The Hard Climb toward Jaw-dropping, Mind-bending . . . Equations!

by Gerald Proietti, Ph.D., teacher of Geometry, Latin, and Greek

“No forced study abides in the soul.” Plato’s Socrates used these words in presenting a cardinal principle of education: that it must develop in a spirit of freedom, not compulsion. At the same time, Socrates emphasized that a rigorous training of the mind takes a great deal of work on the part of the student; so a strong education also requires that students develop a “love of labor” in their studies—an appetite for hard work when the learning becomes difficult.

Cultivating this work-appetite is one of the things that makes teaching an especially challenging art. Besides diverse forms of small encouragements, it requires careful pacing so that the work leads to discoveries that would not have been possible without that work. As often as possible, the joy and the ongoing radiance of those discoveries should be the primary reward for all the struggle, and the work should feel invigorating. The study of mathematics provides beautiful examples of how the long path of striving can be punctuated by very distinct insights, including surprising moments of perspective-altering insights. In working with students in geometry, one often gets to see eyes pop, jaws drop, and other signs of minds orienting themselves to new dimensions of thinking.

Plato suggested that intuitions about equality or sameness lie at the root of our powers of reasoning; but it was writers like Euclid, in the Elements of Geometry—still today the foundation of our understanding of plane geometry—who documented how deeply the intuition of “equal” versus “not-equal” is fundamental to our mathematics, and how our thinking can build on this intuition. Mathematics begins with the simplest kinds of equalities and progresses to ever more complex equations. Equations reveal definite relationships between things that we may previously have thought to be unrelated or even incommensurable.

In his most famous allegory, Plato’s Socrates speaks of a way “upward” from the deep cave of customary perception into the daylight of real understanding. He proceeds to outline an education that uses mathematical training as a preparation for the later challenge of rigorous thinking about principles of ethics, psychology, and the dynamics of human communities.

Abraham Lincoln—who studied Euclid—in a speech to farmers at the Wisconsin State Fair (1859), related “thorough work” in farming to America’s potential to remain a nation of free-spirited, self-governing citizens. He spoke of education itself as “cultivated thought” and urged that it “can best be combined with agricultural labor, or any labor, on the principle of thorough work . . . [whereas] careless, half performed, slovenly work, makes no place for such combination.”

At LCA, we study Euclidean geometry, including the thorough, logical reasoning; in all of our studies the faculty strive to cultivate this love of thoroughgoing work; and this, too, is a labor of love.

A Day in the Life of an LCA Second Grader

by Kelsey Castaneda, Second-grade Teacher

There are so many elements that make Louisville Classical Academy what it is: a first-rate educational home to bright, inquisitive, and motivated students from diverse backgrounds. An exceptional classical approach to education, small class sizes, and an erudite curriculum help our unique students reach their potential from kindergarten all the way through high school. Our students are able to participate in Chess Club, Cross Country, Junior Classical League, fencing lessons, drama productions, the local and national spelling bees, academic team, and more to build their social skills and relationships. To get a better idea of how all of these disparate elements work together, let’s go through a typical day in my second-grade classroom. 

Our day begins bright and early at 8:30. Students come in and start their morning routine by completing their weekly morning jobs, such as changing the class schedule or collecting homework. Responsibility can never start too soon! 

My students begin their day with free reading for the first 10 minutes of class. This daily practice of independent reading for fun helps students develop a love for reading as it is integrated into their everyday lives. After morning reading, students transition into completing daily grammar and literacy exercises in their Blue Books, another unique LCA tradition! The Blue Book is full of all sorts of language activities — paragraph editing and writing, grammar practice, creative and analytical writing, spelling, and reading comprehension practice. My second graders are currently working on properly punctuating dialogue, as well as writing letters and using possessive apostrophes. Wow, right? 

After daily grammar work, we move on to study our class novel. This is everyone’s favorite part of English, by far! Yes, even in second grade, LCA students read and discuss novels as a whole class. Currently, second graders are reading the classic Stuart Little by E. B. White. For each chapter, we focus on new vocabulary words, figurative language, comprehension practice, summary skills, and responsive writing. In addition, we spend a lot of time discussing proper discussion habits. When is it my turn to speak? I have an important comment, but do not want to interrupt another friend. What should I do? It is important to discuss these speaking habits from a young age in order to create a respectful classroom. 

Currently, we are on chapter 4 of Stuart Little. In this chapter, students learned new vocabulary words like “abdominal” and “shrill,” practiced identifying metaphors within the text, answered comprehension questions (multiple choice and short answer), and wrote a paragraph summarizing the chapter. Students also wrote a creative letter from the perspective of the Stuart Little himself, and created illustrations to accompany their letter. 

In the midst of all this novel-talk, we always work in some kid-necessary things, like moving around or taking mental breaks, because focusing for an hour and a half is difficult for any elementary-age student. We rotate from group circles on the floor, to table work, to small group work, and so on. Occasionally, we work in some drama, acting out parts of the story, or making crafts that complement the reading. 

After English, students have a short snack break followed by 15 minutes of morning recess. At LCA, we believe that play, especially outdoor play, is essential to elementary students. They need to release energy and play with friends. Exercising and building social skills are an important part of our social-emotional curriculum. 

Second grade math is interactive, too. On a daily basis, we use manipulatives like counting blocks, marker boards, clocks, scales, games, and everything in between. We complete work as a whole class, in small groups, or individually in workbooks. Currently, second graders are learning about length (cm, in, m, ft, yd) and weight (lbs, kg, tons). Students experiment with using different measuring tools and learn to compare different units of measurement. We even measured the length of our classroom!
After math, students head to a 30 minute long lunch followed by a second recess (20 minutes). We encourage parents to pack healthy lunches that represent all food groups! With the second recess, students have a total of 35 minutes of recess per day, where they can play outside, play with hula hoops or jump ropes, or, most importantly, create imaginative games with their friends. 

Students transition to Global Studies or Science after second recess. In Global Studies this month, second graders are learning about early 20th century immigration. We read immigration stories from the perspective of kids their age, learn about passage through the Atlantic and Ellis Island, and discuss the reasons for the immigration boom of this time period, to name a few things. Eventually, students will create their own family history timeline! 

Second graders loves science at LCA because it is not just something that they learn about from a textbook. Starting in kindergarten, LCA students practice hands-on, experimental science. My second graders just began a unit on the deciduous forest environment. We will not only discuss the parts of flowers and plants, but also dissect them to identify these parts first hand. We will not only learn the shapes of leaves and identifiers of trees, but also go out on a walk to explore them up close! 

Following Global Studies or Science, LCA students have two more afternoon classes. Drama, P.E., Music, Art, and Choir are all part of our curriculum. Students come back to my class at the end of the day reciting Hamlet or with a beautiful watercolor painting to show me. 

At the end of our day, we (hopefully) add some Positivity Pom-Poms to our class jar. One of the three most important school rules at LCA is “be friendly,” which includes being kind, respectful, and a helpful peer. Our classroom thrives on kindness. For kind or friendly behavior, students can earn pom-poms for the class jar. Unkind behavior can result in a loss of pom-poms, though. Once students fill the jar up, they earn a whole class reward, like time at the park. Having a common class goal that is rooted in kindness creates a positive and loving classroom environment where students encourage each other to consider the feelings of others on a daily basis. 

For most kids, the day ends after those two afternoon special classes, like P.E. or drama. For some students, though, LCA’s after-care program is a place where they continue to create, read, complete homework, do puzzles, or play outside until parents can arrive to pick up their children. 

As I hope is evident, a day in the life of an LCA second grader is a day full of learning, friends, experimenting, creating, reading, exercising, and trying new things. Before I came to LCA last year, I taught at my university during my graduate school work. I truly think that my second graders could give some of those undergraduate students that I taught a run for their money academically. LCA students are the students that teachers dream about teaching. They are students who ask questions, who solve problems, and who love to learn.