Illuminating Truth and Beauty in Grammar and Math
I once asked Andrew Kern how to seek the true, the good, and the beautiful when we’re so bogged down with the need to drill and review things like grammar and math.
Of course, his answer was that grammar and math are very beautiful (I knew he was going to say that!). Then he issued this challenge: see the beauty of bringing order out of chaos.
In everything, ask yourself- who am I imitating?
This week, I’m contemplating this note from Ann. She wrot:
How can we illuminate truth, beauty, and goodness when we are covering nuts-and-bolts subjects like math and grammar? I know conceptually that math is lovely and orderly and related to music, but how can I get there when we’re in the thick of drilling addition tables? I would love to hear others’ practical ideas!
Well, quite frankly, so would I! :)
It doesn’t really feel like we’re illuminating truth or contemplating beauty when we’re drilling the multiplication table or memorizing prepositions. But if what we are really doing is bringing order out of chaos, then we are participating in a most creative act.
That is, after all, the work of Our Creator: bringing order from chaos. It’s part of what we, busy homeschooling mamas managing homes and little people all at once, do every single day.
We know that teaching is the art of being imitated
We know that God delights in the order of His creation- whether that be a mathematical equation or a perfectly diagrammed sentence. But how do we make evident the truth and beauty therein?
In the comments of our Sister-to-Sister on Imitating Delight, Lisa Amer shared this quote from Charlotte Mason:
The principality of Mathematics is a mountainous land, but the air is very fine and health-giving… you cannot lose your way, and… every step is taken on firm ground. People who seek their work or play in this principality find themselves braced by effort and satisfied with truth.
On her blog, Lisa goes on to share her experience of recently falling in love with mathematics, even though she never thought of herself as a math person. That’s the kind of teacher I want to be!
A teacher who falls in love with the truth and beauty in what otherwise would be considered a mundane slog.
Great article on math starting at page 13:
http://www.societyforclassicallearning.org/images/journal/SCL%20Fall%202013%20-%20FINAL.pdf
Oooh! Thank you for sharing that!
Found an excellent article on math here starting at page 13 by Doreen Howell:
http://www.societyforclassicallearning.org/images/journal/SCL%20Fall%202013%20-%20FINAL.pdf
A thought I just had about delighting in grammar:
If one thinks of the elements of grammar as the building blocks of language, then it’s pretty awe-inspiring to look at great writing (most especially lyrical, poetic writing) and think that these beautiful compositions are the result of putting those blocks together in a specific way in order to produce a specific reaction.
A friend and I have been talking for months about math and how our kids hate it just because the lessons are so long and brutal. Recently we both switched to Life of Fred. It’s only been a few weeks, so I can’t say if they’re learning math concepts any better, but I can say they are loving it. I think a more cheerful approach allows their minds and hearts to be more open to the math all around us. I’m also trying to play math-based games with them once a week or so, some really easy for the little ones (which the older ones also seem to love to play) and some more abstract ones for the older kids.
If you want your kids to learn skip counting, I cannot recommend One Hundred Sheep highly enough. It’s a skip counting CD with songs based on the gospels and we just love it. Even me! My kids still hum the songs when they’re working on their multiplication facts. It can be hard to find, but Adoremus Books carries it.
So those are my weak suggestions just so I can get in on the conversation.
I love the idea of bringing order out of chaos!
I really wanted to offer some sort of concrete, practical helps I’ve discovered over the years (probably because I love the practical – that’s where I live)…and those kind of great resources are out there…but to be totally honest, in these subjects in particular, I’ve discovered how valuable my own attitude (which, I confess, sometimes had to be “fake it til you make it”) was/is. I think over the years I rather clumsily stumbled, with God’s grace, into a posture that helped me model delight and my own growing awareness of truth and beauty within the discipline of these subjects. So, while it can’t be pocketed as nicely as a link to a great resource, my own answer lies in the idea of posture.
I suppose it all really just goes back to modeling. There may be a tendency to overcomplicate or become myopic in choosing a curriculum based on a litany of considerations, but in the end, it’s about the teacher & driver with eyes open to beauty and truth and possessing the ability to model that wonder.
Stratford Caldecott, in his book, Beauty In the Word, has a quote which inspires me:
“Making known to the child or student the special way of ‘waiting on truth’ in every problem, whether in language or mathematics or any other subject, is what (Simone) Weil identifies as the first duty of the teacher. For this makes it an exercise in ‘waiting on God,’ which God will one day reward with tenderness.”
So for me, illuminating truth and beauty means slow and steady with short lessons and plugging away consistently. It means allowing the child to uncover the truth for themselves. It means providing enough unstructured time to explore language and numbers and at times backing our focus out so that a child has an opportunity to see how numbers relate within a larger context – how numbers and shapes relate to each other…in patterns of symmetry, in the order of the Created world, in music. In math especially, it means driving the curriculum (which means brainstorming within rather than changing curriculum every time we encounter a challenge). In grammar, I follow the same pattern of short lessons in the context of a studied dictation lesson. Slow and steady.
Once I moved to this format consistently I found that though we *seemed* to cover less, the children retained and applied more. They saw more readily the worthiness of the lessons. Since I wasn’t overfilling, their eyes were open to the truth waiting for them in those lessons.
I really appreciated your comment Jen! Thanks for sharing what this looks like for you as well as what you think it means to illuminate truth and beauty. I hadn’t really thought about how illuminating truth and beauty could come in the form of short lessons (whereby allowing more time and room to discover truth, goodness, and beauty in the lesson).
You said: “Once I moved to this format consistently I found that though we *seemed* to cover less, the children retained and applied more. They saw more readily the worthiness of the lessons. Since I wasn’t overfilling, their eyes were open to the truth waiting for them in those lessons.”
What does this look like though, practically speaking in terms of workload, at the high school level when you are looking at college prep, graduation requirements, test prep, etc.?
Great question, Karen! What does this slow-and-steady illumination look like practically in high school? Well I’ll be honest first off and tell you that continuing to live out our Classical principles in our Charlotte Mason education in high school was a big step out in faith for me. I knew it would yield fruit, but would it *translate* into those forms of assessment that I don’t regularly embrace – like college entrance tests – and further would my Classically educated graduate be able to handle post high-school job interviews, college discernment, and building the business she wanted to start? The quick answer to all of them is YES – it did!
I’m going to share two practical examples, from math and grammar, because everyone wonders – how does it translate in terms of college prep and tests like ACT/SAT?
MATH —
My first high school graduate is not naturally gifted in mathematics. Brace yourselves – we use Saxon for math from 4th grade +. It’s not a popular curriculum choice these days, but I’d be willing to challenge thinking on it if you find it dry, boring, overwhelming and unworkable. Most people do at some point (myself included – but this is the time to brainstorm and drive the curriculum, not walk away.) Saxon conveys mathematical truth logically (for the most part…I do have a few minor quibbles), and the student’s challenge of grappling with truth and uncovering it through their work builds skill in discipline, logical thinking, and confidence in being able to know truth through their efforts. It is EXACTLY the kind of illumination we’re talking about here!
We began with Algebra I in 8th grade, and it soon became clear that my student really needed the review, spiral approach, and thorough treatment of topics that Saxon provided. Our lessons remained short so that she didn’t feel overwhelmed. Practically this meant teaching the lesson one day and completing a very small handful of problems. The next day I would ask for a narration of the lesson concept, and she’d complete 40 min. worth of problems. We’d check them and pick up the next day if needed, and we just kept on pace until the lesson was complete, errors were corrected, understanding was in place. You can see that this meant we moved S-L-O-W-L-Y through the book.
Charlotte Mason talks about spreading a feast of ideas before a child, and the importance of regulating the intake of that rich feast by scheduling short lessons and short readings so that the child does not experience the “indigestion” that comes of over-indulging: reading too much in one sitting – or being force fed: long math lessons and painfully long homework sessions. Both of these result in a net loss – the child doesn’t remember what was read, or in the case of math, didn’t have time to consider concepts and neurologically shut down at some point. Provide small amounts of digestible concepts, narrated through the child’s exercises, and then give the student time to rest. Schole’ is no less important in high school!
By 10th grade we were wrapping up Algebra 1. It *seemed* we were covering less….but…she was mastering it, and at this point, she saw the worth in what she was learning. We were moving at a pace that didn’t overwhelm her. She was digesting and coming back to the feast. However, it was clear to me at this point that her upper level math trajectory was not going to go very far. Did I panic? (Maybe a little…or at least there was an awareness that we were well off the beaten path) We stayed the course. I was certain the fruit I saw was genuine and that changing our pace and pedagogy at this point would yield artificial results and could undermine this child’s ability to see truth and beauty in a subject that was very challenging for her.
She took the PSAT at this point and scored acceptably well. She ended up near the end of Algebra 2 by the end of her senior year. By the time she graduated, her ACT scores in math were very good – near scholarship level, and well above college entrance score minimums. Keep in mind, she only completed Algebra 2 at this point. Our slow-and-steady, short lesson approach yielded mastery that translated on a standardized test, and more than that, it illuminated truth for this student. She saw logic and order within math and felt richer for having conquered what was a challenging course. Our restful approach allowed my high school student the time to choose to dig into business based math on her own so that she could start her own photography business.
GRAMMAR —
I just don’t stress about formal grammar lessons, and by that I mean that I try not to overcomplicate it. My kids read excellent, worthy literature and learn a great deal about sentence structure, form, and mechanics through their reading and our weekly studied dictation lessons.
**Weekly**: I approach a simple grammar lesson through our weekly studied dictation lessons. If there is a semi-colon in the selection, we discuss the semi-colon – that kind of thing. Do this every week, from 4th grade-12th grade, and you will cover a lot over the years through those short dictation lessons, consistently completed. The way I find this illuminates truth and beauty in grammar is that the lesson is within the context of a literary selection the child is reading, not a random exercise sentence. The context gives the grammar lesson meaning…a relationship has formed between the child and the author and the ideas in that particular book, and that relationship allows for a generosity in asking questions:
**Why did the author choose to set off this phrase with a dash?
**How does it affect the sentence?
**How would this sentence read if we didn’t have commas to help us?
**Look at all this dialogue – how can we tell someone is talking?
**Identify the parts of speech in this selection – how did the author convey the mood through the adjectives chosen?
Words and form have meaning, viewing them in context helps illuminate that truth.
I approach only one grammatical/mechanical issue at a time in each dictation selection because we’re also covering spelling through this dictation lesson. We study two dictation selections/week. I keep the lessons short – studied dictation lessons are 15 minutes tops regardless of grade.
I do use Winston Grammar 3 times for each student: one year in elementary, one year in Middle school, and one year in high school. I began using it and continue using it because it’s a program that fits my short lesson paradigm and I can just include the grammar topic in my dictation lesson (so if we’re identifying adjectives in the Winston lesson, I ask the student to identify adjectives in their dictation selection rather than complete worksheet exercises.)
And that’s it. How did grammar translate? My daughter scored at scholarship level on the ACT in English, both in usage/mechanics and rhetorical skills.
WRAPPING UP:
Does the workload proportionally increase in high school? Yes. It should. And the lessons are also proportionally longer. BUT…in high school there is a tendency to slip into disproportionate lesson times (especially for math), assignments that are analytical and no longer focused on relationships and ideas, and there is certainly a tendency to hyper-focus on test prep in high school. Anything disproportionate is at odds with order and restful learning.
Karen,
I can’t believe that in all that wordiness, I didn’t address one of your specific questions about graduation requirements when following an educational path preferring rest, truth and beauty over testing and texts! >> Insert embarrassed grin here <<
We didn't have a problem at all in completing high school graduation requirements.
This will vary from state to state, but check to see what an academic transcript looks like for your state. Print it so you can write on it. You'll be able to see how many credits are required in upper level math, history, PE, etc.
The one area I was concerned about (because we completed less than I had planned) was math. Because we used Saxon, and because Saxon integrates Geometry in Algebra 2 we were able to claim Algebra with Geometry for credit on the transcript. Obviously, how you list upper level math will depend on what you use, the concepts covered, and how far you get. Because our senior also independently studied business math we were able to count that for credit as well.
We packaged our transcript so that it would "look and quack" like a standard state academic transcript. In other words, instead of listing European History from "x" period…our transcript simply said: 10th grade World History – like every other high school transcript from our state. Make sense? In other words, we didn't get creative with course names on the transcript.
Let me know if something is unclear in either of these responses, Karen! :)
I appreciate your wordiness, Jen. I have a highschooler and another one approaching highschool. Things have changed since we entered these years and I don’t like the changes. I want to go back to the mindset that I had when they were younger. Your words have given me much to think about. Thank you.
Jen, thank you SO much for such a detailed response! I will try to come back later to comment. :)
Jen,
I wholeheartedly agree with your comment. I have homeschooled for 22 years in a CM, classically inspired manner and I am only just getting below the surface. Can I tell you it is a wonderful journey of delight for me and I should allow it to be for my children as well. We have pared back and work on one or two concepts in math and grammar. Our large dry erase board has become a place of fun and fellowship. I have a math puzzle and two sentences to be discussed up and ready to go most mornings. I also use flash cards and charts a bit with Latin and math. This has become fun as well. We incorporate games and silliness which includes squirt guns from time to time, and my children are middle school and high school. Jollification, Cindy Rollins’ word, has entered our learning spaces and it is good and sacred.
I wanted to add another comment for thought. Please have relationships with your children outside of learning time. Children often feel like their parents’ work or lab rat and do not like or trust it. They desire to be loved and nurtured as a whole person, not just as a student. Don’t ask me how I know about this? ;-)
Thank you for your time and commitment,
Sharyn
Regarding grammar — like math, it is a language of logic. That logic explains something complex in a simple way, and I believe that simplicity is beautiful. It may seem complicated when you’re studying it, but compared to the complexity of a language itself, and more than that all the many languages that can also described by the same grammatical ideas — it really is quite amazing that it can be distilled to such a simple set of terms.
In some ways, I think the process of studying math and grammar is as important as the knowledge itself. There is a beauty in that act of striving for understanding. The struggle to answer hard questions is a cultivation of one’s character. And the success at the end of it is an accomplishment of great value. A mind that has been improved by thinking about difficult problems is itself a beautiful thing.
Thank you for this comment Laura,. Grammar being the language is language itself….. I am inspired already!
Meant to type “grammar being the language of language itself”
I realize the more I dig into each subject, relying on the wisdom of God discovered by the masters and the ancients, the more I am discovering good, true and beautiful things. The wonder I experience and am able to pass on to my kids is motivation for me to continue reading and learning to seek God’s fingerprints within these subjects.
I’ve been reading The Liberal Arts Tradition : A Philosophy of Christian Classical Education by Kevin Clark and Ravi Scott Jain. In it, he references Aristotle: “…Aristotle realized that multiple things can also be one in essence or quality…Only a few generations after the pagan Nicomachus, the early Church fathers elaborated the doctrine of God’s Trinitarian nature as the true foundational mystery grounding the problem of the one and the many. How God can be one nature and three persons is certainly inscrutable, though demonstrated as true in Christ. Augstine then recognized that if the Creator were a Trinity, creation might bear that imprint.” Wow! Evidence for the trinity in math! A way to more deeply understand the trinity–sign me up! As I was thinking more about this, I realized there is an “infinity” in math (God’s infinite wisdom, our soul’s existance etc.) and single numbers (God’s personal relationship with each of us, God’s incarnation in his one and only Son). There is truth in math that is not relative. In our culture, where truth is considered a matter of opinion, this is a way to speak on the one Truth.
I’m so thankful for this journey of discovery and wonder. We can be drawn into a closer relationship with the Creator through this discovery. What a gift.
Thank you, Schole sisters, for this forum. I’m looking forward to more posts since I only have 2 eyes and can only read a few minutes a day. I know there is so much more to discover! Here’s to discovering God’s goodness with you all!
This is such great help for Math, I can get my head around the beauty of math, but grammar? I am fairly convinced that if I could get more excited about it we wouldn’t be struggling in this area so much.
Any suggestions for finding beauty in grammar?
At the moment. I think I may have to just fake it till I find some:)
Starting on Monday grammar and spelling time will be renamed “bringing order from chaos time” (maybe bofc for short?) just to convince myself that’s what I’m doing:)
I get excited about grammar by diagramming. Maybe that’s just because I’m an English major, but I have always LOVED diagramming sentences. Especially Scripture. Especially Psalms. Those longer sentences can be broken down and you can see exactly what it is that God’s love/mercy/truth/whatever does and promises, etc.
A fun book for grammar: Eats, Shoots and Leaves by Lynn Truss. She has a few other books out that are geared toward adults and also several for children. My kids get a kick out of them. There are also some grammar YouTube videos that are funny, but I can’t in good conscience post them here for fear of offending. My sense of humor borders on the strange sometimes.
Also, giving children a part of a sentence (creative subject or predicate) and having them come up with the other part can be amusing. My 13 year old son loves those. And his creativity really shines. Nothing is wrong unless grammatically it doesn’t work.
“There is truth in math that is not relative. In our culture, where truth is considered a matter of opinion, this is a way to speak on the one Truth.”
I think this gets at how I feel about math. The elegance of that one answer that you will get no matter which way you solve it, and the joy of that moment of understanding — this is the beauty of math to me.
Math as bringing order from chaos. I love that. I’m looking forward to hearing how others emphasize the goodness and beauty of math in their home schools…
I do things like showing this video: http://youtu.be/kkGeOWYOFoA “Nature by Numbers.”
I love love LOVE this kind of thing, and loved it from childhood. My problem with math was that the love of this kind of thing — that is, the beautiful, the contemplative in mathematics — got drilled out of me by school math, and I’m only recently recovering it.
I will second the Let’s Play Math book. Here’s Denise’s blog, and you can follow her on Facebook. Another good website to follow is Moebius Noodles.
Another fascinating YouTube channel is Vihart: https://www.youtube.com/user/Vihart
This is a situation where I think you need to be in tune with your child’s learning style. Predominantly left-brain learners do fine with the way math is conventionally taught. When they get to high school or college they’ll be developmentally ready for the more abstract, conceptual part of mathematics — what it’s all ABOUT, that is. But predominantly right-brained kids aren’t developmentally ready for formal arithmetic until middle school or later. Instead, they need to “play” math, to think about order and patterns, so their arithmetic instruction needs to be something like the manipulative-based oral lessons from Horace Grant’s Arithmetic for Young Children.
But even left-brained learners will benefit from watching these videos, where they can SEE the beauty of mathematics.
Actually, I’ve been blogging a lot about math lately, but I haven’t yet gotten down to a lot of practical stuff, or to an orderly way of instructing our children. This is something I’m exploring, and just blogging stuff as I learn it — so it’s a work in progress. My latest blog post is about mathematics leading to theology. And you can click the “math” label and bring up my earlier posts on the topic, if you’re interested.
Thanks for posting my question! I’ve been enjoying the responses already and look forward to reading more.
Our daughters are 6 and 8 years old, so we are really in the basics right now. My best idea lately — just beginning to implement this — is for us to keep a “beautiful math” section of our journals in which we look for ways that things add up nicely or create pleasing patterns. We will see how this goes! I bought a half-size binder for each of us (Mama included) to use as commonplace books and nature journal and math journal.
My one other favorite fun math thing: Schoolhouse Rock videos! They are beautiful in their own crazy way.
I am so looking forward to seeing what everyone has to say on this topic! I’ve wondered the same thing myself: how can we find the good, the true, and the beautiful in the subjects like math and grammar. I hadn’t thought of it in the sense of how these subjects can bring order out of chaos. Interesting point.
Just wanted to come back really quick and share a couple resources that have been awesome in helping me to present math as a living, breathing subject that’s worth studying just for the fun of it.
“Let’s Play Math” by Denise Gaskins. I bought it as an ebook, but I think there was talk of publishing a hardcopy. Don’t know if that’s been done yet or not.
The videos at EducationUnboxed.com have been invaluable for showing concepts that are hard to grasp abstractly.
This blog is fun to follow: http://rarefied.weebly.com/
And Stratford Caldecott’s book “Beauty for Truth’s Sake” is amazing for showing the depth and beauty and significance of mathematics. It’s truly wonderful!
Thank you, Lisa, for these resources! I think I may use some of the Education Unboxed videos today!
My daughter is going to third grade after two years of homeschooling. I notice her teachers take a very relaxed approach to Math and the kids seem to get their choice of math activities. She likes a game called, Top It. I’m also very impressed with dreambox math online. My preschoolers are both excelling at it. Modeling delight rather than workbook pages everyday…. Sounds like a good plan to me. Good job ladies.
How fun to see myself mentioned today! :)
Like Tristan said above, it’s sometimes hard to communicate the beauty inherent in things like math and grammar (I’ve been stuying up on grammar lately and am becoming excited about that now as well). But I’m confident that if I just continue to model delight, they will at least grow up knowing that there is something worth loving there, even if they don’t always see it.
Lisa, you said: “But I’m confident that if I just continue to model delight, they will at least grow up knowing that there is something worth loving there, even if they don’t always see it.” Great point!
For me this has been one of those struggles because even when I as an adult can see and appreciate the beauty inherent in a subject, I cannot always open my children’s eyes to it. I think that some of it takes perspective that children do not always acquire until they’re older. I love the order and predictability of math now, as an adult. I find satisfaction as I am reteaching myself math when I grasp a concept and work the problems and ‘get it’. My children are not so impressed when their turn comes to work the problems. They may accomplish a page of good, solid work, but they do not appreciate it usually. :) I’m working with eight children 8th grade and younger. Occasionally they do see the beauty and feel the satisfaction of bringing order to an assignment. I love when that happens. But I have learned to accept that right now I can only share my enthusiasm and let it simmer under the surface of their minds until they are ready to understand it too.
Tristan, you said, “let it simmer under the surface of their minds until they are ready to understand it too.”
I completely agree. This points to the only thing I know to imitate regarding the reality of bringing order out of chaos. Dorothy Sayers talks about waiting on Pentecost. There is actually a teaching method that makes provision for this very thing, called the mimetic sequence.
It helps us set before our children things to imitate, but then allows them to wrestle until they apprehend. Never micromanaging, always leading and then getting out of the way.
So one way I think we can “illuminate truth and beauty in the areas of the curriculum where we are least inclined to think it exists.” is through the mimetic sequence. Because through teaching that way we can help our kids encounter the delight of discovery, which is of course a way of illuminating truth and beauty.