Plain of View

    By Shilo Bartlett

IMG_0065Our children as a whole are incredible creations. They have minds that were meant to be shaped and molded from a very young age into what they will eventually become as adults. I personally haven’t been a mom for an incredibly long amount of time (11 years to be exact), but I have observed enough to know that it is much better in the long run to encourage that shaping and molding than to push against it.

I say that because we are in a phase right now with our children where we are greatly appreciating our decision to homeschool them with the Garden School as our supplement. Our kids are shaping and molding every day, and we are watching this happen rather than observing it happen from a distance. The children imitate behaviors they see every day, and we are glad that we can have them watch us and then help change what needs to be changed. We understand that days are not to be thrown away; that every moment needs to be grasped, and that the little things in life matter very, very much.

I have had moments lately with my children where they have challenged me greatly in the area of discipline. They have chores every day that must be taken care of, and then their school needs to be attended to. And we have come to an agreement that they have to be somewhat self-motivated, as I am only one person, not five, and cannot be constantly following their little hands everywhere to pick up after them. But along the way, we have found a very nice key to life… something I have known, and yet hadn’t fully grasped until recently. Let me share a short story to illustrate:

We as a family were at the Sukkot festival at the school a few weeks back, going from booth to booth and enjoying the crafts. At one particular booth, I sat down with my girls on the grass to help them. A little one-year-old girl from another family came alongside us and started watching what we were doing. Pretty soon, we had her saying the words and touching the craft too. We moved to the next booth, and the same thing happened. She was right there beside us on the grass, watching attentively and trying to touch and say what we were doing. Now, the interesting thing is, the minute that we stood up (i.e., were above her plain of view), she would wander away and find something else that she could touch and feel. But the minute we were back down on the grass, she was right there.

Why is this important? Well, my kids and I get along much better when I am living in what I like to call “their plain of view.” Just like the little girl on the grass, she does not see what you see, or hear what you hear. She has her own little world going on at her level every day! Same thing applies to my kids. When I am on their “level,” I see things I would have never seen, hear things I would never have heard if I was just living in “my world.” My children are teaching me every day about all the new amazing discoveries they make, just by being them!

Now the neat part about this is that when applied to our school at home, this principle becomes (and has become), an integral part of how I interact with them. When school needs to be done, I take into account what they have been doing, what they are doing currently, and then how best to apply that to their learning habits. As a practical tool, it has meant the world to us.

I hope that you have enjoyed this little excursion into our world!

How do you apply your child’s learning into your school plan every day? Let me know in the comments–I would love to hear your thoughts!

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Shilo_BShilo Bartlett is a super organized, over reaching, strong-willed mother of three. She loves having the hands-on time with her kids that homeschooling and The Garden School have allowed her. She grew up in the Colorado River Valley, and went to public school until 6th grade. Her mother homeschooled her and her three siblings through high school, and then she attended CMC graduating with a degree in Applied Science in the Veterinary Field. She has always read voraciously, and written throughout her life for many publications. Her family is her passion. Her driving motivation is to encourage a love of learning.

Finding the Music in Math

    By Dawn Lamping

      “Mathematics is the language with which God has written the universe.” -Galileo Galilei (1564-1642)

      Photo credit: Wikimedia Commons

      Photo credit: Wikimedia Commons

      Something very sad has happened to numeracy in our culture. Most of us were educated in a school system that isolates mathematics, teaching one single path to math: memorization of abstract facts and algorithms. Cut off from its context, its separation renders it dead, lost, decidedly “other”- easy to dismiss or feel antagonistic towards. Consequently, many of us have divorced ourselves from math.

      But as Galileo told us, math is important, a vital and fundamental part of this beautiful Creation we are gifted to live within. Creation is its context. Math is a blueprint from which we cannot separate ourselves: it is in music, in our bodies, in the structure of elements, in color and in dance. In some deep way, to separate ourselves from math separates us from God. Or alternately, when God is alive in our hearts, math comes alive in our minds.

      To give our children the gift of a Classical Christian math education is to open a door for them they will journey through all their lives. With the right viewpoint, drilling and memorizing numbers can be fun; it feeds confidence and builds a foundation for success. Even better, when beauty is found in numbers, it feeds the hungers of the soul and sets a foundation for truth in the heart.

      For the very young, finding numbers they know in nature and life is like a treasure hunt. Flowers exhibit petals in multiples of three and six (monocots), or multiples of four or five (dicots). There is one sun, one moon, seven continents, one mother, one father, two parents. Families come in many number combinations, and drawing a family tree will reveal patterns of the powers of two (aptly named!). It can be fun and revealing to keep a number journal with photos and drawings representing the numbers.

      For older students, the history of numbers is fascinating. A math timeline illustrates the relationship of man to number in a graphic way. The writing of numbers predates writing of literature! The earliest examples of writing we have show tallies of moon cycles and the trading of goods. The ancients saw numbers as having color and personality. Musical scales were an essential element of the study of geometry, and instruments were based on mathematical models of tone and form. The ratios of the lengths of strings were the basis for the discovery of harmonies in math, while the golden ratio (www.goldennumber.net) of 1: 1.618 was the basis for beauty in art and architecture. Even the dimensions of Solomon’s Temple and the Ark of the Covenant follow this pattern.

      A project the “tweens and teens” enjoy is one I call “Meet the Numbers.” We divvy up the list and research each number from 0 – 12 to “introduce” the number to the group as one would a new friend. Each number has its own configuration of factors, multiples, and shape. Sometimes amazing stories of the “lives” of numbers pop up, such as the strange battle over the number zero in the Middle Ages. Zero was a new number in Arabic culture (called the “sifr”), and the rulers of Western Europe actually outlawed its use until it was finally accepted in the 1500’s.

      One sequence of numbers-which adds each new term to the previous one-looks like this: 0 + 1 = 1; 1 + 1 = 2; 1 + 2 = 3; 2 + 3 = 5; 3 + 5 = 8. It was discussed by Leonardo Fibonacci of Pisa, c. 1130. The “Fibonacci Sequence” can be found in the measurements of the human body (all ages love measuring themselves), in musical scales, in church architecture, in natural spirals of leaf growth in plants and sunflower seeds, in the cycles of the solar system, and many more.

      We are quite lucky, we who get to explore this pattern with our children, because it also teaches us the things we never had the opportunity to learn about math. When children are young, they can find the numbers in nature. As they get older, they can draw things such as the golden spiral (see the “Nature by Numbers” video, below), or compare proportions through algebra.

      To step forth on this path as mothers and teachers asks us to let go of our assumptions about what math looks like and add another dimension to our work. This can seem strange at first until we form a new conception of what math means. Without shorting on memorization, adding space for math discovery will enrich and motivate both us and our kids.

      It’s time for us to relax and discover numbers afresh; resting in the truth that when numbers have meaning and depth, facts are just plain easier to memorize anyway!

      Let’s chat: How do you view math? Is it a blessing or a curse?

      (Readers: as an extra bonus, check out the “Freebies” tab at the top of this page for one last piece of advice from Dawn!)

      A few good resources:

      Living Math (www.livingmath.net)
      Math From a Biblical Worldview
      Nature by Numbers (www.youtube.com)
      The Golden Ratio (www.goldennumber.net)
      Donald in Mathemagic Land (Disney, 1959)

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    Dawn Lamping didn’t see much of fifth grade recess because she was held in to try to “catch up” in fractions. That experience cooled any interest she had in mathematics until she started her family in 1994. Through the journey of homeschooling two children, Dawn discovered the “blueprints of Creation” within mathematics. She feels blessed to share the joy of math and enjoys exploring and mastering numeracy in the classroom through hands-on experiments, fun drill games, geometry, and art. She holds an Honors Degree in Psychology from the University of Missouri and completed teacher training at Arizona State University.