Louisville Classical Academy    Porter     Stevenson

JCLCA Service

posted May 16, 2018, 9:16 AM by Louisville Classical Academy

By Althea Porter
Teacher and LCA Kentucky Junior Classical League sponsor

    It has been one of my great pleasures to serve as the sponsor for our local chapter of the Junior Classical League. It’s the thing I do that makes the most sense to me. It’s the thing I do that makes the least sense to others. My fellow JCL sponsors always want to know just how a non-Latin-teaching person got involved with the “Latin Club.” My friends, who are probably much like you, always want to know just what exactly is the JCL?
    The Junior Classical League is a student-run national service organization that seeks to promote the Classics. Students compete in academic testing focused on Greek and Roman History and Latin. At convention, they dress in togas -- toga pura, toga pulla, toga, picta -- is anyone else feeling shocked that kids know the difference? They make Latin puns, Greek puns, Caesar jokes, translate pop songs into Latin, speak to each other in Latin, and just Latin, Latin, Latin! But somewhere in this Latin fray is a small group of students working on a project for veterans, the homeless, or kids in hospitals. These small service projects are not a point of emphasis at convention and are barely acknowledged by the state delegation.

    Sadly, for a majority of the JCL chapters in Kentucky, these very small projects at convention are the only community service that any of them do all year. For LCA, on the other hand, community service is a regular part of our JCL experience. It’s just what we do. Our delegation has completed the most community service in the state of Kentucky for at least 6 years. In 2016, LCA was awarded first place for community service at the National JCL Convention.

    The executive board of the KYJCL tried to encourage other delegations to follow our example and created an annual service award -- the Service Stick -- to be awarded to schools who did the most community service each year. LCA has the proud distinction of being the first school to be awarded this Service Stick. The next year, we were the second school to be awarded the Service Stick. The third year, the board changed the standard and openly pledged to award the Service Stick to any school that did half as much service as LCA. We were the third school to be awarded the Service Stick. This year, we heard a rumor that the board would award the Service Stick to any school who did any service at all. We are the fourth -- and final -- school to be awarded the Service Stick. LCA was also awarded our state’s Spirit Stick as an acknowledgement of all the service we did this year.

    How? Why? How can our humble Academy do so much and why doesn’t it seem like so much? Because it’s not just service that’s being done. It’s a response. It’s a dialogue that is being had between the JCLCA and the community around us. It is a conversation that seeks to include all others. It’s just what we do.

    Some of our service projects this school year have included cleaning a park, sponsoring the LCA food drive, spreading the “JoyCL” with holiday gifts for teachers, and making Valentines for Vets. You can find a more complete list of the JCL service projects here.


posted Mar 30, 2018, 5:37 AM by Louisville Classical Academy   [ updated Mar 30, 2018, 5:56 AM ]

By Kelsey Castaneda

Second-grade Teacher


    When I first moved back home to Louisville to continue my teaching career, I interviewed at several different schools in the city. Louisville is home to so many different types of schools with different approaches to education, and it was of the utmost importance to me to teach at a school that I felt was making new, exciting, and important leaps in education in our city. LCA’s classical approach to education is already unique to Louisville, especially as this approach is taken at both the upper and lower campuses. But, what is even more important, I think, is that the LCA Primary Program has hands-on science and global studies courses integrated into the core curriculum.


    While many schools do teach elementary students science, LCA teachers take a different approach, allowing students not simply to complete worksheets, but to participate in hands-on activities and experiments. LCA believes it is imperative for students to begin learning research procedures and conducting experiments at a young age. Rather than simply reading about how the amount of sunlight a plant gets affects its growth, LCA third graders conducted an experiment with tomatoes, leaving them under different window seals and observing how the lack of sunlight stunts the growth of one tomato over a couple of days. My second graders were pleased to have Mrs. Kelly Stevenson, science teacher at the upper campus, come over to do a flower dissection experiment, giving them a first-hand look at the different parts of the flower, and how those parts all work together. Our entire Primary Program spent a day at the University of Louisville’s Rauch Planetarium, where they learned all about our solar system’s planets in a virtual reality experience that made them feel like they really were in space.


    Most other schools have some kind of social studies or history courses for elementary students, but those courses usually focus on American history only. LCA students study globally, meaning they start studying not only U.S. history, but also the history and cultures of other countries all around the world from the time that they are in kindergarten.

    My second-grade students, for example,  have had the opportunity to study a plethora of countries and cultures throughout the year. The second-grade curriculum emphasizes Asian cultures, and we have studied China, Japan, India, Mongolia, Afghanistan, Iraq, and reviewed the biographies of significant leaders of these countries, such as Gandhi and Genghis Khan. We have examined the cultures of these countries and their differences from ours, from language to cuisine and holidays to religions. We do special projects to really help the students understand these new places. LCA teachers have organized everything from Greek feasts to Kamishibai plays, to reenactments of Seneca Falls and the Women’s Suffrage movement. Teaching children about other cultures at a young age encourages an open mind, better understanding, and an inclusive attitude, benefiting them in their future endeavors.


    In addition to this global approach, second graders do learn about American history. We began with America’s rebellion from England, resulting in the establishment of our country. From then on, we examined the Civil War and the importance of figures like Harriet Tubman. It is astounding to hear first-grade students chat about Greek gods and goddesses they've enjoyed learning about during lunchtime or to see kindergarteners pretending to be soldiers in the Revolutionary War during recess time.


    LCA is special for so many reasons. Our curriculum, I think, is one of the critical reasons and really sets our school apart from others in the area. I am so pleased to be teaching at a school that encourages students to think outside the box in all subjects, especially at a young age.


posted Mar 5, 2018, 9:10 AM by Louisville Classical Academy   [ updated Mar 5, 2018, 9:17 AM ]

By Dewey Kincade

History, Greek, Latin, and Art Teacher

    “What does that mean?”

    That is a favorite question of my three-year old son, Theo.  The question never fails to bring me a smile.  He is busy acquiring the building blocks of meaning--the meanings of words.  These building blocks are the foundations of a great tower of meaning, and as such, he needs his meanings to be clear, concise, and concrete in order to support the weight of this tower.  

    As a teacher, I’m fortunate to be able teach students of all ages.  They are all in one way or another asking what things mean.  At the foundational level, meaning is understood like an equation.  This word equals this definition.  Primary students spend a lot of time at this level.  These students are not ready to take on ambiguity or nuance.  Instead, they need reinforcement.  Word games, puns, and any activity that allows students to assert their knowledge will help build a solid foundation. The foundation should not only be strong; it should also be broad.  Students should be learning as many new words as they can, and finding a book series they like is a great way to do this.  

    As students continue building their tower of meaning, they encounter the interpretive level where = becomes ≅.  Unlike the foundational level, meaning at the interpretive level is not fixed.  A poem can mean a lot of things to different people.  A sentence in Latin can be translated several ways.  This is a challenging time for most students because the very foundation of their tower seems to be in jeopardy.  Whereas before meaning was fixed, now it has become more malleable.  It’s not enough to say what a story means, students must also support their statements. Arguments must be made.  

    This is a great time to engage in debates with your children.  The best way to encourage a child to construct arguments is by having fun debates at home.  Who would win in a matchup between the Hulk and Wolverine?  Who would make a better friend: Elsa or Moana?  Your children will come up with an answer, but make sure they can support their answer with evidence.  One of the challenges with debates is that people expect there to be a winner.  When a child confronts the notion that there may not be a best interpretation (but many good ones), they may take it a step too far and say that any interpretation is valid.  If they do, demand hard evidence for this assertion.  

    The importance of our interpretive abilities cannot be over-emphasized.  We don’t simply apply these skills in language classes like English and Latin, but in history as well.  The past can be interpreted in a myriad of ways. Even the sciences provide students with an opportunity to hone their interpretive skills.  Raw data doesn’t always provide us with an obvious conclusion.  Sometimes we must forge ahead by finding the best interpretation of the data.  

    The bulk of middle school and high school is spent exploring the interpretive level of meaning, but lurking around the periphery is an even higher level of meaning--the existential.  What is the meaning of life?  That’s a big one, but what we really mean is: what is the meaning of my life?  As seniors approach the end of their education at LCA, they shift from following the plot to constructing their own plot.  Unfortunately, we can give no answers to the question, what is my life’s purpose?  And I have no advice to parents as their children begin to tackle this question, but I’m confident that students getting an LCA education will acquire the tools to answer the question for themselves, whatever direction they head in.  


posted Feb 9, 2018, 8:19 AM by Louisville Classical Academy   [ updated Mar 5, 2018, 9:16 AM ]

By Sharlette Cullen

Kindergarten Teacher

    Prior to joining LCA, I taught in the public school system for 18 years, in Georgia and New Jersey. While I have always loved being an elementary teacher, I often felt overwhelmed by large class sizes, extensive state-mandated testing, and mounds of daily paperwork. I moved to Louisville two years ago and serendipity, somehow, led me to become a kindergarten teacher at LCA. Here, I have found my bliss as an educator.

    The nurturing environment, small class size, and extensive curriculum that LCA provides has taught me that I love teaching classical kindergarten.  My students are eager and enthusiastic to learn as much as they can each and every day.  Our daily routine is full of activities to encourage children to be inquisitive, creative, and active.  Whether it be painting, going on a nature walk, re-enacting an explorer’s journey, or engaging in imaginative recess play, my students are active and engaged in all aspects of our kindergarten curriculum.

    We are obsessed with books in our classroom.  Throughout our day, we enjoy picture book, read-alouds, and Magic Tree House chapter books. We listen to books on CDs, explore biographies, savor fairy tales, examine Greek myths, and investigate as many non-fiction texts as possible. I follow the students’ interests and explore, in great detail, the chosen subjects in our curriculum that intrigue them. I am amazed at their ability to absorb new information and acquire new skills. Whenever we read and discuss a text, we model the “shared inquiry” method, encouraging each child to listen, speak, and take turns during our discussion. Their pointed questions often lead to new opportunities for learning.

    Our tightly-knit classroom community allows me to foster kindness, manners, and compassion on a daily basis. With such a small class size at LCA, my kindergartners are able to feel safe to take chances and be as imaginative as possible. They encourage one another and cheer each other on. My students often cite examples of how they follow our class motto: “be the reason someone smiles today.”  I am grateful for the many opportunities I have to smile at my students every day.


posted Jan 9, 2018, 11:44 AM by Louisville Classical Academy   [ updated Mar 5, 2018, 9:15 AM ]

By Dr. Laurie Duesing

English and Latin teacher

    I did not study Latin for any of the right reasons.  I was in the first year of a Ph.D. program in English Literature at UC Davis and attempting to dispatch ‘nattering requirements.’  Among such requirements was proficiency in two foreign languages.  French was my college language, and I dispensed with the requirement quickly.  Now what?  I took a look at a very long list of acceptable languages, and with one exception, three semesters of study were required.  The exception was Latin.  I am a practical woman, and I was also teaching full-time at Solano Community College, which offered two years of Latin in our evening program.  Perfect!  I could teach my classes in the day session and stay on one evening a week for two semesters and fulfill my second language requirement.  I thought, “How hard can it be?”

    My first Latin teacher was Ken Bubb, a former Jesuit priest, who was charismatic, knowledgeable and kind.  Just as we do at Louisville Classical Academy, I started my Latin study with Wheelock’s Latin, and I was almost immediately blindsided for one simple reason: Latin made sense.  Already a seasoned English instructor, I was accustomed to the irregularities, inconsistencies and bewildering plethora of rules (and exceptions) governing English grammar, pronunciation, you name it. . .   I was stunned: Latin was orderly.  It had constant rules.  All I had to do was learn them and apply them, and I could do the homework and translations as if I were a first century Roman.  A few weeks into the semester, Mr. Bubb said, “You can almost count the number of irregular Latin verbs on one hand.”  Astonished, I yelled out, “I’m in!”  

    The clincher came when Mr. Bubb showed a clip from The Gladiator where Russell Crowe is speaking to his troops and utters “Hold the line” and “Stay with me.”  Explaining how this dialogue truly replicated Roman ideals, Mr. Bubb launched into a further exposition of Roman culture.  I was so moved, I wept.  

    So Latin had its way with me.  I fulfilled my second language requirement and made a vow I would study Latin in depth whenever I had some time.  That time finally came when I moved to Louisville and discovered that U of L had an undergraduate minor in Latin.  Since 2007, I have taken every Latin course offered (and more because the Chair of the Department keeps changing the authors in the senior level classes so that I can repeat those classes for credit.).  At last count I had garnered 84 Latin credits.

    The irony in all of this is that I have learned more about English language (my specialty!) from studying Latin.  Latin is the ideal; it shows how a language should operate.  It’s gorgeous rhetorically and poetically.  (To my chagrin, I now believe that Vergil is a poet superior to Shakespeare.)    At the conclusion of every semester at U of L (when I was teaching Latin 101 and 102), one or two or three of my students would come up to me and say, “I understand English now better than I ever did.”  Of course.  Latin is the illuminator, the illustrator, not to mention the firm basis of the English language.  (Percentage estimates range from the low 90s to the 97th percentile.)

    Is it any wonder that Classics majors (more than any other major) invariably perform better on all kinds of graduate school qualifying exams?  This is no surprise to me because graduate entrance exams are language exams.  And Latin is the grand template of them all.  


posted Oct 31, 2017, 6:50 PM by Louisville Classical Academy   [ updated Mar 5, 2018, 9:15 AM ]

By Kelly Stevenson

    While thinking through what I wanted to share about science education at LCA, I was trying to find an analogy that would explain the importance of experiential learning. It hit me that I have been living through the perfect analogy for experiential learning—teaching my son to drive.

    I am sure that when you get into the car to go somewhere today, you do not have to think about how to make the car work or the myriad traffic rules that govern your transit. But it was not always that way. At some point, all of us who drive had to learn how to do so. Reflect back on that experience with me for a moment.

    Did reading the permit manual and having someone TELL you what you needed to do make you a good driver? Was it sufficient to know which pedal was the gas and which was the break? Maybe, like me, you learned on a manual transmission, and also had to deal with the clutch pedal and the subtle movements that allow for a smooth drive. Didn’t the real learning occur when you actually sat behind the wheel? Through the experience of DOING, you probably learned more than from all that reading and listening combined. You needed that background information as a starting place; it informed how you went about figuring out all those controls and making the car go where you wanted it to. However, the real experience of learning came from you making your own meaning from that background information you had been given. You constructed your own understanding, and through practice, you mastered a new, complex skill.

    This reminds me of one of the important ways that education happens at LCA. There is more to learning than reading textbooks and listening to teachers lecture. In the sciences, I feel this is particularly important. In my experience, for so many schools, science education is made up of just reading the book and completing worksheets: learning the facts, the names of things, reciting the steps of a process, but nothing more.

    Yes, there is a role for direct instruction. There is a place for learning what the scientific method is. What are the steps you should go through to test how things work? What do words like observation, hypothesis, and conclusion mean? But after a relatively short instruction period on the underlying concepts, students need to jump into creating their own understanding of HOW science works. Students must USE the scientific method in real experiments to truly understand how it works, as well as its power as a learning tool.

    From the very beginning of their science education at LCA, students are making predictions about what they think will happen. How will this action affect what we see? How can we change things to get a desired result? This methodology is built upon and formalized as students grow in their science education. I know that the 3rd graders this year are maintaining science journals in which they are keeping records of their observations and recording results from many classroom experiments in tables. My 4th and 5th grade students work through planned experiments, but also get the chance to start choosing variables and discussing the best ways to find out what they want to learn. By 6th grade, students are working to design their own experiments, including controlling variables and analyzing what their results mean. Lab experiments and reports get more thorough and complex as students get older.

    To me, this process of learning HOW to do science is even more important than memorizing facts. Yes, you need to know the names of things; yes, you need to know some underlying facts; and yes, you must learn from those who went before you. But meaning that is constructed from the student’s own experience is so much more powerful than anything that he or she just hears a teacher say. True understanding comes from experiencing something yourself. This is the way science is done. Science is not just a collection of facts: it is a vibrant, living discipline that is about learning new things through experimentation. New research is constantly making new discoveries that expand our understanding of how this world works and help make it a better place. That is the nature of science. THAT is what I want my science students to learn—and experience.


posted Sep 26, 2017, 9:37 AM by Louisville Classical Academy   [ updated Sep 26, 2017, 11:45 AM ]

Amanda Proietti

By Amanda Proietti

    At our opening school ceremony, I urged students in grades 4-12 to spend time in silence every day.  With the presence of music and news or audiobooks streaming through our ipods and phones and computers, and music in supermarkets, elevators, waiting rooms, and while on hold, we have to work hard to find silence.  Few of us succeed.  And I worry about the implications of that.


    I worry about it for several reasons.  One is that we have reduced music to wallpaper, to mere background noise, and I think music deserves better than that.  Another is that most students perform worse on cognitive tasks when they are listening to music.  And though there is some evidence to suggest that extroverts perform better in the presence of background noise such as TV or chatter, introverts perform significantly worse (Furnham and Bradley, 1997), and we don't need one more way to put introverts at a disadvantage.  We also don't need any more ways to fragment our already restless attention, jumping from texts to emails to Facebook posts to TV screens to a textbook.  We need mental rest.


    A recent study points to a connection between silence and permanent growth of neurons in the brain (Kirste, 2013).  We have heard about the beneficial effects of silence on blood pressure.  Such medical and cognitive effects of silence are wondrous, but what interests me more is how silence aids us in forming our personalities.  It is in quiet that we hear our own voice, that we ponder and muse and give thoughts space to develop, that we confront the less attractive aspects of our personality and work to refine them.  I don't know that we can know who we are unless we learn that in silence.  It is the source of our strength and authenticity.


    Can parents and teachers find space in the day to cultivate silence for ourselves and our children?  Could we have silent car rides or walks in the neighborhood or chores or crafts or homework performed in amiable, companionable (not rigidly enforced) silence?  In moments of high drama or tension when we lose touch with ourselves, can we resist reacting with torrents of words but find space for silence, too?  


    If, as a community, we could undertake to find periods of silence in every day, would our younger students become more imaginative and resourceful, our middle-schoolers more accepting and confident, and our high-schoolers more optimistic and discerning?  Would we adults find ourselves calmer and clearer headed?  


    To find out, what do we have to lose but noise?



posted Sep 26, 2017, 8:37 AM by Louisville Classical Academy   [ updated Sep 26, 2017, 9:20 AM ]


By Kelly Stevenson

Over the summer, a number of LCA faculty were lucky enough to get to hear Richard Louv speak when he came to town. Louv’s national bestseller, Last Child in the Woods, introduced people to the idea of Nature-Deficit Disorder in 2005. In this work, Louv brought together many sources that indicate that most children today (and adults, for that matter) are suffering from a lack of exposure to nature in their everyday lives. There have been many studies that show increases in both psychological and physical health associated with time spent in natural settings. Being outside in natural settings can lower stress, increase attention and focus, exercise multiple senses, and stimulate many diverse areas of the brain. All of these things lead to better learning as well as happier, healthier people, so it seems like a logical cause for educators to take up.

And some educators have. Since the publication of Last Child in the Woods, many people have made a point to have children spend more time in nature. In the last ten years, with this increased awareness, there has been much more research on the topic. This research has lent even more support to Louv’s thesis. Schools based on his ideas, in which children spend significant time in nature, have higher test scores than comparable schools--despite the apparent loss of “instructional time.”

One of the biggest areas of improvement when children spend time in nature is creativity: children spending unstructured time outside are much more creative in their play, and there are indications that this creativity carries over into other aspects of their lives as they grow. One study demonstrated that children playing in a more natural, less planned environment are more likely to play with other children who do not look like them than children in a more structured playground environment. There was also a noted decrease in the amount of bullying found in the natural setting. The Richard Louv event I attended was geared toward families, so there was a wide range of ages represented. While the adults sat under a tent and listened to Louv talk about these studies, behind him, a diverse group of children who had never met each other before were running around, unknowingly making his point even more eloquently than he. Their play was creative, physically active, and engaging. I never heard a single tear shed through the whole evening, though there were certainly plenty of squeals of laughter and joy.

All of us who listened to Richard Louv are newly energized to apply what we learned at LCA. We want to continue to incorporate more experience in nature into our school days, and invite you as families to join us in making sure that our children do not grow up with Nature-Deficit Disorder. In small ways, we have already begun this transformation. More students are enrolled in PE this year. During our daily recess, students get free time outside. We have also added a bit of time on Friday afternoons in which 4th and 5th graders will get some explicit “nature time.” This could include a nature hike, using natural materials in an art project, or games that take place in nature as well as demonstrate aspects of how nature works. Many of the ideas will come from Richard Louv’s newest book, Vitamin N, which is a great resource if you are interested in finding ways to incorporate more time in nature with your family. I look forward to taking some time to reconnect with nature myself, as well as seeing it anew through the eyes of these interested young students this year.

Richard Louv’s books:

Last Child in the Woods: Saving Our Children from Nature-Deficit Disorder

This book lays out the case that children are suffering from their lack of exposure to nature and why that is important, as well as what we can do about it. Apparently, the newest addition has much more information added.

The Nature Principle: Reconnecting with Life in a Virtual Age

This book focuses on the importance of relating to the natural world for adults, businesses, and society. He calls for a “nature-balanced existence” that will allow both humanity and the earth to thrive.

Vitamin N: The Essential Guide to a Nature-Rich Life

This is a guidebook to ways connect with nature, chock full of ideas of things you can do to get more nature in your life.



posted Sep 26, 2017, 8:35 AM by Louisville Classical Academy   [ updated Sep 26, 2017, 10:37 AM ]

Proietti, G.

By Dr. Gerald Proietti

    Across our first decade, people have often asked us: What does the “classical” in our name signify? Its meaning can be traced to the ancient Greek development of two interconnected sets of principles that we strive to cultivate: “shared inquiry” and “habits of mind.”

    We refer to the antiquity of these principles, not because we want to revere their old age, but because it is helpful to keep in mind that these are not modern inventions—they are deep-rooted sources of vitality in our own striving to be free, to understand the world, to understand ourselves, and to live good lives.

    Socrates of Athens developed shared inquiry into a method of pursuing truth. While he himself did not leave any writings that we know of, his students Plato and Xenophon show him using dialogue (dialogos) to pursue clarity about universal human principles such as love, justice, courage, and integrity.

    Socrates did not mean the kind of dialogue that merely seeks practical compromises, but instead something like the kind of discourse among modern scientists, gradually sifting out invalid theories, that has led to our enriched understanding of the fundamental forces of physics, the quantal nature of matter—the periodic table of the elements!—and the cellular basis of plant and animal life. All of these advances required rigorous, truth-seeking dialogue among scientists across many generations.

    One of Socrates’ sober observations about democracies is still humbling today: that one of our most prized possessions, freedom of speech, leads to a constant, confusing clash of diverse ideas—and as a result, many citizens come to believe that moral principles are merely cultural creations with no universal basis as guides for human life. But he also argued that this diversity of ideas, if used carefully—in productive dialogue—can make democracies a great environment for the pursuit of universal moral truths that lie concealed beneath the surface differences of opinion.

    We cannot use experimental methods or microscopes as evidence in pursuing the truth about moral principles; so it is harder for dialogue to produce such decisive agreement about the human fundamentals as it can in the physical sciences. Yet in some ways moral principles are more self-evident to us than the fundamental forces of physics. Socrates compared basic moral principles to the elementary principles of geometry, such as “straight.” Their reality is not proven by logic; yet courageous and artful dialogue can help us to sift out their core meanings.

    This ancient thinker showed, ironically, that in pursuing moral inquiry through rigorous dialogue, we are compelled to continually practice the very goodness that we are seeking to understand: we have to practice courage and self-control in striving, through dialogue, to understand them.

    Explicit, direct inquiry about moral principles arises more naturally in some classes—in literature, especially—than in others. But at LCA our diverse studies, with teachers using diverse methods, have this in common: we explicitly, consciously strive to practice the “parts” of both intellectual and moral excellence—which the ancient Greeks and Romans called virtues, and which we call good habits of mind—through the challenge of honest, truth-seeking dialogue.


posted Sep 26, 2017, 8:13 AM by Louisville Classical Academy   [ updated Sep 26, 2017, 9:22 AM ]

By Alan Krome 

    This is a salute to Bill Harvey, my algebra teacher at Norfolk Academy.

    I salute him because he was able to take a word-nerd and imbue him with awe at the mysterious and echoing beauty of mathematical pattern. I already knew by the time I was in his tenth-grade class that I wanted to be a poet, so most of my demigods were wordsmiths. I was good at math, but it didn’t engage me any more than history or geography, two other courses that seemed to me encrusted with facts as dull as dried mud cracking in the sun. (The fact that I later learned to love these disciplines is another story for another day . . .)

    But Mr. Harvey took a few minutes one day to point out that any time you took a square, such as 10 x 10 and instead multiplied its square root + 1 times the square root - 1, you would always get one less than the square: 10 x 10 = 100, 11 x 9 = 99; 7 x 7 = 49, 8 x 6 = 48, etc. I don’t recall why he pointed it out--possibly as a short-cut for finding the product of two numbers separated by 2? What I do remember is wondering how far this pattern went; surely when you got into larger numbers, the difference must get larger. So I tried 80 x 80 and got 6400; 81 x 79? Whoa, it was 6399! The fact that this held true despite the size of the numbers defied my understanding of multiplication. [So I continued noodling with the numbers. Before long I tried adding and subtracting 2 from the square roots. 12 x 8 = 96, which was 3 less than the 99, 4 less than the 100, and 9 x 5 3 less than the 48, 4 less than the 49. Subtracting 3 gave me 91 and 40, each 5 less than its predecessor or 9 less than the original 100 or 49 . . .]

    Highly excited, I took these findings to Mr. Harvey, who—may blessings shower upon his memory—said, “Wow, Alan, that’s a fascinating discovery. It certainly means something—I want to you to figure out what.” [So after several hours of chasing this elusive mathematical mystery down into a simpler form, I discovered that if (x + 1)(x - 1) = x² - 1 and if (x + 2)(x – 2) = x² - 1 - 3 = x² - 4 and if (x + 3)(x – 3) = x² - 1 -3 - 5 = x² - 9, then possibly (x + y)(x – y) = x² - y². I tried it by adding and subtracting 4, then 5—Eureka: I’d found a pattern powerful enough to predict things I hadn’t tested yet!]

    Then felt I like some watcher of the skies when some new planet sweeps into his ken . . .

    It was the first time I was aware that numbers are magical because they can give us some slight insight into all the rhythms that pulse beneath the surface of the universe, keeping it in balance. I became aware of it because Mr. Harvey planted a seed that happened to take root in my imagination. But much more importantly, because he didn’t short-circuit the power of that seedling’s growth by explaining it to me: he made me explore it for myself. For that insight and the awe it still can evoke within me, I owe Bill Harvey more than I can ever explain, much less repay.

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