Musings of an Old Chemist

A Chemist's Perspective on the Habits and Skills STEM Students Need For Success

Tag: education

The Grade Illusion: Why High Test Scores Don’t Necessarily Equate With Concept Mastery (And How to Fix It)
If you are an aspiring STEM student, or the parent of one, I want you to consider a terrifying possibility: It is possible to have a 4.0 GPA and know/retain almost nothing.

I saw this contradiction in the students I would tutor. They were bright, hardworking, and ambitious. They had mastered the art of getting the “A.” They knew how to take tests, follow instructions, and allocate their time to receive a high score.

However, if I asked them to apply a physics concept from two weeks before to a new problem assigned that day, they would freeze. Their knowledge of the material (data) was gone.

This is the Grade Illusion. We have built an educational culture – especially in high-stakes fields like STEM, where the “High Score” has become the product. But in the real world, the test scores from high school and college courses are irrelevant. The only thing that matters is mastering the content.

If you want to survive the transition from “A-student” to “successful scientist,” you need to understand how your own mind works. You need to stop renting knowledge and start owning it.

The Knowledge Retention Misconception: RAM vs. Hard Drive

To understand why intelligent students often feel like impostors, we need to examine how the brain stores information.

Think of your brain like a computer. You have two types of storage:
1. RAM (Random Access Memory): This is short-term, high-speed memory storage. It holds the data you need right now. It is volatile; when the power cuts (or the test ends), the data is wiped to make room for the next task.
2. The Hard Drive: This is long-term storage. It is slower to write to, but the data remains there forever, ready to be recalled years later.
The modern educational system encourages you to use your RAM, not your Hard Drive. We call this Cramming, or as we discussed in an earlier blog post, the act of memorization/regurgitation.

When you cram for a calculus midterm, you are loading complex formulas into your RAM. You hold them there—stressfully—for 24 hours. You walk into the exam, dump the RAM onto the paper, and get a 95%. You feel successful.

But 48 hours later, that RAM is cleared to make space for Chemistry. The “Save to Hard Drive” function never happened.

The Science of Forgetting

This isn’t just a metaphor; it is a biological fact. In the late 19th century, psychologist Hermann Ebbinghaus mapped the “Forgetting Curve.”

The curve shows that without deep processing (the struggle necessary to understand something), humans lose roughly 50% of new information within a day and 90% within a week.

The student who crams and gets an “A” peaks at 100% on Tuesday morning. By next Tuesday, their retention dropped to nearly the same level as that of the student who failed. The grade is a record of what you knew for one hour, not what you carry into your career.

From an economics perspective, consider this as the difference between Renting and Owning.
- Cramming is Renting. You pay a high price in stress and sleep deprivation. You get to “live” in the knowledge for a day. But once the test is over, your “lease” is up, and you are evicted. You have zero equity.
- Deep Learning is Owning. You pay a “mortgage” of daily, consistent study. It feels slower. It feels harder. But two years later, when you are designing a load-bearing bridge, for example, that physics principle is yours.
The Illusion of Competence

“But I got an A!” you might argue. “The test says I know the material.”

Does it?

In 1956, in the publication “Taxonomy of Educational Objectives: The Classification of Educational Goals,” a committee of educators chaired by Benjamen Bloom developed a framework to rank levels of understanding called “Bloom’s Taxonomy.”

Shutterstock

Most high school tests—and frankly, many college exams—operate at the bottom three levels: Knowledge (learn the formula), Comprehension (understand when to use the formula), and Application (plug numbers into the formula).

If you are good at memorization, you can ace these tests without ever moving up the pyramid. But a career in STEM fields lives entirely at the top three levels:
- Analysis: Why did the experiment fail?
- Evaluation: Which method is best for this specific application?
- Synthesize (Create): Develop an improved solution that isn’t in the textbook.
The Illusion of Competence

This creates the Illusion of Competence. You have a transcript full of “A’s” that certify you are an expert, but your internal drive has never been stress-tested at the “Analysis” or “Synthesis” level. When you eventually hit a problem that requires those skills, you don’t just struggle—you crash.

The most dangerous side effect of the Grade Illusion isn’t academic; it’s psychological.

The Performance = Identity Misconception

When you spend your entire life chasing the “High Score,” you begin to associate your Performance with your Identity. You believe the equation: My Grade = My Worth.

In STEM, this is lethal. In English class, a grade of “C” might seem subjective. In Physics or Chemistry, a “wrong answer” is objectively wrong. If you tie your self-worth to getting the right answer, every mistake feels like a character flaw.

You need to adopt the mindset of a Scientist:
- You are the Learning Process itself. You are the curiosity, the work ethic, the resilience.
- The Grade is just Data. It is simply the output of a single, specific experiment on a single specific day.
For example, if a Ferrari engine performs poorly because it had bad fuel, we don’t say the engine is trash. We say the input (fuel) was wrong. Similarly, if you fail a test, it doesn’t mean you are broken. It means your variables—your study habits, your sleep, your preparation—were off.

A bad grade is not your identity. It is guidance.

Breaking the Cycle

Ready to shift from being a “Grade Hunter” to a true “Learner”? Use these two simple techniques to pinpoint where you are in that transition and determine the necessary steps to move forward.

1. The “Two-Week Audit.”

I challenge you to a challenging experiment. Take a test you aced two weeks ago. Sit down and take it right now, without reviewing your notes.

The difference between your score then (95%) and your score now (55%) is your Fake (Lost) Knowledge. That 40-point gap represents wasted energy. It is time spent renting, not owning. If the gap is huge, your study method is broken, regardless of your GPA.

2. The Feynman Technique (The Ownership Test)

Physicist Richard Feynman had a simple rule for understanding, which he borrowed from Albert Einstein. To prove you have mastered a concept, you must be able to explain it in simple language, without jargon, to someone who has no background in the topic (like a smart 12-year-old).

If you can’t explain it simply, you don’t understand it. You have only memorized the definition. You are stuck at the bottom of Bloom’s Taxonomy.

The Bottom Line

The world is full of influencers and algorithms showing you the easy way to obtain a high test score on the ACT and achieve the most sought-after degrees, jobs, and accolades. Yet they rarely show you how to retain the knowledge required for long-term success.

Success in STEM requires three “old school” prerequisites that cannot be skipped: Curiosity, a Passion for Learning, and a Passion for Solving Problems.

If you have these, the grades will eventually follow. But more importantly, later in life, when the grades stop mattering, the expertise will remain.
January 4, 2026
The Impact of Calculators on Fundamental Math Skills
To follow up on my previous post, I cannot stress enough that four basic math skills: dimensional analysis, scientific notation, estimation, and significant figures – are prerequisites for anyone interested in math and sciences. Mastering these concepts helps stop the “operator headspace” mistakes that happen when you use your calculator as a crutch.

My biggest concern is that leaning too much on calculators is actually making students worse at fundamental math. For example, in the students I tutor, I’m seeing a drop in their ability to do mental math, a poor sense of estimation, and a failure to build that crucial “number sense” – that gut feeling about how numbers work and whether an answer makes any sense.

It’s a bit disappointing to me when I can perform math functions such as addition, subtraction, multiplication, division, and PEMDAS calculations faster and more accurately in my head than my students can on their fancy $100 calculator.

Therefore, the question I’m asking is:

“When kids let the calculator do the work, do they skip the mental practice needed to really lock in these vital skills?”

What Do the Experts Say?

Educational research points to a broader consensus: the impact of calculators isn’t automatically negative. The general feeling among experts is that when calculators are used correctly, they don’t inherently make students less capable at math. Instead, they suggest that any negative results usually come not from the calculator itself, but from using it poorly or too much. This often boils down to schools failing to have an intelligent, deliberate plan for when and how to bring this technology into the classroom. When the calculator becomes a crutch – used for problems students could easily do in their heads or on paper – that feared skill loss can definitely happen. But on the flip side, when they’re introduced as tools for digging into tougher concepts, checking answers, or handling the annoying arithmetic in advanced problem-solving, they can be helpful. They let students focus on deeper mathematical thinking and understanding.

How Should We Address These Concerns?

Math educators strongly advocate a structured, phased approach to the introduction of calculators:
- Prioritize Traditional Methods: Students must first be required to build a strong foundation in mathematics through traditional mental math and written arithmetic methods. This guarantees that these techniques and number sense are firmly established.
- Introduce Calculators as a Tool, Not a Replacement: Calculators should be introduced later in the elementary school years (not second grade), transitioning from an everyday practice to a valuable educational tool. Their primary function should be to support the student, not replace mental calculations.
- Introduce Calculators as a Resource for Checking Answers: Confirming answers acquired through mental or written technique.
- Introduce Calculators for Exploring Complex Numerical Systems: In secondary and post-secondary classrooms, calculators are introduced as a tool for investigating sequences or statistics on large data sets where calculation time is prohibitive.
- Introduce Calculators for Solving Conceptually Challenging Problems: Working with complex problems where the challenge lies in understanding the concept and setup, not in the basic arithmetic calculation itself.
This is an intelligent approach to introducing the calculator in the classroom, as it allows students to actively check their work. This is all about helping them master the calculations and truly understand how the math works. The goal here is to boost their learning, not get in the way of it.

High School and College STEM Courses: The Dangers of Calculator Over-Dependence

When you get to advanced math and science courses, relying too much on a calculator isn’t just about whether you can do the basic arithmetic (you should be able to); it’s about some more concerning issues. Specifically, whether using the calculator too often can affect your grasp of the concepts, make you rusty at solving problems algebraically, and weaken your crucial ability to estimate answers quickly to check your work.

Using powerful tools like TI graphing calculators can be a risk for learning. Certainly, these instruments make complex math operations simple, but that convenience can slow down a student’s development. Students who always simply punch numbers into their calculator to get an answer often miss out on building important “number sense.” This basic skill is key to quickly seeing if an answer is logical. Without it, students are more likely to accept completely wrong answers due to simple input errors because they haven’t developed the gut feeling that an answer is just plain wrong. Getting that immediate result skips the necessary learning steps of estimating and checking the math in your head.

Graphing calculators, while excellent tools that may assist a student’s understanding of the relationship between an algebraic equation and its graph, may also lead to over-reliance. When students rely too heavily on the calculator, they may be satisfied with merely seeing relationships – such as the curve’s shape or the location of an equation’s roots – without making the effort to understand the fundamental mathematical reasoning.

True mathematical mastery requires knowing not only what the graph looks like, but why it is structured that way. This deeper knowledge develops through hands-on engagement, not just by pressing buttons. The danger is that the calculator becomes a black box: it provides correct answers without explaining the logic behind the calculations, ultimately blocking the development of real mathematical understanding.

I must admit I am not a fan of the Ti-83/84 series of graphing calculators, perhaps because I have not used them as much as the students I‘ve tutored. I use the Ti-30 series for calculations, and for graphing functions, I use Desmos (www.Desmos.com), which I find to be a powerful tool that produces graphs I can easily manipulate and that are easier to see on my computer screen. I recommend it to every student I work with.

Personal Commentary

I believe it is crucial to learn how to evaluate a graph, a skill that goes beyond just plugging an equation into your graphing calculator and seeing the resulting graph on the screen. I had a Physics professor at Centre College, Dr. Marshall Wilt, who insisted that we learn how to graph and interpret the experimental data we obtained in the laboratory, as well as the relationships between small changes in inputs and the resulting output for equations such as the distance equation: ( $x_f=\;x_o+vt+at^2$ ). Albeit this was in the late 1970s, before graphing calculators were available, this was a skill that I used throughout my career.

Learning to evaluate graphs, regardless of how they are produced, and understanding the data they represent is a critical skill, useful, for example, on the ACT Science section, where graphical interpretation determines the correct answer.

Also, understanding graphical components such as slope and y-intercept is important for data interpretation, especially in chemistry, where they represent the reaction rate and the endpoints of a reaction.

From a Positive Perspective: How Calculators Help

Calculators are beneficial because they automate the long, repetitive mathematical calculations. This automation means you don’t have to waste time doing tedious work manually; for example, long division problems, complex multiplications, or solving big sets of equations.

The payoff? Students can focus their attention on bigger concepts. Instead of endless drills, the focus shifts to building higher-order thinking skills, figuring out the best way to tackle a problem, and really getting the math – like understanding of why a procedure works and when to use it. Basically, students can put their energy into setting up the problem, interpreting what the answer means, and grasping the core math ideas rather than getting bogged down in the steps of calculation itself.

Graphing calculators are great tools for exploring, questioning, and visualizing math concepts, turning complex equations into graphs. Students can quickly try out ideas and immediately see what happens when they tweak a function—like instantly watching how changing the numbers in a quadratic function ( $y=ax^2+bx+c$ ) shifts the parabola’s shape, direction, and peak. This fast, back-and-forth feedback encourages students to ask “what if?”, sparks their curiosity, and helps them really see the connection between the formula and the graph.

Calculators promote real-world data analysis skills. Restricting math problems to simple, whole numbers creates an artificial learning environment that fails to prepare students for the “messy” data they will encounter in professional fields such as science, finance, and engineering. Real-world applications invariably involve complex and irregular numbers. By using calculators, students can engage with authentic, complex data sets. This practice not only allows them to tackle applicable, practical problems that mirror professional scenarios but also reinforces the practical application of mathematics, thereby significantly boosting their skills in data interpretation and analysis.

Summary

The answer to my initial question:

“When kids let the calculator do the work, do they skip the mental practice needed to really lock in these vital skills?”

is complex. The expert consensus suggests the answer is no, not necessarily. The problem isn’t the calculator itself, but how it is used.

When a calculator is used too soon, as a replacement for mental math and estimation, it becomes a crutch for problems a student should solve independently. It clearly sidesteps the mental exercise required to master fundamental skills such as dimensional analysis, estimation, and significant figures.

The path forward is clear: a structured, phased approach to integrate this technology is essential.
- Foundation First: Students must first master fundamental arithmetic and algebraic manipulation using traditional methods. This ensures the critical development of number sense and the ability to estimate and check answers quickly.
- Calculators as Investigational Tools: Once the foundation is solid, the calculator changes from a potential crutch into a powerful tool for learning. It allows students to automate tedious calculations in advanced problems, freeing them to focus on setting up the problem, understanding the concept, how changes in variables affect the algebra, and interpreting results.
- Understanding the “Why”: For advanced topics, particularly in STEM, the goal is not just the correct answer, but mastering the math itself – understanding why the graph looks a certain way or why a procedure works. The graphing calculator can illustrate the relationship between algebraic equations and their graphs ( $y=ax^2+bx+c$ ), but it must be paired with a conceptual understanding beyond merely pressing buttons.
The goal is to develop mathematically proficient students capable of determining when to rely on mental calculation, when to use written methods, and when to employ a powerful device like a calculator. While the calculator is an essential instrument for today’s STEM students, it must serve as a secondary aid to mathematical reasoning, not a substitute for it.
December 14, 2025
Weekly Quotation: August, 6, 2025: Rethinking Education to Prioritize Personal Growth

“We are a culture that worships the winning result: the league championship, the high test score. Coaches are paid to win, teachers are valued for getting students into the best colleges. Less glamorous gains made a long the way – learning, wisdom, growth, confidence, dealing with failure – aren’t given the same respect because they can’t be given a grade.”

– William Zinnser (On Writing Well, 30th edition) (pg. 253)

I wonder if the same can be said about the process of personal growth. I am absolutely certain that there are teachers whose passion lies in seeing they’re students grow as people of substance, encouraging their passion for learning, challenging students with inquiry-based lessons. I know this because I have worked alongside many of them. However, the pressure to meet state and federal established testing benchmarks by which schools are judged and state curriculum standards leaves little time for creativity and discussion in the classroom. So many feel like they are fighting a losing battle. And it not only these restrictions that affect the development of our students’ personal growth in the classroom.

I have also experienced a paradigm shift in the STEM students I work with. While there are still some who are open to new ideas and are willing to explore and develop the foundations of personal growth: curiosity, a passion for solving problems, and a passion for learning. There is a growing majority of students whose primary interest is in just getting the grade, whose focus is on getting the highest ACT score possible, not through learning the baseline knowledge to support the score, but only in the quick techniques to “cheat” the test with the least amount of effort. And, with minimum ACT test score standards being implemented in school systems as graduation requirements, schools now offer courses teaching these methods. ” Memorize and forget” is now the status quo for many of our students.

We are doing a disservice to our students. For when they get to college, and especially when they graduate and join the workforce without a solid foundation in knowing how to deal with failure, learn from their mistakes, develop a strong support network, to be resilient and to persevere – essential skills and traits that cannot be given a grade – I guarantee you they will struggle.

August 6, 2025
Why Do I Have to Learn This? I’ll Never Use It.

By our very nature, we are inquisitive – always asking “why?”; usually in response to being asked or told to do something. Have you ever asked the question:“Why do I have to learn this? Or, “Why do I have to do this?” I’ll never use it.” I know I did, more than once. Rarely are you given a reason why it is essential to understand the information presented in your high school or college courses and how it relates to what you want to accomplish in life. Sometimes, the answer is simple: you need to know it for the next test. But other times, there are deeper reasons. For example, learning about history can help us understand the present. Learning about science helps us make informed decisions about the world around us and how systems work together. And learning math teaches us to think logically and solve problems in our everyday lives.

Speaking from experience, there is a great deal of information taught in your math and science classrooms, the facts, figures, formulas, dates, and names, you will never use again – whether you intend to go to college or not. And don’t think you will stop asking this question once you decide on your career path – there will always be a training session you don’t want to attend, with more information you don’t see as being vital to you doing your job. It’s a never-ending cycle. What if I told you that the challenges and struggles you face in your classes, more than content knowledge, are vital to your overall growth as a student and will positively impact your success in any career you choose? Content knowledge measured by test scores and grades may or may not be your ultimate objective; that depends on your priorities. I believe what’s truly important and what we sometimes fail to realize is that the “process of learning” equips us with the “tools” for our success.

May 28, 2025