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  • Why Adults Struggle to Learn Spanish—and What Actually Helps Them Improve

    By Evan Flaxman, JD, MBA

    One of the most common misconceptions about learning Spanish is that adults struggle because they are too old to become proficient in another language.

    In reality, age is only one factor in language learning, and it is often far less important than the way someone studies, practices, and responds to mistakes.

    Adults bring considerable advantages to the learning process. They have established communication skills, life experience, professional knowledge, and the ability to recognize patterns. They can understand grammatical explanations and connect unfamiliar concepts to things they already know.

    Yet many adults spend months or even years studying Spanish without becoming comfortable speaking it.

    The problem is frequently not a lack of intelligence or effort. It is a mismatch between how the language is being taught and how the student needs to use it.

    Understanding Spanish Is Not the Same as Speaking Spanish

    A student may recognize hundreds of Spanish words, understand basic grammatical rules, and perform well on written exercises while struggling to carry on a simple conversation.

    This happens because recognizing information and producing it are different skills.

    When reading, a student has time to examine a sentence, identify unfamiliar vocabulary, and consider its meaning.

    Conversation requires a different process.

    The speaker must listen, understand, decide what to say, select the appropriate vocabulary, conjugate verbs, and pronounce the words—all within a matter of seconds.

    That process can overwhelm someone who has studied primarily through textbooks, vocabulary lists, or language-learning applications.

    The solution is not to abandon those resources. It is to supplement them with regular opportunities to produce spoken Spanish.

    Students need practice forming sentences, responding to questions, and expressing ideas without having unlimited time to prepare.

    Why Memorizing Vocabulary Is Not Enough

    Vocabulary is essential, but isolated word memorization has limitations.

    Consider a student who memorizes the Spanish words for house, work, food, and tomorrow.

    Those words are useful, but knowing them individually does not necessarily enable the student to say:

    Tomorrow I have to work, but afterward I’m going home to prepare dinner.

    The student must understand how words connect, how verbs change, and how Spanish expresses relationships between actions.

    For that reason, vocabulary becomes more useful when learned in complete sentences.

    Rather than memorizing trabajar solely as the verb meaning to work, a student might practice:

    • Trabajo todos los días. — I work every day.
    • Mañana tengo que trabajar. — Tomorrow I have to work.
    • Ayer trabajé hasta las seis. — Yesterday I worked until six.

    Each sentence introduces vocabulary in a meaningful context while reinforcing grammar and sentence structure.

    Over time, the student begins recognizing patterns that can be applied to new situations.

    The Importance of Learning Verb Conjugations

    Spanish verbs present a significant challenge for English-speaking students.

    In English, many verbs change relatively little across different subjects.

    Spanish requires students to become comfortable with changes in verb endings that communicate who is performing an action and when it occurs.

    Consider the present tense of hablar, meaning to speak:

    • Yo hablo — I speak
    • Tú hablas — You speak
    • Él o ella habla — He or she speaks
    • Nosotros hablamos — We speak
    • Ellos hablan — They speak

    These patterns become more manageable when students understand the structure rather than trying to memorize every conjugated verb as an unrelated word.

    I generally favor establishing a solid foundation with regular verbs before introducing large numbers of irregular forms.

    Students who understand how regular -ar, -er, and -ir verbs work have a framework for learning thousands of additional expressions.

    Irregular verbs are unavoidable, but they become less intimidating when students already understand the underlying system.

    Why Adults Become Afraid to Make Mistakes

    One of the greatest obstacles to speaking another language is the fear of sounding foolish.

    Adults are accustomed to expressing themselves competently in their native language.

    They may have professional responsibilities, advanced education, and decades of experience communicating complex ideas.

    Suddenly being unable to express a simple thought can feel uncomfortable.

    A student may know what they want to say but become frustrated while searching for the correct Spanish words.

    That frustration can lead to hesitation, self-correction, and eventually silence.

    Unfortunately, avoiding conversation also means avoiding one of the most important opportunities for improvement.

    Mistakes are not evidence that language learning is failing. They provide information about which skills need more attention.

    A productive learning environment allows students to make mistakes, receive constructive corrections, and try again.

    The goal is not perfect speech from the beginning.

    It is progressively more accurate and confident communication.

    Grammar Should Support Conversation, Not Replace It

    Grammar provides the structure that makes meaningful communication possible.

    However, studying grammatical rules without applying them can produce students who understand explanations but struggle to speak.

    Consider the difference between the Spanish preterite and imperfect past tenses.

    Both describe past events, but they serve different purposes.

    The preterite commonly describes completed events:

    Ayer estudié español durante dos horas.

    Yesterday I studied Spanish for two hours.

    The imperfect can describe habitual or ongoing past situations:

    Cuando era niño, estudiaba español todos los días.

    When I was a child, I studied Spanish every day.

    Understanding that distinction is important.

    But the student must also practice selecting the appropriate tense while speaking, rather than relying exclusively on written exercises.

    An effective lesson introduces a concept, demonstrates its use, and then gives the student opportunities to apply it in original sentences and conversation.

    Grammar becomes more meaningful when students understand what it allows them to communicate.

    Listening Is a Skill That Requires Separate Practice

    Students sometimes assume that speaking and listening will improve automatically at the same rate.

    They do not necessarily develop together.

    A student may be able to construct a sentence correctly but struggle to understand a native speaker responding at a natural pace.

    Spoken Spanish includes connected sounds, regional accents, informal expressions, and variations in pronunciation.

    Words that appear distinct on a printed page may sound quite different when spoken quickly in conversation.

    Listening practice should therefore be a regular part of language learning.

    Television programs, interviews, podcasts, and everyday conversations can all provide useful exposure.

    However, the material should be appropriate for the student’s current level.

    A beginner may benefit from short, clearly spoken exchanges that can be repeated.

    A more advanced student may benefit from authentic news broadcasts, interviews, or discussions that introduce unfamiliar expressions and faster speech.

    The objective is gradual improvement in comprehension rather than expecting immediate understanding of everything.

    Consistency Matters More Than Occasional Intensive Study

    Many adults approach language learning enthusiastically but struggle to maintain a consistent schedule.

    They may study intensively for several hours one weekend and then do nothing for the following two weeks.

    Although longer sessions can be valuable, regular exposure is generally more effective for developing and retaining practical skills.

    A manageable routine might include fifteen or twenty minutes of vocabulary and grammar review, a short listening exercise, and several minutes of speaking practice.

    These activities do not need to be complicated.

    Students can describe their daily routines, explain what they did yesterday, or discuss what they plan to do tomorrow.

    Even brief exercises create opportunities to retrieve vocabulary and reinforce grammatical patterns.

    A student who practices consistently is more likely to retain material and become comfortable using it.

    Lessons Should Reflect the Student’s Actual Goals

    Not every student needs Spanish for the same reasons.

    A construction worker may want to communicate more effectively with coworkers.

    A traveler may want to navigate restaurants, hotels, and everyday situations.

    A student enrolled in a Spanish course may need help understanding verb conjugations, reading assignments, and examinations.

    Someone with family members who speak Spanish may want to participate more naturally in conversations.

    These objectives require different emphases.

    A student preparing for an examination may need structured grammatical instruction and written exercises.

    A student learning Spanish for work may benefit from occupation-specific vocabulary and practical conversation.

    An advanced student may need help improving pronunciation, understanding idiomatic expressions, and speaking with greater fluency.

    The most effective instruction begins by identifying what the student already knows, where the difficulties occur, and what the student wants to accomplish.

    A single teaching approach is unlikely to serve every learner equally well.

    Why Individual Attention Can Make a Difference

    Classroom instruction offers important benefits, including structure, shared activities, and exposure to other students.

    However, students do not all learn at the same pace.

    Some grasp grammatical concepts quickly but struggle with pronunciation.

    Others speak comfortably but repeatedly make errors in verb conjugation.

    Some need additional practice listening, while others need help organizing their thoughts into complete sentences.

    Individual instruction allows the pace and content of lessons to be adjusted to those differences.

    It also provides opportunities for immediate feedback.

    A student who repeatedly makes the same grammatical mistake may benefit from a focused explanation followed by several original examples.

    Another student may need less explanation and more conversation.

    The objective is to identify the obstacle preventing progress and address it directly.

    Measuring Progress Beyond Test Scores

    Traditional assessments can help evaluate vocabulary, grammar, and reading comprehension.

    But practical language development should also be measured by what students can actually do.

    Can a beginner introduce themselves and ask simple questions?

    Can an intermediate student explain what happened yesterday or describe future plans?

    Can an advanced student discuss unfamiliar subjects, understand natural conversation, and express opinions without constantly translating from English?

    These abilities provide meaningful evidence of progress.

    A student may still make grammatical mistakes while becoming substantially more capable of communicating.

    That improvement deserves recognition.

    Language proficiency develops through accumulated gains, not through a single moment when someone suddenly becomes fluent.

    A More Practical Approach to Learning Spanish

    For adults who want to improve their Spanish, I recommend focusing on several complementary habits.

    First, establish a strong foundation in basic sentence structure and common verbs.

    Second, learn vocabulary in context rather than relying exclusively on isolated word lists.

    Third, practice speaking regularly, even when sentences are imperfect.

    Fourth, listen to Spanish frequently, selecting material appropriate to your current ability.

    Fifth, seek corrections that explain recurring mistakes without interrupting every attempt to communicate.

    Finally, maintain a consistent routine that can realistically fit into everyday life.

    None of these practices is particularly complicated.

    Their value comes from applying them together and continuing long enough for the skills to develop.

    The Goal Is Communication, Not Perfection

    Learning Spanish as an adult can be challenging, but the difficulties are manageable when instruction and practice address the skills students actually need.

    Progress depends on building a foundation, using the language actively, recognizing mistakes, and gradually increasing the complexity of communication.

    Adults do not need to speak perfectly before participating in conversations.

    They need enough confidence to begin, enough structure to improve, and enough consistency to continue.

    The ultimate measure of success is not simply how many Spanish words someone knows.

    It is how effectively those words can be used to understand and communicate with another person.

  • From One Finance Class to Thousands of Students: Knowing When to Build and When to Leave

    By Evan Flaxman, JD, MBA

    The first session sold out all 200 seats.

    There were still students waiting who had to be turned away.

    That was the moment I realized we might have something.

    The idea had started almost casually. Matt’s office was next to mine at the University of Florida. Because my actual office hours were held in another office, I often spent time in his. We became friends, talked about everything, and bonded over a shared love of poker. We played in a highly competitive PhD poker league, and somewhere in the middle of all those conversations, an idea began to take shape.

    Matt had already been tutoring individual students and small groups. I was the Head Teaching Assistant for FIN 3408, one of the university’s large undergraduate finance courses, and I knew firsthand how many students needed additional help understanding the material.

    One day, I asked Matt a simple question.

    Why don’t you teach a course on FIN 3408?

    He thought it was a great idea. He asked whether I would have a problem with it, since I was the Head TA for the course.

    I told him I wouldn’t.

    Then he asked how we would work it out.

    We’ll figure it out, I told him.

    We did.

    The First 200 Seats Sold Out

    I helped with the marketing. I told students that there were private tutoring groups with a strong grasp of the material and that, if they studied and did the work, they should be able to pass—and hopefully earn a B or better.

    Then Matt held the first session.

    Two hundred seats sold out. More students were waiting. Some had to be turned away.

    And the demand didn’t disappear after that first night. It continued throughout the semester.

    The business was largely cash-based, the expenses were limited, and the revenue was substantial. But what interested me most was the question the success raised.

    Was this really a finance problem?

    Or was it a much larger problem that existed throughout the university?

    During that semester, I had become friends with PhD students in other disciplines. I began wondering whether students in their fields were experiencing exactly what I had seen in finance.

    If students needed this kind of help in FIN 3408, why wouldn’t they need it in accounting? Marketing? Mathematics? Statistics?

    I began to see the possibility that we hadn’t merely found a successful tutoring opportunity in one course. We might have identified a need that existed across the university.

    We Went After the Low-Hanging Fruit

    We started close to home.

    We added other business courses, including accounting and marketing. Then I looked at mathematics and statistics, where the opportunity seemed obvious.

    I didn’t want to expand into every subject simply because we could. There were areas, including some of the sciences and engineering, where I didn’t have the same network or familiarity with the people teaching those subjects. I was much more interested in going after what I considered the low-hanging fruit: courses where the need was clear and where we could put a qualified instructor in front of the students.

    Matt was a genuine people person. He was in the PhD program and knew a tremendous number of people. As we expanded, his relationships helped us identify talented instructors across different departments.

    My role was largely deciding what we should take on next. Which courses should we offer? Where was the demand? And could we staff the course with a PhD instructor we trusted to deliver the quality our students expected?

    We didn’t need to become everything to everyone.

    We needed to identify the right courses and teach them exceptionally well.

    Then the Word of Mouth Became a Wildfire

    After the first semester, we didn’t need to manufacture demand.

    The students did it for us.

    Students who had been struggling were passing. Students who did not normally consider themselves B students were earning Bs. They told their friends. Their friends told other students.

    The word of mouth was incredible.

    It spread like wildfire.

    By our second semester, we had ramped up to at least ten courses. After that, we continued adding approximately two to four new courses each semester.

    What had started with one finance class was becoming a company serving thousands of students at the University of Florida.

    And it was exciting in the rawest sense of the word.

    I wasn’t worried about overhead choking us. There weren’t enormous monthly expenses that had to be met just to keep the business alive. We had limited fixed expenses, substantial revenue streams, and numbers of students beyond anything we could have reasonably hoped for.

    The business model was phenomenal.

    Eventually, our biggest problem wasn’t finding students.

    It was finding enough places for them to sit.

    Success Began to Change the Economics

    For years, we held large tutoring sessions in hotel ballrooms.

    But as the number of courses and students continued growing, physical space became a real constraint. We began discussing the need for a much larger permanent location.

    And that was when I started looking at the business differently.

    The economics that had made the company so attractive were beginning to change.

    A permanent facility large enough to meet the demand would require a substantial investment. There would be buildout costs, fixed overhead, additional employees, and monthly obligations that hadn’t existed in the same way before.

    The original business had been remarkably lean. We could scale quickly without being strangled by fixed costs.

    Now, to reach the next level, we would have to invest heavily in infrastructure.

    The business model wasn’t becoming bad.

    Far from it.

    But it was becoming a different business.

    And at the same time, I was seeing another opportunity.

    Two Good Opportunities Began Competing With Each Other

    The University of Florida had an enormous student population, and I saw an overwhelming need for housing.

    I began looking at individual homes and realized that I could buy houses and rent them to college students for more than the mortgage and other expenses. I could generate cash flow while building equity in a tangible asset.

    And I could do it with less capital than what we were discussing investing in the tutoring company’s next phase of growth.

    Suddenly, I wasn’t choosing between a good business and a bad one.

    I was choosing between two good opportunities.

    On one side was a tutoring company I had helped build from the ground up, one that had grown from a single finance course into a multimillion-dollar business.

    On the other was an opportunity to take capital out of that business and put it into student housing, where I saw enormous demand and attractive economics.

    I understood how valuable the tutoring company was.

    I also understood that the next stage would require a level of investment and fixed overhead that fundamentally changed what we had originally built.

    So I decided to sell my half.

    There Was No Drama in the Valuation

    Matt had a PhD in finance and was one of the smartest human beings I had ever met.

    When we discussed the value of my half of the company, there was no need for gamesmanship. We were both capable of understanding the economics, and we were honest about them.

    We looked at cash flow.

    We looked at multiples.

    And we reached a valuation.

    That was it.

    I sold my 50% interest and moved my capital into real estate, ultimately investing in four apartment units and making approximately four times my money.

    Matt stayed with the tutoring company for another eight years. He took the business through the expensive transition from rented hotel ballrooms into a permanent facility and absorbed the substantial costs associated with that growth.

    Eventually, he sold his interest for approximately twice what I had received eight years earlier.

    I have never looked at that outcome and thought I made the wrong decision.

    Building Something Doesn’t Mean You Have to Own It Forever

    It is easy to judge a business decision by looking at what happened afterward.

    If an asset increases in value after you sell it, you sold too early.

    If someone else eventually receives more money for the same business, you should have stayed.

    But that ignores time, risk, capital, opportunity cost, and what else you could have done with the money.

    I knew the tutoring business was exceptional when I sold my half.

    That was never in doubt.

    Matt and I had started with one finance class. From there, we expanded into other disciplines, built relationships with PhD instructors, and created something far larger than either of us had imagined.

    I was proud of what we had built.

    But I also understood that the next phase of the company’s growth would require transforming the economics of the business. More infrastructure. More overhead. More fixed expenses. More capital.

    At precisely the same time, I saw another opportunity that I believed offered a better use for my money.

    So I made a choice.

    I didn’t sell because the tutoring business had failed.

    I didn’t sell because I had stopped believing in it.

    I sold because sometimes the same judgment that tells you when to build something also has to tell you when it is time to leave.

    Related reading: From Cleaning Wheelchairs at 11 to Helping Build a Nine-Location Business

  • Why Intelligence and Education Are Not the Same Thing

    By Evan Flaxman, JD, MBA

    For much of my life, I assumed that intelligence and education were closely related. The more people I taught, however, the more I realized they were fundamentally different concepts. Education measures what someone has learned. Intelligence reflects how someone thinks. Neither guarantees wisdom.

    Over the course of my career I taught university students and adult learners whose educational backgrounds could not have been more different. Some excelled in demanding academic programs. Others entered the classroom convinced they simply were not capable of learning. Those experiences taught me that educational achievement and intellectual ability are related, but they are not the same thing.

    One of the most intellectually gifted students I ever taught studied finance. What distinguished him was not merely his ability to memorize formulas. He recognized relationships among variables that other students overlooked. He wanted to understand why an answer was correct and how changing one assumption affected the entire problem. His combination of natural ability and relentless curiosity ultimately led him directly into a Ph.D. program.

    At the opposite end of the spectrum was an adult GED student who had spent roughly twenty years trying to earn his diploma. Many people had concluded that he simply could not pass. I reached a different conclusion. I believed the problem was not intelligence but that no one had discovered the teaching approach that matched the way he learned. By changing the instructional method, strengthening the fundamentals, and building confidence one step at a time, he ultimately earned his GED.

    Those two students taught me the same lesson. Intelligence reveals itself in different ways, and effective teaching is not about delivering information—it is about creating understanding.

    I believe one of the greatest mistakes many educational systems make is forgetting the true purpose of teaching. Too often success is measured by whether material was presented rather than whether it was actually learned. Those are not the same thing. Teaching is not measured by the amount of information presented. It is measured by the amount of understanding created.

    Throughout my teaching career I never believed my responsibility ended when I finished explaining a concept. My responsibility ended when the student understood it. If that required another explanation, a different example, more repetition, or an entirely different approach, then it was my responsibility to adapt.

    The longer I taught, the less interested I became in asking, “How intelligent is this student?” Instead, I asked, “What is preventing this student from demonstrating what they already have the capacity to learn?” That single question changed the way I taught and, ultimately, the results my students achieved.

    Knowledge matters. Degrees matter. Education matters. But curiosity, humility, judgment, and the willingness to keep learning determine whether knowledge becomes wisdom. Great teachers never lose sight of that distinction.

  • The Student Who Said He Could Never Learn Math

    By Evan Flaxman, JD, MBA

    For approximately three years, I ran a GED program in a federal prison setting.

    During that time, more than 350 students earned their GEDs, and I taught approximately 95 percent of the time in Spanish.

    The students came from vastly different educational backgrounds. Some had been in the GED program for years before I arrived. Some wanted desperately to learn. Others were dismissive, disruptive, or convinced that they simply weren’t capable of succeeding academically.

    One student refused to learn math.

    For six months, he was emphatic about it.

    “I’m not going to learn math. There’s no way I’m going to learn math. I’m just not doing it.”

    So I didn’t force him.

    I let him sit there.

    Then one day, after about six months, I asked him a simple question.

    “Would you give me one chance to see if you know more math than you think you do?”

    He agreed.

    I told him, “I guarantee you know fractions.”

    He told me he didn’t know anything about fractions.

    I told him I knew that he did.

    He wanted to know how I could possibly know that.

    I had learned enough about his background to know that there was a real-world example he would immediately understand. Because of the nature of that example, I first asked the correctional officer supervising the classroom for permission to use it.

    Then I turned back to the student.

    “If somebody came to you and wanted a quarter of a pound, how many ounces would you give them?”

    “Four.”

    “How did you figure that out?”

    “There are sixteen ounces in a pound.”

    “You just did division.”

    Then I asked him how much he would charge.

    “Two thousand.”

    “How did you get that?”

    “I charged five hundred a quarter.”

    “So that’s multiplication.”

    In a matter of minutes, I hadn’t taught him division, multiplication, or fractions.

    I had shown him that he already knew them.

    Before I Could Teach Them, I Had to Know What They Knew

    When I took over the program, I inherited students at radically different academic levels. Some had already spent years in the GED program. Others had different educational backgrounds, different strengths, different weaknesses, and very different levels of motivation.

    The first thing I did was give everyone a practice GED exam.

    But the exam itself was only the beginning.

    I sat down with the students and went over their results with them. I wanted to understand not only what they knew and didn’t know, but something equally important: Were they interested in learning? Were they willing to admit that they didn’t understand something?

    And could I help them do that without making them feel inadequate?

    I never believed that showing someone everything he didn’t know was the same thing as teaching him.

    Once I saw a student’s weaknesses and we had discussed the exam, I started at the first step.

    Not the first step in a textbook.

    Not the first step in a standardized curriculum.

    The first step for that particular student.

    Time in a Classroom Is Not the Same as Progress

    Some of my students had started their sentences years before I arrived and had already spent years in the GED program.

    That made it difficult to get up to speed with everyone. I couldn’t simply assume that because a student had been in a classroom for years, he had mastered the material supposedly covered during that time.

    So I went back to what I could actually see.

    I looked at the practice exam. I talked to the student. I identified his weaknesses. Then I started from the first missing step.

    For many students, mathematics was one of the greatest barriers.

    But the student who refused to learn math taught me something particularly important. His problem wasn’t simply that he didn’t know mathematics. Part of the problem was that he had already decided that mathematics was something he was incapable of learning.

    Yet he understood fractions. He understood division. He understood multiplication.

    He just didn’t call them that.

    Sometimes the first job of a teacher isn’t to give a student new knowledge.

    Sometimes it is to show him the knowledge he already has.

    This Was Not an Ordinary Classroom

    I don’t want to romanticize the environment.

    It was difficult.

    Some students were abusive or dismissive. There were fights. Some would attend class but deliberately disrupt the learning environment and make themselves a jackass.

    Violence was not an abstract possibility. At the higher-security institution above the camp where I taught, a teacher was stabbed with a pencil in the middle of class.

    Creating a genuine educational environment under those circumstances was hard.

    But I did my best.

    And it worked.

    I believe a large part of the reason it worked was that the students knew my interest in them was genuine.

    I wanted them to learn, but it was more than that. I wanted them to become better versions of themselves.

    I wasn’t pretending to care about them as a teaching technique.

    I was sincere.

    And they knew it.

    More Than 350 Graduates

    I was able to attend all of the GED graduation ceremonies.

    I watched the men put on caps and gowns. I watched the warden hand them their diplomas. I watched them have their pictures taken while holding something that, for many of them, had once seemed impossible to earn.

    For many, it was one of the proudest moments they had experienced while in prison.

    I knew what it had taken to get some of them there.

    I knew about the students who had struggled for years. I knew about the resistance, the disruptions, and the fights. I knew about the student who sat for six months insisting that he would never learn math.

    And then I watched them graduate.

    More than 350 of them over approximately three years.

    Teaching Is One of the Purest Ways of Giving Back

    I know that my time on this earth is limited, and I believe I am here to help people in whatever ways I can.

    Of all the ways we can give something to another person, teaching may be one of the purest.

    Knowledge isn’t diminished when you share it. You can give someone something that changes what he believes he is capable of doing, and you lose nothing by giving it away.

    For me, teaching has never been only about passing an exam.

    It is about helping someone become a better version of himself.

    Sometimes that begins with a practice test and an honest conversation about what someone doesn’t know.

    Sometimes it means finding the first missing step and beginning there, regardless of how many years a student has already spent in a classroom.

    And sometimes it means waiting six months for someone who has completely given up on learning math to finally give you one chance.

    I couldn’t solve every problem. I couldn’t reach every student. And I couldn’t always create the kind of educational environment I wanted.

    But I could try.

    And when I watched those men put on caps and gowns, receive their diplomas from the warden, and pose for photographs, I knew that the effort had meant something.

    If I was able to help somebody, then my time had meaning.

  • What Teaching Thousands of Students Taught Me About How People Actually Learn

    By Evan Flaxman, JD, MBA

    Over the years, I have taught students in environments that could hardly have been more different from one another. As an undergraduate at the University of Florida, I served as Head Teaching Assistant for introductory finance, where I worked with college students trying to understand everything from basic financial principles to mathematical formulas and their applications. I also spent years in the private tutoring business, teaching and helping build an educational company that ultimately served thousands of students.

    Years later, in a very different environment, I spent 27 months teaching primarily Spanish-speaking adults working toward their GEDs at the federal prison camp in Florence, Colorado. During that period, more than 350 of the students I worked with earned their GEDs.

    The students were different. The subjects were different. Their educational backgrounds, abilities, motivations, and circumstances were different.

    But one thing remained remarkably consistent: people learn best when you understand where they are, start with the fundamentals, move slowly enough for real understanding to take hold, ask questions, and don’t give up on them.

    The Difference Between Knowing an Answer and Understanding It

    One of the clearest lessons I learned from teaching thousands of college students was that the difference between a B student and a C student was often not intelligence. It was effort and engagement.

    The B students were more likely to attend free tutoring sessions, ask questions when they didn’t understand something, and take a more active role in their own education.

    Natural ability certainly matters. Some people are extraordinarily gifted, and it would be dishonest to pretend otherwise. I have known exceptionally intelligent people who could achieve extraordinary academic results with comparatively little effort. But I also saw students who were not exceptionally gifted perform just as well as gifted students when they were willing to study and do the necessary work.

    The more important question for me as a teacher was not simply whether a student could produce the correct answer. I wanted to know whether the student understood why the answer was correct.

    If a student gave me the right answer, I would ask:

    How did you arrive at that answer?

    Sometimes the reasoning showed genuine understanding. Sometimes the student had memorized a formula without understanding what it represented. And sometimes the student had simply guessed correctly.

    A correct answer by itself doesn’t always tell you which of those three things happened.

    Start at the Bottom of the Stairs

    My approach to teaching was to start at the bottom of the stairs.

    I would not move to the next stair until I felt the student understood the issue we had just discussed well enough to build upon it. One of the biggest problems in teaching is adding too many things too quickly. When that happens, students can become confused and even lose their grasp of the fundamentals they had just begun to understand.

    I saw this frequently with students struggling in finance. Often, their biggest problem wasn’t an inability to learn formulas. They lacked an understanding of the foundational principles beneath those formulas.

    So I would go back to the beginning.

    What is finance? How does finance work? What are we actually trying to accomplish? What does this formula represent, and why are we using it?

    The fundamentals are the pillars of the subject matter. Without those pillars, there is very little a student can do with the formulas. A student might memorize an equation, but if he doesn’t understand what it represents, he won’t know when or how to apply it.

    A good teacher has to connect those dots.

    True Understanding Survives a Change in the Question

    How did I know when a student was ready to move to the next stair?

    I would ask essentially the same question in a different way.

    I wanted to see whether the student recognized the nuances and whether the underlying understanding remained consistent when I changed the wording or presentation of the question. If a slight change caused the student’s understanding to collapse, then the student probably hadn’t fully understood the principle yet.

    That became one of my basic tests of understanding:

    True understanding survives a change in the question. Memorization often doesn’t.

    And even when a student reached the right answer, I wanted to hear how he got there. If his reasoning contained a gap, I preferred not to simply tell him what he had done wrong. I would leave breadcrumbs and see whether he could follow them back to the mistake himself.

    Students fared much better when they were the ones who found the gap in their own thought process.

    There is an important difference between being told, You’re wrong, and here is the answer, and experiencing the moment when you recognize for yourself exactly where your reasoning broke down. In my experience, the latter creates a much stronger and more durable understanding.

    The Smartest Person in the Room Is Not Necessarily the Best Teacher

    You cannot simply put the smartest person in the room in front of a class and assume that person will be the best teacher.

    Teaching is both a skill and an art.

    A strong teacher needs to know the subject matter, of course. But that isn’t enough. A teacher must also recognize the nuanced differences between a student who lacks foundational knowledge, a student who misunderstands a particular principle, a student who knows the answer but doesn’t understand why it is correct, and a student who understands the concept but hasn’t yet learned how to apply it.

    As Head TA for introductory finance at the University of Florida, I had five sub-TAs working under me. Dr. Joel Houston and I interviewed candidates separately and then compared our assessments of who we thought was most talented, including each candidate’s particular skills and deficits. Approximately 95 percent of the time, we agreed immediately.

    When I asked a substantive question, I wasn’t interested only in whether the candidate could solve the mathematical equation. I wanted to know whether that person could also see the 30,000-foot view.

    Could the candidate explain what the equation meant? Why it was being used? How it fit into the broader principles of finance?

    A good teacher needs to understand both the equation and the idea the equation represents.

    Different Students May Be Standing on Different Stairs

    My fundamental approach to teaching remained the same when I later taught GED students, but the environment created a different challenge.

    Students entered the classroom with widely different abilities. Some were much more advanced than others. I had to be careful about where I set the target. If I taught to the most advanced students, I risked losing much of the room. If I taught only to the lowest common denominator, I risked failing to challenge everyone else.

    So I didn’t use one universal lesson plan for the entire class.

    I would teach for a period of time and then give individual students different workbooks, assignments, and lesson plans based on their particular skills and deficits. I used progress tests to determine their levels in reading, reading comprehension, mathematics, and other specific learning areas.

    The goal was to determine where each individual student was standing on the staircase.

    One student might need to strengthen basic mathematics. Another might be ready for more advanced material. A third could be strong in one area and significantly behind in another.

    The right lesson taught at the wrong level is still the wrong lesson for that student.

    Teaching Primarily in Spanish

    For 27 months at the federal prison camp in Florence, Colorado, I taught primarily Spanish-speaking students working toward their GEDs. I would estimate that approximately 95 percent of my teaching was conducted in Spanish, which is not my native language.

    Reading comprehension was largely an area the students handled independently because their command of Spanish reading comprehension was generally better than mine. But for the other subject matter, I taught overwhelmingly in Spanish.

    There was another challenge: many students were not initially motivated to earn a GED.

    For inmates who didn’t have a GED, education was mandatory for at least part of the day under the circumstances I encountered. That meant I was not necessarily teaching a room full of people who had voluntarily chosen to be there and were already enthusiastic about education.

    I tried to explain why earning a GED was important to functioning in society after release. Before you can teach someone effectively, sometimes you first have to give that person a reason to want to learn.

    During those 27 months, more than 350 of the students I worked with earned their GEDs.

    The Student I Couldn’t Give Up On

    One student in particular has stayed with me.

    He was an Arab man who had been in prison for approximately 20 years and had extremely limited vision. His glasses were extraordinarily thick, and he had to hold a page about an inch from his face to read it.

    I would teach him mathematics and fractions until he seemed to understand everything we were working on. Then he would lose his comprehension of what we had just covered.

    So we would do it again.

    And again.

    And again.

    There was no magic technique and no shortcut. I simply kept going over the material with him until it became second nature. Eventually, he had done it so many times that he couldn’t forget it again.

    And after approximately 20 years in prison, he passed his GED.

    That experience reinforced something I had learned throughout my years of teaching: different students may require very different paths to reach the same destination. Some need a new explanation. Some need a different example. Some need to discover their own mistakes by following breadcrumbs. Some need individualized assignments. And sometimes, a student simply needs someone willing to go over the same thing again and again until it finally sticks.

    Go Slowly. Ask Questions. Don’t Give Up.

    If I could give one piece of advice to a parent, teacher, or tutor trying to help someone who is struggling to learn, it would be simple:

    Go slowly. Ask questions. Don’t give up on him.

    Start with the fundamentals. Find out where the student actually is rather than assuming where he should be. Don’t add complexity so quickly that the foundation collapses. Ask the same question differently. Ask how the student arrived at the answer.

    When possible, leave breadcrumbs and let the student discover the gap in his own reasoning.

    And recognize that sometimes the person who appears unable to learn simply hasn’t yet been taught in the way he needs to be taught.

    Start at the bottom of the stairs. Make sure the stair beneath the student is solid. Then help him take the next step.