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CCEC – Enchanted by Fibonacci

November 14th, 2024

Do you recall a time when you delighted in learning something? Somewhere in the realm of elementary school, I was introduced to the Fibonacci sequence, and it fascinated me. I’ve always been drawn to patterns and puzzles, and here was a codified number pattern that warranted having its own moniker.  

On a recent episode of Basecamp Live, guest Bill Stutzman spoke of learning within the context of Proverbs 25:2, that we are doing the work of kings when we search out knowledge.

Proverbs 25:2 (NASB) 

It is the glory of God to conceal a matter, 

But the glory of kings is to search out a matter.

Searching out matters— a quest for discovery and for revelation is noble work that God has set before us! The pursuit of knowledge yields wisdom like treasures. The Fibonacci numbers were (and still are) a treasure to me. After learning how to read, this mathematical concept was a gold mine to delve (and children do yearn for the mines).

The Fibonacci sequence is often referenced when exploring the irrational number Phi, Φ, as the sequence mimics a close approximation. If you need a quick refresher, an irrational number is a number that cannot be expressed as a fraction, the most widely known being Pi, π. So, while using the Fibonacci sequence as a starting point 8/5 (1.6) all the way up to 6,765/4,181 (1.618033963166707), gets us closer to Φ. Phi is called the golden ratio and is also reflected in the golden spiral, which is found throughout history in the various visual arts from paintings to architecture. The patterns of Fibonacci and phi are also found in God’s creation, observed in the spirals of shells and horns, the spread of dahlia petals, and even the double helix of DNA.

Perhaps it was this early experience that allowed me to do something that is often missed in modern math education—become enchanted. I don’t know what came first—a delight in math or being comfortable with math—but I’m inclined to think that by first becoming enchanted with math, it became something I found comfortable (not necessarily easy but not insurmountable to work through) and even welcomely anticipated. If a student dreads a subject or is even apathetic toward it, something has gone amiss as we’ve disenchanted that area of knowledge. As Ken Myers points out in his introduction to Beauty for Truth’s Sake, “modern culture has disenchanted the world by disenchanting numbers. For us, numbers are about quantity and control, not quality and contemplation” (4).

Stratford Caldecott, the author of Beauty for Truth’s Sake, shares his delight and contemplations around phi. He writes about how subjects that we now typically refer to as STEM and often erroneously pit against the humanities, are vital to a complete liberal arts education. Caldecott writes, “If we look at the underlying principles or ideals that led the ancients to codify the seven Liberal Arts in the first place, we find there a vision in which the arts and sciences, faith and reason, are not separated, as they have been since the Reformation and the Enlightenment in our mainstream philosophies; rather they profoundly complement each other” (132).

We at Trinitas often speak of educating the whole child. If our and’s become or’s, “art or science,” “faith or reason,” we are in danger of teaching only a half or encouraging a student to choose only a half, we are in danger of stunting not only a student’s cognitive abilities, but their humanity as well. This is the beauty of a liberal arts education, that education is not merely a transmission of facts and figures, but the formation of whole persons. 

“The fragmentation of education into disciplines teaches us that the world is made of bits we can use and consume as we choose. This fragmentation is a denial of ultimate meaning… We do not need to be content with our fragmented worldview, our fractured mentality. It is not too late to seek the One who is ‘before all things’ and in whom ‘all things hold together’ (Col. 1:17),” writes Caldecott (17). 

If you have been around Trinitas for a while you’ve heard us speak of the trivium—grammar, logic, rhetoric—an ordering of how students learn. Caldecott spends most of his time focused on the other four facets of a liberal arts education, the quadrivium—arithmetic, music, astronomy, and geometry—and how they work with and expound the foundation laid by the trivium. “The ‘purpose’ of the quadrivium was to prepare us to contemplate God in an ordered fashion, to take delight in the source of all truth, beauty, and goodness, while the purpose of the trivium was to prepare us for the quadrivium. The ‘purpose’ of the Liberal Arts is therefore to purify the soul, to discipline the attention so that it becomes capable of devotion to God; that is, prayer” (90). 

Let us continue doing the work of kings, and let our curiosity lead us to pray without ceasing.

© SES 


Latin Lunchtime Play: The Little Red Hen

November 8th, 2024

smiling studentsMrs. Tellinghuisen wishes to thank everyone for offering such warm greetings upon her return. She is happy to be back and sharing some Notae Latinae again.

Thank you to the Latin Alive class for presenting “Gallina Rufa” (The Little Red Hen) last Friday during our Community Lunch. It was a wonderful way to kick off Latin at Lunchtime plays this year.


Friday Focus Felting

November 8th, 2024

student hands holding felted bowlstudents with fake felt mustachesLast Friday Focus, students tried their hands at wet felting using roving from Mrs. Hinthorne’s Icelandic sheep! Students in grades K-4 heard from artist and author Barb Soet and made animal ornaments, and students grades 5-8 made acorns (and some other creative pieces!).


Grandparent/VIP Day

October 29th, 2024

Earlier this month students welcomed Grandparents and other VIPs to school for a morning of sharing, fellowship, and worship.

Guests enjoyed food prepared by the students, before spending time together visiting in classrooms and getting a first hand taste of what it’s like to learn in a classical Christian environment.

To close the morning, younger students recited grammar chants and geography jingles, while older students recited Shakespearean monologues, Psalm 104 (in English) and Genesis 1:1 (in Latin). All students sang under the direction of music teacher, Mrs. Andrea Boyd.

Thank you to all the teachers, many parent volunteers, and students for this wonderful show of hospitality.


Altus Adventures and Virtue of the Quarter

October 29th, 2024

Thanks to Altus Adventures, our students recently enjoyed adventures near and far!

This Christ-centered organization guided our signature grade 7/8 backpacking trip, a grade 5/6 day away at the park, and a grade 3/4 workshop.

The games and challenges presented to our students supported our virtue of the quarter, FRIENDSHIP, challenging our students to grow in their relationships with God and each other.


CCE Corner – Where Everybody Knows Your Name

October 3rd, 2024

If you read Mrs. Tellinghuisen’s recent post “There’s No Place Like Home,” then you’ll understand the delight I felt as she opened our August in-service devotion with the suggestion that all stories are about seeking and/or finding home, and that if each story had to be condensed into one word, she would choose the word hospitality. When I heard her say that, I wanted to jump up and shout, “That’s my word too!” Well, one of my words. Without any prior conversation with Mrs. Tellinghuisen, I had planned for the afternoon’s professional development session to set the stage for a year-long focus on two things: scholé (more on that in an upcoming CCEC) and… you guessed it, hospitality. 

I began the session by playing part of the theme song from the popular 80’s television show Cheers. While referencing a sitcom might not seem particularly “classical,” I’d argue that in this case it’s not so far off. First, staff members of my generation quickly recognized the song from the popular culture of our teen years. Such recognition demonstrates the power of a classical pedagogical (and advertising) principle: content set to music often sticks with us, for better or for worse. Second, the song captures something central to human nature, and human nature is a central subject of classical education.  

Here’s how it begins:  

Making your way in the world today
Takes everything you’ve got
Taking a break from all your worries
Sure would help a lot
Wouldn’t you like to get away?… 

Sometimes you wanna go
Where everybody knows your name
And they’re always glad you came
You wanna be where you can see (ah-ah)
Our troubles are all the same (ah-ah)
You wanna be where everybody knows your name 

The song expresses quite well the deep human longing to be known, to feel “at home” and to be convinced others are glad to be with us. Because it satisfies this fundamental longing, Mrs. Tellinghuisen suggests that “hospitality is the point of all virtue.” I tend to agree. 

Of course, classical Christian education should help us to go deeper than the Cheers theme song (and it should give us better content than the show provided). The lyrics reference the sitcom’s setting when the singer croons, “Be glad there’s one place in the world/ Where everybody knows your name/ And they’re always glad you came…” That “one place in the world” that feels like home for the characters of Cheers is a bar in Boston. Where is that “one place” for us? At Trinitas, we hope there are several places—that in our school, our homes, and our churches we feel a deep sense of belonging. We hope these are all places where the forms of hospitality are learned from our Lord himself and demonstrated in acts of invitation, preparation, sharing, service, listening, and welcome.  

Our upcoming Grandparent/VIP Day provides an occasion for us to practice these forms of hospitality. Invitations have been sent. We’re preparing a program and classroom activities to share our school with grandparents and VIP’s. Early next week, with help from our faithful Parent Service Fellowship volunteers, students in grades K-8 will make all of the treats to serve our guests. Some will arrange flowers. Discussion questions are planned so students can listen to loved ones’ memories of what life was like for them when they were young. In these ways and more, we hope to welcome our guests so they will know we’re very glad they came. 

Such occasions for hospitality are mere imitations of the hospitality our Lord extends to us. Scripture teaches that he is preparing a place for us and that he makes these preparations out of love for us. Out of that same love, he became incarnate, lived and died and rose and will come again in the greatest acts of sharing and service ever known, for he rejoices in finding and restoring the lost. Scripture also teaches that the Word, through whom all things were made, does not talk all the time. After declaring it “good” and “very good,” God welcomed his creation with rest and with silence, and he built these into the rhythms of the world. The wise and the hospitable have learned from this that there is a time to speak and a time to be silent, a time to listen.* Perhaps most remarkable of all is that the creator, sustainer, and ruler of the universe invites us by name. He knew each of us in our mother’s womb, even choosing us before the foundation of the world. There are no greater acts of hospitality and no greater ways of being known and welcomed home than these.**  

 

*Neal Plantinga, “A Rhythm as Old as the World,” LaGrave Christian Reformed Church, July 28, 2024. 

**Some of the Scripture referenced: John 14:1-3, John 3:16, Romans 5:8, Luke 15, Genesis 1, Ecclesiastes 3:7, Proverbs 18:3, Isaiah 43, Isaiah 49, John 10, Psalm 139, Ephesians 1:4. 

© ALP


CCE Corner – There’s No Place Like Home

September 12th, 2024

Mrs. Tellinghuisen opened our August staff in-service with the following devotion. We were blessed by it and asked her if she would share it as our opening Classical Christian Education Corner piece for the school year.

Think of a good story you once heard. It can be from a book, film, play, or even sitting around a campfire. What was it about? Not just interesting characters, compelling plot, what did it say to you that really mattered? Can you condense that story—and more than the story, your experience of the story—into one word or a simple phrase? I would choose the word hospitality

It seems all stories are about seeking and/or finding home. Not just a home. But home, in the deepest, truest sense of the word. And though I’m not trained in philosophy or ethics, I suggest that hospitality is the point of all virtue. I’d call the source of all virtue love, the love of the divine maker who made us what we are and is making us much more than what we are. Love is the foundational what. But hospitality is the foundational why. Why love? Why grace? Because we all want to sit down, put feet up, just breathe, just be. Just be home.   

In the years I’ve taught Latin, I’ve found certain word pairings that students mix up. I see it the most with hospes and hostis. ‘Guest’ and ‘enemy’. There’s a big difference there, and while they are easy to decipher if you think of the derivatives (hospital, hospitality; hostile, hostility), they do look and sound a lot alike. And maybe it’s telling that they are so similar. The Bible says that we, even while we were yet sinners, separated from God, enemies even, even then we were invited to the banquet, guests of the master. Welcomed and loved.  

Now the tax collectors and sinners were all gathering around to hear Jesus. But the Pharisees and the teachers of the law muttered, “This man welcomes sinners and eats with them.” Then Jesus told them this parable: “Suppose one of you has a hundred sheep and loses one of them. Doesn’t he leave the ninety-nine in the open country and go after the lost sheep until he finds it? And when he finds it, he joyfully puts it on his shoulders and goes home.” (Luke 15:1-6a) 

He gives the lost sheep a home. The Good Shepherd is hospitality itself.  

This is the honest truth. I wrote my idea for this devotion on my phone at some ridiculous overnight hour when inspiration struck. When I typed hospes, the auto-correct function changed it to gospel. I loved that.   

At the June staff in-service, our first-day devotions were from the last few pages of Professor Jennifer Holberg’s book, Nourishing Narratives. She shares four things she most wants her Calvin University students to know: You are loved. You are enough. I want you to succeed. Your voice matters.  

The teacher-to-student messaging here is essential, of course, but so is the self direction. We want our students to be able to say these things to themselves. And we want them to say them, in words and actions, to one another. In our relationships, we’re all of us, at different times, on one side of the door or the other: invited as guest or inviting to a guest. And let us not forget, in our eternal home relationship, we’re all guests, and our host is all generosity.  

Imagine what this school (or any place) would look like if, at any time, a person felt invited and welcomed here. Valued here.  

Here at Trinitas we love books! And reading books about virtue is important and beneficial. But reading about virtue does not, in fact, make us virtuous. The gospels have plenty to say about hearers of the word as opposed to doers of the word, those who study the law and those who actually see its purpose of loving God and neighbor. 

You are loved. You are enough. I want you to succeed. Your voice matters.  

To these four, I would add a fifth that naturally follows: You belong here. 

Every story is essentially about seeking home. The best stories are where home is found. So, by all means, let’s teach those stories here at Trinitas and in our homes. But more importantly, let’s embody them by opening doors, pulling out the good chairs, and offering refreshment to any and all, but especially to the hungry, the hurting, and the overlooked. 

School is starting soon. Classrooms and hallways will be full of activity. And because we’re all human, on any given day, we surely have among us those who are hungry, those who are hurting, and those who are feeling overlooked. Our hospitality will tell them they belong here.  

Be devoted to one another in love. Honor one another above yourselves. Never be lacking in zeal, but keep your spiritual fervor, serving the Lord. Be joyful in hope, patient in affliction, faithful in prayer. Share with the Lord’s people who are in need. Practice hospitality. (Romans 12:10–13) 

© RRT, September 2024


Apples Never Fall Too Far From the Tree

March 22nd, 2024

Trinitas was excited to host Dana VanderLugt, author of Enemies in the Orchard, last week during Friday Focus. Students who read (or were in the process of reading) enjoyed a time of hearing from Mrs. V about her experience of writing a book (revise, revise, and then revise some more!) as well as her inspiration for researching this often-overlooked bit of history. As Mrs. V shared during her talk, “The historian will tell you what happened. The novelist will tell you what it felt like. D. L. Doctorow 


Apples Never Fall Too Far From the Tree

March 21st, 2024

Trinitas was excited to host Dana VanderLugt, author of Enemies in the Orchard, last week during Friday Focus. Students who read (or were in the process of reading) enjoyed a time of hearing from Mrs. V about her experience of writing a book (revise, revise, and then revise some more!) as well as her inspiration for researching this often-overlooked bit of history. As Mrs. V shared during her talk, “The historian will tell you what happened. The novelist will tell you what it felt like.” – D. L. Doctorow


Congratulations, 7th and 8th Graders!

March 15th, 2024

Congratulations to six of our students in our 7/8 class upon the selection of their essays for the National Civics Bee! This year the 7th and 8th graders entered the first ever National Civics Bee in Michigan, sponsored locally by the Grand Rapids Chamber of Commerce. Each student studied an issue he or she felt was important for the community and wrote an essay about the problem and a proposed solution with attention to Founding Principles and civic virtues. The larger goal of the contest is to engage students in their communities and build their awareness of how citizens’ voices and involvement are crucial to the flourishing of society.