice.
Fluency precedes understanding, and a deep understanding of complex subjects can only be achieved through fluency.
Unfortunately, in the field of math and science education, there is often a tendency to prioritize understanding while overlooking the value of repetition and practice.
My language learning experience revealed that understanding alone is not enough.
Fluency requires rigorous practice and familiarity with the subject matter.
As I pursued my new career in engineering and became a professor, I left the Russian language behind.
However, many years later, when I embarked on a trip across Russia, I discovered that my fluency in Russian had not vanished.
Despite feeling like a 2-year-old initially, my foundation allowed me to improve day by day.
In moments of need, the fluency resurfaced, helping me navigate and communicate effectively.
This active approach to learning, commonly seen in Japan, is highly regarded and emulated.
However, what often goes unnoticed is the significant role of methods like the Kumon method in Japan, which emphasize memorization, repetition, and rote learning alongside developing mastery.
Many parents in Japan and worldwide supplement their child’s participatory education with structured practice and intelligent rote learning to build fluency.
In the United States, the focus on understanding sometimes overshadows traditional teaching methods that have proven effective in helping the brain learn complex subjects like math and science.
The introduction of the Common Core standards aimed to establish consistent and rigorous benchmarks across the country.
However, critics argue that these standards fall short compared to high-achieving countries.
On the surface, the standards appear sensible, advocating for equal emphasis on conceptual understanding, procedural skills, fluency, and application in mathematics.
However, the devil lies in the implementation details. In the current educational climate, memorization and repetition in STEM subjects are often dismissed as demeaning and time-wasting.
Many teachers prioritize conceptual understanding, which can be easier to foster through discussions, rather than grading math homework.
I gained my understanding of math and the learning process outside of traditional K-12 education.
As a young person, I had a passion for literature and languages, which led me to study language at a prestigious institute.
However, financial constraints pushed me to join the Army instead of pursuing a college education. In the Army,
I found myself drawn to the field of engineering, inspired by the problem-solving abilities of West Point-trained engineers.
At the age of 26, after leaving the Army, I decided to embark on a new journey and learn the language of calculus to explore the world of engineering.
Given my limited math skills, I started with remedial algebra and trigonometry, even though it was far behind what most college students were learning.
Drawing from my experience in learning Russian as an adult, I recognized that fluency was crucial, not just understanding. In language learning,
I focused on developing a deep-rooted familiarity with words and language structure through repeated practice and interaction. I applied the same approach to math and science.
When encountering an equation like Newton’s second law, I would internalize its meaning, memorize it, and play with it, similar to conjugating a verb.
Reflecting on the shortage of math and science majors and our current approach to education,
I believe we can do better. By using accessible methods that deepen understanding and make it practical, we can encourage ourselves and others to embrace disciplines that may initially seem challenging.
Developing a basic fluency in math and science is crucial, as it opens doors to exciting career opportunities.
Looking back, I realize that my passion for literature and language was intertwined with my love for math and science,
ultimately enriching and transforming my life.