issue 115 fall 2013
A PUBLICATION OF
Oak Meadow
Living Education
Curriculum & School
Innovative Math and Science
IN THIS ISSUE…
Math: An Exercise in Balance e Citizen Science
Living Math e Backyard Science e Curriculum Spotlight
Earth Cycles: Seasonal Activities e Fun with Pattern Puzzles
CONTENT
PAGE
Guest Contribution
8 Kathleen Morse: Math: An Exercise in Balance
rticles from Oak Meadow faculty and staff
A
6 Julie West: Citizen Science
4 Jacquelyn O’Donohoe: Living Math
Oak Meadow families and community
PARENT CONTRIBUTION
10 Heather (Only Passionate Curiosity) on Backyard
Science
12 Camilla and Saffron: Lavender Lemon Cupcakes
STUDENT WORK
2 Emma Agudelo (science journal 7th grade)
19 Rohini (physics lessons 8th grade)
3 Andrew Stein (habitat video 6th grade)
7 Sasha Bauer (ASP)
15 Lexi Wallace (6th grade architectural drawing)
Activities
14 Earth Cycles: Seasonal activities for harvest
16 Math and Science for Multiple Ages
Crafts
18 Little Acorn Learning: homemade wormery
28 Oak Meadow: Leaf print tiles (Kindergarten:
First Book of Crafts)
22 Fun with pattern puzzles
ews and Resources
N
21 Math and Science resources
27 Facebook Rewind: Math toys
19 Curriculum spotlight: K-8 math
21 Book Review: What’s Math Got to Do with It?
25 OM News
Living Education
A publication of Oak Meadow
To contact Oak Meadow
802-251-7250
[email protected]
Fax: 802-251-7258
oakmeadow.com
LIVING EDUCATION is the educational journal of Oak Meadow
and welcomes submissions from our readers. Send all inquiries
and submissions to [email protected]. We look
forward to sharing your story!
2
Emma Agudelo
Grade 7—science journal
Living Education, a publication of Oak Meadow
As everyone around the Oak Meadow office knows, the
excitement builds as each issue of Living Education
comes to fruition. We look forward to sharing all the
ideas and information that have inspired us around
the current topic. Each issue is special in its own way,
but this one was particularly exciting to put together.
Innovative resources for learning about math and
science abound in unprecedented ways, thanks to the
Internet and the free and enthusiastic sharing that it
encourages.
With STEM (Science, Technology, Engineering, and
Mathematics) education in the news frequently, it’s important
to remember that combining STEM with the humanities (or
transforming STEM to STEAM, which is RISD’s clever call to action) best prepares our students
for a successful career and life. Recent articles on the topic are everywhere: the Washington
Post and WP Opinions, the Chronicle of Higher Education, Huffington Post, Informal Science, and
TeachThought, where author Ben Stern writes, “the study of the humanities affects a person’s
character, intellect, and judgment… [The humanities] might make a person a better doctor
or engineer, since both careers require ethical decisions and value-judgments. But they
also help a person enjoy thinking, feeling, and learning, pleasures we owe to our students.”
At Oak Meadow, we believe that character development and artistic development enhance
and support intellectual development on
all levels. There is heart at the core of an
Oak Meadow education, and it’s there for a
reason.
Thanks to reader feedback, in this issue of
Living Education you will find more practical
ideas than ever, plus links to Internet sources
that may surprise and delight you. New in this
issue, we’ve included a way for you to “like,”
share, and comment on individual articles.
Your feedback helps us create a more useful
publication to supplement your lifestyle of
learning. Many thanks for your interest in
Andrew Stein—Grade 6—Pennsylvania
Oak Meadow, and happy reading!
Wildlife video for Basic Life Science
At Oak Meadow, we believe all students deserve an education that
nurtures confidence, curiosity, and a love of learning. Since 1975 we’ve
crafted homeschooling curriculum that is infused with imagination
and heart, builds on a solid foundation of educational principles, and
integrates learning and life.
INDEPENDENT LEARNING SINCE 1975
Living Education, a publication of Oak Meadow
We call it a living education.
3
Living MATH
by Jacquelyn O’Donohoe
Oak Meadow math teacher
How do you use math in your everyday life? Pause for a moment and try to think of a few examples.
If you’re like many people, your answers probably involve money, measurement, and/or time management.
Most of us use math to make a budget, calculate discounts, and count change. We measure ingredients for a
recipe, keep track of our kids’ growth, and figure out how many gallons of paint we’ll need to cover the living
room wall. We read bus schedules and estimate travel time between the grocery store and the soccer field. We
know we use math in very basic ways.
Now think about what, specifically, all of the examples above have in common. You may notice that they all
involve working with numbers. After all, math is just the study of numbers, right?
OR IS IT?
The truth, surprising as it may be, is that math is not limited to numbers. It is also the study of patterns,
structures, processes, space, change, and so much more. Mathematics is both a science and an art. Indeed,
mathematics is where science meets art; it allows us to make sense of our thoughts and observations by
recognizing and abstracting patterns and structures. Doing mathematics is a creative process.
Math is present everywhere we look. Yes, we use math when we work with numbers, but we also use it
when we think logically, when we observe patterns, and when we consider possibilities.
Math is also at work behind the scenes, forming incredible connections in surprising places such
as nature and fine art. For example, the arrangements of seeds on a sunflower head, of the scales
of a pinecone, and of the florets on a cauliflower head are all related to a certain sequence,
the Fibonacci numbers. So too, the number of petals on many flowers, the number of
branches on some branching trees, and even the number of ancestors on the family tree
of a honeybee relate to the Fibonacci numbers. The connections don’t end there! The
Fibonacci numbers also relate to the Golden Ratio, the ratio formed by the lengths of
the sides of the aesthetically pleasing Golden Rectangle. The Golden Rectangle, in
turn, forms the basis for the spiral-like shapes of the nautilus seashell, hurricanes,
and spiral galaxies, as well as the proportions of certain measurements of the
human body, such as facial features. The Golden Ratio and Golden Rectangles
also make an appearance in the fine art and architecture created by our
Learn more:
predecessors—the painting of the Mona Lisa, the Parthenon in ancient
Fibonacci
Greece, and the Great Pyramid at Giza all contain measurements that
numbers
follow the same proportions.
Unfortunately, many students are unaware of the myriad creative and
awe-inspiring aspects of mathematics. Too often the mere mention of
math evokes memories of dry formulas and repetitive calculations.
The good news is that although many students don’t realize that
the entire world is a mathematical playground, they are almost
certainly already exploring it to some extent without even
realizing it! Children frequently use math in everyday play—
when they perform music, play strategy games, engage in
sports, and create doodles, to name a few.
Homeschooling families have a unique opportunity
to make math a dynamic, engaging, creative,
4
Golden Ratio and
Golden Rectangles
Here’s another fun
source: Donald in Mathmagic Land, produced
in 1959 and now widely
available on the internet
(here’s one site that has it,
SchoolTube) is a 27 minute
educational film that follows
Donald Duck as he learns about
Pythagoras, math and music, the
Golden Rectangle, and more.
Living Education, a publication of Oak Meadow
and
fun
experience.
Here are some
ideas to encourage
students to think
mathematically and
appreciate math in the
world around them.
H
ave a shape hunt. Younger
children can search for circles,
squares, and triangles, while
older students can seek out cylinders, rectangular solids, and pyramids. Look for other shapes, too! Bonus points for lesser-known shapes like
lemniscates (figure eights) and spirals.
P
lay estimation games. How many strawberries are in this carton? How much money will it
cost to fill the gas tank today? Given that we are
traveling at this speed, about how long will it take
us to arrive at our destination? The person to come
closest—and justify their estimate—wins.
C
reate measurement games. Give everyone a ruler
or tape measure and call out a measurement. See
who can find an object closest to that measurement.
Get creative—measuring linear length is great, but
try circumference, area, weight and volume, too.
Quick, find something that weighs one pound.
H
ave the entire family draw a map of your neighborhood. Plan a new route to take for a walk. Or draw
a scale plan of a room in your home using graph
paper. Measure the space taken up by pieces of furniture and cut out to-scale representations for each
piece. Play with ways to rearrange the furniture.
G
et kids involved in vacation planning. Older students can research activities, help create an itinerary,
and plan out the travel route. Consider various routes
or modes of transportation, comparing distance, time
of travel, and cost.
A
s a family, search for patterns wherever you go. Create your own when you feel inspired. When listening
to music, what patterns do you hear? Imitate what
you hear then change it up to make your own pattern.
Look for symmetry. Observe snowflakes on black pa-
Living Education, a publication of Oak Meadow
per with a magnifying glass. Can you create a similar
snowflake using paper? What kind of repetition do
you see on that wallpaper? What designs do the floor
tiles make? Older buildings are fantastic specimens
for pattern observation because they often feature
details like friezes and tiles. Copy some patterns you
like and customize them to your own liking.
I nvolve kids in all aspects of shopping. Before a
grocery trip, announce a budget and have the kids
search advertisements for sale items and make a
grocery list. At the store, have them keep track of
spending so you don’t go over budget. Allow them
to hand money to the cashier and count the change.
Older students can calculate the unit cost of items
to determine the best value per unit. Then discuss
whether something is truly a bargain just because it
is cheaper. Consider how much will actually be used,
whether you really NEED that item, and whether the
quality is sufficient.
E ncourage children of all ages to make observations,
ask questions, and experiment to find the answers.
What size and shape rock works best for skipping
stones, and why? Can you throw a small, heavy ball
or a large, light ball higher? How can you compare
the heights? Will we arrive at the library faster if we
walk on this road or that one? Be supportive of kids’
exploration of answers to their own questions.
As a teacher of mathematics, I consider it my duty to
teach not only the “how” and “why” of traditional math
topics, but to also encourage students to notice and
engage in the mathematics at work in the world around
them. While it is imperative that we equip students with
practical math skills to help them succeed as adults, I
believe it is equally important to introduce them to the
beauty and wonder of mathematics so they are inspired
to ask and answer their own “hows” and “whys.”
Jacquelyn O’Donohoe holds a BS in Mathematics.
She has been teaching and creating mathematics
courses at Plymouth State University since
2007 and currently teaches high school math
at Oak Meadow. Jacquelyn particularly enjoys
encouraging students to develop an appreciation
for the beauty and relevance of mathematics in
the world around them. Jacquelyn lives among
the picturesque lakes and mountains of New Hampshire, where she
homeschools her own children. 5
Citizen Science: how YOU can get involved in real science!
by Julie West, Oak Meadow science teacher
there is a new craze
hitting the streets, and hopefully this one
is here to stay. It’s called citizen science.
With the advancement of technology,
smartphones, and instant data retrieval
and input, it has become easier and easier
for “regular” people to do real science.
So much of science research is the
methodical, sometimes tedious, collecting
of data. When you read scholarly scientific
articles and reports, it is not readily apparent
how much time went into collecting that
data. Not only time, but often infinitely
monotonous hours of recording time in
seconds, counting, observing, watching.
And then sometimes the technology breaks
down. Cameras freeze up in the Arctic.
Animals shed their radio tags, data cards
go bad, or electrical systems short out. My
daughter, whose research entails recording
whale sounds, had a hydrophone in the
ocean for seven months. With excitement,
they went to retrieve the appliance, only to
find that something had fried inside and
they had only three weeks of data. There
goes another season!
The fieldwork is the fun part! Now we
have to go back to the office or lab, do
more observations, and then spend days
and weeks at the computer, entering data,
collating, interpreting. And then we have
to go back out there and do it again and
again and again, because as any scientist
knows, the more samples that are studied,
the more validity there will be in the results.
Why not get some help? The old answer was
“because it costs too much and we have no
funding.” Now we have a new answer: Yes,
let’s! There are people everywhere interested
in contributing to science, especially if it’s
made easy for them. With citizen science,
it is. Citizen science is rapidly gaining
acceptance in scientific circles. Not only do
citizens collect and report data, but they are
becoming valuable helpers in analyzing the
vast amount of data that is now available
due to increased technology.
6
For example, here is a project where
you can help identify what is on the
ocean floor. We have technology to
take millions of pictures, but who is
going to look at all these pictures? This
is something you can do at your leisure.
Or you can look the other direction and
classify galaxies.
If you would rather spend your time outside
observing nature, there are many options for you to help out. Here’s a neat one
where you get outside and record pollinators that come to your plants.
Here’s one of my favorites—categorize roadkill! Do you realize how much
valuable information about animal movements and populations can be obtained
from roadkill, something that is usually ignored? Unlike live animals, roadkill
doesn’t run away from you when you approach! You can help science when you
are out for a bike ride or a walk.
You can record when and where you see an aurora, help create a map of marine
debris, help map carbon-producing power plants, count frogs, watch birds,
measure snow and ice depth—the list goes on and on. It is easy, however, to get bombarded and a little lost with all the data. I recommend
finding a topic you are interested in and sticking with it for a while. Find one
project that gets you outside and one project where you help analyze data with your
computer. Delving halfway in many projects doesn’t really give you the depth that
you need to feel like you’re doing real science. Learn the subject that you are getting
involved in and use this as a tool to broaden your scope of science.
There are many citizen science projects, both outdoors collecting data and indoors
analyzing it, described on the following websites:
Scientific American
Cornell Lab of Ornithology (well-developed citizen science birdwatching
projects adaptable for all ages)
NASA
Zooniverse (a “master list” of citizen science projects)
The best part is that these are not just classroom activities using hypothetical
scenarios to mimic how science is done. While those activities are inherently
valuable, think of the additional value of being an active contributor. The scientific
world appreciates every contribution. Science is now something that is not up to
them to do, but for us to help with. As Albert Einstein said, “the whole of science
is nothing more than a refinement of everyday thinking.” Regular citizens doing
real science—ride the wave of citizen science. Surf ’s up!
Julia West is passionate about the environment and science and is
continually finding ways to combine her interests in science and
the outdoors. In addition to teaching science, Julia spends time
biking, whitewater rafting, and is currently training to run a halfmarathon. This summer she returned to Alaska to learn more about
helping students open their eyes to the wide world around them. (See
Oak Meadow News for details of her Alaska trip.)
Living Education, a publication of Oak Meadow
Students who plan to graduate from Oak Meadow are required to
design and complete an Advanced Study Program. This capstone
project exemplifies the spirit of independent learning and
offers students the opportunity to develop a particular area of
interest. Alexander (Sasha) Bauer’s Advanced Study Project is a perfect
example of how Oak Meadow students can collaborate with and learn
from professionals in any field of interest, gaining practical experience
while making valuable contributions in the wider world.
Sasha Bauer’s interest in mathematics and computer science
led him to participate in a complicated research project and
use this as the basis of his Oak Meadow Advanced Study
Project (ASP). The project called for using applied calculus
to create a more reliable and efficient procedure for analyzing
data from blood samples and positron emission tomography
(PET) studies of the human brain.
Oak Meadow
STUDENT
Alexander
(Sasha) Bauer
For those who are curious about what this type of data looks
like, here is a graph from Sasha’s final project:
Using highly technical applications of advanced calculus, Sasha
set out to find a computer solution to a differential equation
that described the transport of a radioactive tracer between the
cardiovascular system and the brain. The title of Sasha’s project,
“Numerical Differentiation of Blood/Brain Barrier Equation for
Studies of Dopamine Receptor Regulation,” indicates the complexity of his involvement. His work was aimed at helping to
clarify the mechanics of the brain’s response to an excess of the
neurotransmitter dopamine. Since dopamine irregularities are
indicated in problems such as Parkinson’s disease, compulsive
gambling, social anxiety, ADHD, and drug addiction, this work
may have significant practical applications.
Sasha’s father, William Bauer, is an applied mathematician who
advised and supported Sasha’s project. He explains, “Sasha
showed the blood-brain barrier equation can be reliably (and
reliability is crucial) solved on a computer, with a specialized
form of well-known numerical differentiation techniques.
Sasha came up with the specialized form himself. It was
basically a matter of trial and error (hundreds), but Sasha was
eventually successful. I remember the exact moment when he
said, ‘Got it.’”
During this project, Sasha was mentored by Dr. Dean F.
Wong (Vice Chair for Research at the Johns Hopkins School
of Medicine, Department of Radiology), Dr. Albert Gjedde
(head of the Institute of Neuroscience and Pharmacology at
the University of Copenhagen), and Dr. Rodger D. Parker
(Professor Emeritus, Bloomberg School of Public Health,
Johns Hopkins Medical Institutions). The Oak Meadow
teacher who evaluated Sasha’s participation and final project
noted that he demonstrated an impressive tenacity and
commitment to his work that garnered the praise of his
professional mentors. Sasha achieved his goal of developing a
valuable new tool for the medical science community to use in
analyzing neurological data.
Living Education, a publication of Oak Meadow
Some explanations to help us better understand and appreciate
Sasha’s work:
• me indicates the mass of tracer in cerebral-spinal fluid
• mb indicates the mass of tracer bound to brain receptors
• measurements are in picomole/milliliters
• one picomole is one trillionth of a mole
one mole of water is a little over one tablespoon
•
one milliliter is about 12-20 drops of water (depending on
the size of the drop)
• “compartments” refer to capillaries, cerebrospinal fluid, and
“binding sites” (brain receptors)
• radioactive
tracer molecules are capable of crossing the
blood-brain barrier, so tracer molecules may be in one of
these three “compartments” (blood, fluid, or stuck to a receptor in the brain)
• radioactive
tracers (in this project, raclopride) have about
the same dose of radiation as a dental x-ray
7
by Kathleen Morse
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Let’s talk about math, baby! (No, not
the annoyingly catchy ’90’s song by
Salt-N-Pepa.) Many teachers (and
parents) choose not to have formal
academic lessons in the nursery and kindergarten. This is especially true in Waldorf early childhood programs,
like the one where I work. However, math learning does begin very early in life, and young children are
exploring and using math continually.
Math in the Early Years
Let’s start at the beginning: a new baby is born. The first months
of a child’s life are spent integrating movement patterns. From
flailing hands and feet to that first moment of focusing on and
realizing he has hands. Then turning over, crawling, standing
up, and then that magic moment, that moment when he lets
go of your pants leg, balances unaided for a brief instant, and
takes that first step. Having had the opportunity to go through
all the small steps leading up to this point, that magic moment
is an early experience of math.
How did I get from an infant’s movement patterns to math?
The key word in the last paragraph is balance. An infant must
coordinate all of his limbs and systems in order to achieve, on
his own, balance. Let’s look at a common toy for nursery and
kindergarten children, a see-saw, as an example. A see-saw can
be made of any long branch or board put over a stump or tree
or rock. Children climb onto one end and at least one child
or teacher on the other. Together, both sides must navigate
balance to create the fun situation of going up and down. Too
much on one side and the children need to scoot forwards or
backwards, add or take away children. Children can also move
the fulcrum and create a different balance situation. These
children are balancing equations with their physical bodies.
Having had the opportunity in nursery and kindergarten to
play, they gain an inner sense of balance, equality, and physics.
Math in the Early Grades
Take this into the early years of formal learning, when
students are introduced to all four operations—addition,
subtraction, multiplication and division. The common
denominator in all of these operations is the equal sign. The
equal sign is sometimes introduced to the children through
a story because stories offer an imaginative representation of
complex concepts, which children of this age respond well to
as an entry into the conceptual. This story could be a dispute
between a farmer and customer regarding the fairness of the
8
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−
×
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measurement of a scale. The scale is introduced
pictorially to the children and later the image
is taken away to leave the symbol of the equal
sign. This moving from pictorial image to
abstract symbol recapitulates the progression of
humanity from oral language (tribal cultures)
to pictorial images (hieroglyphics in Egyptian
cultures) to abstract symbols (equal sign). Not
only have the children had a bodily experience
of the equal sign and balancing an equation,
but they are also led through this progression
of human development.
This work with the four operations is brought
about in a way that’s not one added to one is
two, but rather introduced from the beginning
as an exercise in balance and sets the stage
for algebra as it is formally taught in middle
school. This way of introducing the operations
encourages circular thinking rather than just
linear processing based on accumulation (1+1+1, more and
more and more).
Of course, elementary school children are also expected to
memorize their number bonds (addition and subtraction
facts) as well as multiplication and division tables, but this
is not the starting point. The starting point is balance and
the opportunity for children to develop the flexibility of
thought to solve problems (rather than just getting an answer)
and, at the same time, to see the interconnections between
the different operations. These capacities are invaluable for
the introduction of algebra in seventh grade and topics like
quantum mechanics and calculus in high school as well as
for living a balanced life.
Allowing the Time and Space for Innovation
Letting children gradually and imaginatively enter mathematical
concepts, taking their time to understand on a deeper level the
Living Education, a publication of Oak Meadow
real meaning of mathematics, brings
to mind a recent TED Talk by Carl
Honore called “In Praise of Slowness.”
A wake up call came in Carl’s life when
he was first elated and then repulsed by
the “One Minute Bedtime Story.” He
began to stop and reassess the fast pace
of his and his family’s life. Carl even
brings his TED talk to the ridiculous,
talking about “Speed Yoga” classes in
NYC. He then goes on to talk about
how we fail to notice the toll that speed
takes on our health, environment,
families, and life.
You might know of the “Slow Food
Movement,” “Slow City Movement”
and “Slow Parenting.” There’s even a “Slow Education
Movement.” Carl sites research from a high achieving private
school which banned homework for all children under 13 years
old. The high achieving parents freaked out: “Our children will
fall behind!” The principal stood his ground. The exams came
in at the end of the year and marks went up 20 percent. Ivy
League schools are finding that while their students have high
marks and resumes jammed with extracurricular activities, they
lack spark and the ability to think creatively and to dream. This
is something the Ivy League schools are now having to facilitate
in the development in their students.
Our creativity and capacity for innovation are what Americans
have traditionally had as a leg up on other countries. However,
in our zeal to rush forward, our educational system has failed to
allow students the time and space for creativity and innovative
thought. This will lead to problems that are sure to impact the
American business and innovation world.
Math in Action
A few months ago, when I looked out my office window at
Lakeside School (a farm-based Waldorf early childhood and
elementary program in Essex, NY), I saw the first graders
outside working on their “freezer” that they had been building
over the winter to experiment with freezing different objects.
They experienced that the daytime temperatures had to be
warm enough for melting to occur or they had to get water
from the kitchen to pour on top of the ice so that overnight the
objects would freeze into the freezer. Things froze in different
crystalline patterns and layers depending on the conditions. The
intricacies of creating a natural freezer, and the longevity of this
project, would not be possible had the elementary students had
little or no time for outside because there was too much book
work that needed to be done.
This project has gone on as the weather warmed; they are
now working with mud. They told me today that they had
Living Education, a publication of Oak Meadow
turned their freezer into a machine to create anything. When
asked to explain what anything was, they showed me how
they positioned their machine at the bottom of the rain
spout and built a ramp for the water to come down into their
freezer in the winter and now their mud maker in the spring.
One first grader went on to tell me how they were using the
right composition of sand, dirt and water to create the right
consistency of mud in the machine (percentages! proportions!
fractions!). Then, they take the mud and make anything.
Indeed, this is a machine to create anything! They are now
selling their creations at the store they built (more math-inaction). Building math foundations in this organic way gives
students the best preparation for formal academics.
These children are given time to create new inventions– who
knows when the next “green” freezer might be in the making,
or a machine to make anything? Time is the key ingredient.
These children are given time to creatively solve mathematical
situations and time to work through social conflict. Time to be
patient, and time to rest and reflect. Time to create, tell stories,
dream, investigate the world, and be bored. Time to be children.
All the qualities that the Ivy League schools say are missing
in the majority of their students. And, coincidentally, all the
qualities that many homeschooling families regularly encourage
as a natural extension of the lifestyle they have chosen.
Children need to develop the academic, social and emotional
skills to create the world of the future, which will look quite
different from the world we now know. Providing them with
solid experiential foundations—and the time to explore the
concepts underlying abstract academics—gives children the rich
nourishment they need to be able to work with the elements of
the world around them and create a positive future.
Kathleen Morse has worked as a Waldorf school teacher and is
currently the Office Administrator at Lakeside School in Essex,
NY. Her other interests include renovating a 19th century house
and enjoying life in the mountains.
9
Backyard Science
PARENT
Contributor
Heather Aliano
I never used to be the kind of person to hug a tree.
Sure, I always liked them, but after spending a year up
close and personal with our own adopted tree, I am full of
so much appreciation for these amazing plants. This year I want to
encourage you to find a tree to adopt, and hopefully soon you’ll be
hugging trees right along with me.
First things first, you need to find a tree to adopt. Take the kids outdoors and let
them pick a tree or two to make their own special tree. Ideally, find a tree you
can see from your windows. You want a tree you will see and walk past often so
studying it will be easy and become a natural part of your day.
Once you have a tree, go ahead and give it a nice name (ours is Tilly, because
he’s a Tilia) and get to know it better! We take pictures once a month, not only
from a distance so we can see the whole tree, but also detailed pictures of the
little changes that are so easy to miss, like color changes in the leaves, budding,
and the creatures that call our tree home.
During the month, take as much time as possible to stop and look closely at
your tree. We tend to visit it on the way out to the car each day. It only takes a
moment!
Here are some ideas of things to look for:
Look at the leaves. What shape are they? What pattern do the
veins make? What do they feel like under your fingers? I was
amazed to feel the difference in our tree’s leaves throughout
the year. In the spring, when the leaves were new and
uncurling like butterfly wings fresh from the cocoon, they
were oh-so-soft and silky, with the slightest peach fuzz. Now
that summer is here in all its glory, the leaves are thicker and
feel waxy instead of downy.
Is anything a little out of sorts with your leaves? Maybe a bug
has made a snack out of them, or they have a disease. My tree has
a section with little green bumps on the leaves, which broke our
hearts. Our poor tree is fighting a disease. Is yours?
Look underneath the leaves. Are the undersides the same color as the top?
Has anything made its home under there? If you look closely, you may be able
to find bugs in their various stages of life.
Do you see any seed pods growing or buds forming?
This time of the year your tree will be getting ready
for fall, and big changes are coming. Each day these
seed pods will get bigger and more developed.
Look at the branches and twigs. Are they smooth or do they have bumps, knots,
or thorns? Is there a pattern to how they divide? Do you see any new growth?
Get close to the bark. Feel it under your fingers. Bring out a magnifying glass
and see if anything is crawling inside the grooves. Use paper and crayons to
make a rubbing. Teach your children that bark protects the tree and serves a
function a lot like our own skin. Is there any sap coming from the tree? Is there
moss or lichen growing on the trunk?
10
e: Adopt-a-Tree
Check the base of your tree for living things. Our tree is home to a busy colony
of fire bugs. The kids call them love bugs because they are red and are “always
kissing.” In the winter, they hardly moved from the deepest crevice at the base of
the tree. These days they are busy running up and down the trunk and you have
to be careful not to step on them if you get too close!
Are there any birds, squirrels, or other
animals visiting your tree? Have they made
a nest or home in it? Do they eat something
from your tree, or are they going elsewhere
for food?
Don’t forget to look at the roots too! Are
any visible above the ground? How far out
can you trace them? While you’re looking
at the ground, why not see what kind of
shadows your tree is casting?
Older kids can keep a “tree journal” where they can sketch the tree, details of its
leaves and branches, and document the changes they notice. Younger kids can
simply talk about the changes and help you take photographs to document a
year in the life of a tree.
You don’t need to talk about everything each time you look at the tree. One
month you can focus on leaves, and the next month you can learn about the
seeds. Follow your children’s lead and learn more about the things they observe.
Each time they go back to the same tree, they will learn to look at it more
closely and come up with questions of their own.
The learning doesn’t need to stop with simply observing changes. If you’d like,
you can expand your science study by researching your observations more
deeply. You can learn about photosynthesis and respiration and how trees
provide us with clean air. You can study birds and see what kinds visit your tree.
You can lean about the seeds and see how birds and animals help the tree spread
its seeds. You can watch the bugs that call your tree home and learn more about
their life cycles. You can research tree diseases and see how they can be treated
and prevented, and learn more about what your tree needs to grow.
So much can be learned just by paying attention to one tree throughout the
seasons. This past year, not only have we learned more about our tree; we’ve
learned to slow down and appreciate the little things. We’ve
shared Tilly’s shade with new friends and grown closer as a
family. We’re paying better attention to the world around
us and learning to take better care of it. Each day as we go
past our tree, the kids take a couple minutes to check in with
Tilly and his fire bug houseguests. They give him a little pat,
enjoy the coolness of his shade, and appreciate him for the
beautiful resource he is. Give it a try: Hug a tree! It just might help your family
learn to appreciate life a little more too! Heather Aliano is a homeschooling mother of three bubbly kids, blogger, and proud
military wife whose family is currently living in Germany. When she isn’t running
around hugging trees, she’s traveling around their home in Europe as much as possible
and eating all the gelato she can find. You can join her on her adventures with
homeschooling and travel at www.onlypassionatecuriosity.com.
11
PARENT/FAMILY
Contribution
Camilla Gaudioso
and Saffron (1st grade)
virginia
Lavender Lemon
C U P C A K E S
Camilla Gaudioso and her daughter Saffron enjoy baking together as an integral part of
Saffron’s first grade lessons. Saffron was the one who invented this unique flavor combination.
Camilla says, “The idea ultimately emerged as a result of her love for butterflies and
wanting to ‘drink flower nectar.’ We started researching edible flowers and as a result,
ended up making dandelion cookies, putting clover flowers and tulip petals in salads,
and buying some dried lavender. As soon as she smelled it, she said she wanted to
put it in cupcakes with lemon.” This is a three-part recipe and it looks like a big
project, but they are well worth the extra effort. Enjoy!
L AV E N D E R VA N I L L A C U P C A K E S
SCIENCE
IN THE KITCHEN
Inquiry and observation are
basic elements of science.
Here are some questions you
might ask (and search for
answers to!) while baking this
delicious treat:
• What is the difference
between dry and fresh
flowers? What are some
other edible flowers?
• What happens when you
chop flowers or herbs as
opposed to crushing them?
INGREDIENTS
• 1
cup soy milk*
• 3/4
• 1
teaspoon apple cider vinegar
• 2
• 1
1/4 cups flour
• 1-2 tablespoons dried culinary
• 2
tablespoons cornstarch
• 3/4
teaspoon baking powder
• 1/2
teaspoon baking soda
• 1/4
teaspoon salt
• 1/3
cup canola oil
cup sugar
teaspoons vanilla
lavender flowers crushed in food
processor, coffee grinder, mortar
and pestle, etc. (Adjust the amount
based on how pungent you want
the lavender taste to be; we went
for it with the full 2 tablespoons.)
• Why does adding vinegar
STEPS
• What is the difference
1. Preheat oven to 350 degrees. Line muffin pan with cupcake liners.
to milk make it curdle?
between baking powder
and baking soda? Why do
so many recipes use both?
• What is the difference
between shortening and
margarine? What does
nonhydrogenated mean?
• What makes shortening and
margarine get fluffy when
you beat them? Why is this
important to the recipe?
12
2. Whisk the soy milk and vinegar in a measuring cup and set aside for a
few minutes to get good and curdled.
3. Beat together the soy milk mixture, oil, sugar, vanilla, and lavender
flowers in a large bowl. Sift in the flour, cornstarch, baking powder,
baking soda, and salt, and mix until no large lumps remain.
4. Fill cupcake liners two-thirds of the way and bake for 20 to 22 minutes.
Transfer to a cooling rack, and let cool completely before frosting.
* This recipe could easily be “unveganised” by substituting regular milk and butter instead of their
vegan counterparts.
Living Education, a publication of Oak Meadow
VA N I L L A B U T T E R C R E A M
INGREDIENTS
• 1/2
cup nonhydrogenated shortening
• 1/2
cup nonhydrogenated margarine
• 3
1/2 cups powdered sugar, sifted if clumpy
• 1
1/2 teaspoons vanilla extract
• 1/4
cup plain soy milk or soy creamer
STEPS
1. Beat the shortening and margarine together until well-combined and
fluffy. Add the sugar and beat for about 3 more minutes. Add the
vanilla and soy milk and beat for another 5 to 7 minutes until fluffy.
VEGAN LEMON CURD
INGREDIENTS
• 1
1/4 cup fresh lemon juice
• 1
1/4 cup sugar
• 2
tablespoons fresh lemon zest
• 1/4
teaspoon salt
• 2
tablespoons coconut milk
• 4
tablespoons corn starch dissolved in 3 T. cold water
• 2
tablespoons margarine, divided
STEPS
1. In a small saucepan over medium heat, combine the lemon juice, sugar,
lemon zest and salt, stirring well to dissolve the sugar.
2. After the sugar is dissolved, add the corn starch mixture and the coconut
milk, stirring well to combine. Stirring constantly, cook until the mixture
begins to thicken and the first few bubbles appear on the surface, about
8 minutes.
3. Add the margarine and cook, stirring constantly for several minutes
more, or until the mixture resembles a thick pudding. Transfer the
mixture to a heat-proof dish, cover the surface of the curd with plastic
wrap, and let cool completely before placing in the refrigerator to chill.
Chill lemon curd for 2 hours in the refrigerator before using.
Living Education, a publication of Oak Meadow
Here’s a snap of the finished
product—you can just see
them peeking out behind
the toasted coconut cupcake
nests.
Lavender
Lemon
C U P C A K E S
TO ASSEMBLE
• Using the large end of a
pastry tip, remove a portion
of the center of the cupcake
once cooled. (If you don’t
have a pastry tip lying
around, a careful hand and
a spoon can accomplish
the same task!) Impatient
folks can eat the discarded
centers immediately,
or they can be layered
on top of the cupcakes
once they’re frosted as
an interesting decorative
element.
• Spoon or pipe about 1
tablespoon of lemon curd
into the center of the
cupcake.
• Frost cupcake as usual. We
decorated our cupcakes
with sugared wild violets,
but any edible flower would
look amazing.
13
Seasonal Activities
All Ages
forfor
Harvest
Time
e a rt h c y c l e s
Late summer and early autumn bring delicious warm days, long, twilit evenings, and garden bounty.
Everyone is eager to spend as much time outside as possible as the summer season winds down.
Here are two ways to enjoy the outdoors longer.
Build a Harvest Hut
Building a simple harvest hut is a great way for your whole family to celebrate the
abundance of the harvest and prolong your enjoyment of the season. This is a favorite
project from Oak Meadow’s 3rd grade study of ancient cultures. This idea comes from
the Jewish holiday of Sukkot (pronounced sue-COAT) and the tradition of building a
small hut called a sukkah to celebrate the harvest and to commemorate the temporary
dwellings the Jews lived in during their 40 years in the desert. Building a sukkah can be
a fun family or neighborhood project. Once you have built and decorated your harvest
hut, you can enjoy spending time in it, playing, eating meals, and even sleeping in it,
weather permitting.
MATERIALS
• 2 pair hinged-together trellises; or
• 4 pieces garden trellis with 4-6 hinges and associated wood
screws
• 2-3 long (2 meter) bamboo sticks
• Roll of garden twine
• Leafy stalks (cornstalks, pine boughs or palm fronds, grape
vines, etc.), fruits, gourds, or anything else from the harvest
to decorate
INSTRUCTIONS FOR A SIMPLE SUKKAH
1. Join trellis pieces with 2-3 hinges for each. (They should then be able to fold over on each other.)
2. Take each pair of trellises and stand them up in an L-shape. Arrange them together to make 2 adjacent corners
of a square. Where they abut, overlap them. You will have a three-sided hut.
3. Use twine to bind them together at top, middle, and bottom where they overlap.
4. Lay bamboo poles across top. Tie tightly into position with twine.
5. Cover roof with leafy stalks, grape vines, etc., and attach more stalks or dried grasses to the outside walls. Thread
leaves through the walls and roof to hang indoors.
6. Hang fruit, gourds, and other items of harvest from the roof and walls to decorate your sukkah.
7. Add a table and/or chairs, if you’d like. Bring out a harvest-themed snack and invite friends and neighbors to visit.
14
Living Education, a publication of Oak Meadow
Punched Tin Lanterns
Enjoy the lovely late summer evenings by making a tin
can lantern to light the dark and let you stay outside a
little longer. Oak Meadow’s fifth grade students make a tin
can lantern when they are studying Paul Revere and the
American Revolution. Adult supervision is required for this
project, but with help, children are capable of completing
surprisingly detailed designs. Here are simple directions:
Lexi Wallace
Grade 6—architectural drawing
MATERIALS
• A large metal juice can or tomato can • Hammer • A big nail and a small nail
• Wire coat hanger
INSTRUCTIONS
Take the lid completely off of the can and wash the can carefully. Leave the bottom of the can on. If the edges are
sharp, you can cover them with tape or use pliers to bend the edges.
1. Dry the can well and draw a simple design on it with crayon.
2. Fill the can almost to the top with water, and freeze. (This will help the can keep its shape while you hammer on it.)
3. Put the frozen can of water on a towel so it won’t roll.
4. Using the big and small nails, hammer holes at regular intervals along the outline of the design you have drawn.
The more holes you make, the better your design will show.
5. Keep the water frozen. You may have to put the can back into the freezer several times before completing your
project.
6. Make two holes near the top and use a coat hanger wire for a hanging loop.
7. Pour out the ice and put a few inches of sand in the bottom of the lantern. Place a candle in the sand and watch
your design shine and light up the night.
Living Education, a publication of Oak Meadow
15
Math and Science All Around Us:
As adults, we use principles and skills based on mathematics and science on
a daily basis, often without even realizing it. As parents and educators, we know math
and science learning are happening when we let children soak up patterns, explore rhythms, notice
changes, observe without judgment, and let their curiosity roam.
Here are just a few ideas of how math and science skills can be expanded in the natural course of
daily experiences. Hopefully these ideas will give you a jumpstart on recognizing math and science
in its many forms and finding ways to provide daily opportunities to involve children of all ages in
hands-on math and science experiences. Honing foundational skills and demonstrating the value
and necessity of math and science can become part of your family culture and lifestyle.
Math and Science in the Garden
Preschoolers: count and sort seeds; loosen soil to prepare the seed bed and
observe the insects living in the soil.
K-2nd grade: measure the seed bed and how far apart seeds should be planted;
keep a watering chart; observe soil erosion from watering and adjust the soil to
prevent water run-off.
3rd-5th grade: draw each phase from seed to harvest; collect and dry seeds for
next year; record the number of seeds produced per individual fruit/vegetable.
6th-8th grade: calculate the ratio of seed planting depth to plant spacing (or seed size to how long it takes to sprout) and look
for patterns; measure and chart seed growth.
High School: study soil composition and determine soil amendments; chart sun/shade ratio in each part of the garden; design
a planting chart based on soil and sun/shade needs; calculate yield per plant type and plant yield per square foot.
Math and Science in the House
Preschoolers: count and sort while table setting and doing laundry; divide
indoor pot-bound plants or take cuttings to root new plants.
K-2nd grade: measure ingredients in a recipe; compare baking yeast bread vs.
quick bread.
3rd-5th grade: read and follow a recipe; find out how many walnuts need to
be cracked to get ½ cup of nuts or how many lemons to juice for a gallon of
lemonade.
6th-8th grade: double and halve recipes; experiment with how batter
consistency affects pancakes; compare unit pricing when grocery shopping;
calculate price of store-bought vs. homegrown veggies.
High School: create a household budget based on household spending in the prior three months; experiment with recipe
substitutions; calculate cost savings of line drying clothes vs. using a dryer.
16
Living Education, a publication of Oak Meadow
Everyday Inquiry for Brains of All Ages
Math and Science Out and About
Preschoolers: build a sandcastle and then pour water on it; dam up a stream;
count the number of steps it takes to walk across the yard, and then the
number of steps it takes to run across; make rock towers.
K-2nd grade: make and fly a kite; make the longest tunnel possible in the
sand or dirt; build a three-sided structure, a four-sided structure, a five-sided
structure and keep adding sides (you can use sticks, scrap lumber, dirt and
bark, etc.); make a dog agility course (this can be used for kids, too!).
3rd-5th grade: count the number of shells, rocks, insects, etc. found in a
three foot square section of beach, forest, or meadow and compare to another
three foot section somewhere else; find out how long you have to stand under
a sprinkler or in the rain before your hair or clothes start dripping; set up a
lemonade stand and figure out how many cups you have to sell to make a profit.
6th-8th grade: design and build a tree house; measure out how far your bike travels in each gear with ten pedal rotations;
build a campfire (if you don’t have a fire pit, make one or use your sandbox); figure out where the wild animals in your area live
and what they eat.
High School: figure out how much money you need to earn to buy tickets to concerts and events you want to attend; make
a business plan for earning money doing something you enjoy; train a dog or horse; make a solar oven and dry fruit in it;
volunteer for beach or river cleanup, trail maintenance, or at an animal shelter.
Math and Science at Night
Preschoolers: take a walk with a flashlight (and a friend); count lightning
bugs or bats; listen to the night sounds.
K-2nd grade: make animal shadows on the wall with a flashlight and your
hands; watch the stars come out; turn on an outside light and see what kinds
of moths it attracts.
3rd-5th grade: take a walk in the moonlight; look for nocturnal animals
in your yard (or signs of them the next day); map nighttime sounds (which
direction are they coming from) and try to figure out the source.
6th-8th grade: keep track of sunrise, sunset, moon rise and moon phase;
look at the night sky through a telescope; find the dew point.
High School: map a meteor shower (how many sightings and in which quadrants of the sky); measure and chart the
movement of the stars; observe animals coming to a water source at dusk or on a moonlit night.
DeeDee Hughes finds math to be eminently satisfying and science to be endlessly fascinating. She
loves to find fun ways to explore both, for work and for pleasure. DeeDee is the managing editor of
Living Education.
Living Education, a publication of Oak Meadow
17
Enjoy this project from our friends at Little Acorn Learning.
“from wet clay where no
seed will grow the worm”
– Elizabeth St. Jacques
Build a Wormery
Did you know earthworms are sometimes called “night crawlers” because
they shy away from the light and often come to surface when it is dark
outside in order to vegetate? Earthworms can dig very deep underground,
often getting down over four or five feet!
Earthworms feed off of many different things including leaves and roots.
They are very important to our earth as they transport the minerals and
nutrients from what they eat and pass it back into the soil through their
waste. Those nutrients then create a rich soil for other living things to grown
in. Worms help provide fuel for the trees that help us breathe, the vegetables
that we eat to grow strong, and the flowers that we enjoy!
Worms can be considered living composts and are very good for your
garden. Learn more about these interesting creatures up close by building
your very own homemade wormery!
SUPPLIES NEEDED
• o ne large glass or plastic container with opening or holes (worms
need air to live, just like we do!)
• s and and/or dirt
• s hovel
• v egetation (lettuce, grass
clippings, dead leaves, etc.)
1
2
3
Begin by layering dirt and sand in your glass
jar, leaving an inch or two of space on top.
Now the fun begins! Go on an outdoor
adventure to find worms for your new
wormery.
4
Each child can be provided with his or her own
shovel and dig into the earth to find worms.
When you have your worms gathered, place
them gently on top of the soil and sand mixture.
You can also add a small amount of vegetation
on top such as leaves, grass clippings or
vegetable compost. This is the worm’s food.
• b lack cloth to cover wormery
Be sure that your soil is moist (not soaked). Add a small amount of water every few days
when you notice it getting dry. Be sure to allow air to get into the jar by leaving an opening
on top or poking holes in your container if it is plastic.
Eventually you will see the worms have pulled down the vegetation into the lower levels of
the soil. Wait until it all disappears. Where did it go?
When you are done with this wonderful nature study project, be sure to gently put the
worms and fresh soil back into your garden to help continue the amazing cycle of growth
and life that our world produces.
Eileen Straiton is a work-at-home mother to four daughters. She writes and publishes
Waldorf inspired ebooks and facilitates ecourses for parents, teachers and caregivers
at Little Acorn Learning. Eileen applied her love of nature-based learning in her work
as owner and lead teacher at Little Acorn Playgarden in Brookfield, Connecticut for
over 8 years and continues to offer nature clubs and camps in her hometown. Visit her
blog, Eileen’s Place, or her Facebook page, for more great ideas and activities.
18
Living Education, a publication of Oak Meadow
Oak Meadow
CURRICULUM
SPOTLIGHT
Oak Meadow
8TH GRADE SCIENCE
STUDENT
Rohini
Mathematics
in the Early Grades
Oak Meadow introduces the four processes
of mathematics artistically, through story
and picture, to help children gain a true
understanding of the concepts. This
approach, which mirrors Waldorf school
methods, is used because children respond
more fully to an imaginative, artistic
approach and remember more easily what
they have learned.
Here are a few excerpts from Oak Meadow’s
K-3 curriculum that showcase this lively
introduction to math.
Kindergarten
The qualities of numbers are expressed in
the following stories, most of which are
lovely original tales by Rebecca Ide Lowe:
Story of One Big Sun (unity,
1 The
wholeness)
2Princess Daylight (day and night, duality)
Fighting Kings (harmony, two
3 The
conflicting forces that agree to work
together for a common ideal)
Garden of Seasons (the solidity of
4 The
the square, the four elements, the four
seasons)
Star Child (representation of the
5 The
human being)
Story of the Six-Sided Honey Jar
6 The
(nature connections, two joined triangles)
Rainbow Bridge (combination of the
7 The
strength of the square and the harmony
of the triangle)
Golden Spider (lemniscate—figure
8 The
eight—expressing a balance between two
opposite cycles)
Brave Princess Eliza (three sets of three—
9 three
items, three obstacles, three rewards)
Little Caterpillar’s Stripes (the
10 The
beginning of a new cycle—two-digit
numbers)
continued on page 20
Living Education, a publication of Oak Meadow
19
Oak Meadow
CURRICULUM
SPOTLIGHT
continued
Mathematics in the Early Grades
FIRST GRADE
Stories about four gnomes introduce the four processes in a playful way:
Plus: a greedy gnome who is always filling his pockets with jewels for the
king plus extra for himself.
Minus: a raggedy gnome with holes in his pockets and his sack so he never
has as many jewels as when he started.
Times: a quick gnome who is always finding more jewels than the rest,
doubling and tripling the amount collected.
Divide: a gnome who always wants to help others, giving away what he has and making sure everyone has equal amounts.
SECOND GRADE
Work with division continues, and the radical division sign is introduced by Barnaby the Squirrel:
Every fall when the nuts fell from the trees, Barnaby would spend his days gathering nuts to store away
for winter food. One fall, as he was bringing a new supply of nuts to bury in his underground storage, he
noticed that someone had been digging in his storeroom and that his store of nuts was smaller than before.
Just at that moment he saw, behind the tree, a big brown dog with his cheeks full of nuts. Barnaby knew
that if he kept burying his nuts in the ground the dog would take all of them and he would starve when
winter came. Soon he had an idea. He went deeper into the forest and gathered sticks of wood and vines
and began to make a shed against the tree where he lives. When he was finished he had a beautiful storage
shed for his nuts, safe from the dog.
Later, Barnaby is asked to share his nuts with other animals that have lost their winter
stash. He comes up with a plan to share what is in his storage shed equally with all of his
friends who need help. Barnaby draws a picture of his storage shed, with the nuts inside
of it and the animals standing outside of it, and then draws on top of the shed the equal
share of nuts that each will receive.
THIRD GRADE
Place value is presented pictorially and in story form in the second grade, and the story continues in the third grade to
introduce carrying and borrowing. Kind landlord Mr. Placevalue learns that too many people have tried to move into the Ones
House, but he has a wonderful solution:
The Ones House was occupied by seven of the Ones family, and the Tens House had three groups of ten people
living in it. All was going well until the day Father One’s brother arrived from Germany with his wife and five
children and asked to move in with the Ones. As they had no other place to go, Father One agreed to let them
stay. The house was now very crowded. The children were fighting and everyone was getting a headache from all
the noise. It kept getting worse until one day the owner, Mr. Placevalue, came over…
When Mr. Placevalue found out how many people were crowded into the house, he explained, “Because this
house is so small, whenever there are more than nine people living in here, I let one group of ten go live next door
in the Tens House. They have plenty of room! But I do have rules, and the rule is that you must move ten people
at a time, no more and no less!”
Everyone is delighted with this solution, and after “carrying” all the bags for the ten family members who are moving to the
Tens House (Mr. One’s brother and his family are happily joined by Mr. One’s three oldest daughters), everyone gets settled
with plenty of room to spare.
20
Living Education, a publication of Oak Meadow
What’s Math Got to Do with It?
by Jo Boaler
(Viking, 2008)
Stanford University math professor Jo Boaler
believes that every child can learn to enjoy and
be successful at math, and this book goes a long
way toward accomplishing that goal. After a
comprehensive look at why traditional ways of
teaching math are ineffective, Boaler outlines a
series of simple steps that any parent or educator
can use to help math come alive. With careful
logic, real life examples, and practical tips, Boaler encourages educators to
help students view math as a creative network of connections rather than
a static set of rules to memorize (for which no real thinking is required,
invited or allowed!).
Boaler explains that students should have a clear sense of math goals (what
are they trying to do) and how it is linked to larger goals (why are they doing
it). The how it works and why it’s done is just as important as the what to do.
Boaler cites research that suggests talking about math (both the reasoning
and the purpose behind it) is especially vital for girls because the female
brain is designed for communication and connection. Math instruction
that focuses on concepts and allows a deep, connected understanding of
math is good for both boys and girls since all high level work in math,
science and engineering requires collaboration and making connections.
In her work, Boaler has seen students “come to believe that they must
memorize [all the procedures], instead of understanding the concepts that
link the procedures and render memorization unnecessary” (164). She
talks about how to “stretch the problems” by continuing to work after the
solution is found. For example, when a task is complete, ask, “What if we
changed this element?” She explains how to “open the work” to make it
challenging in different ways at different levels, and discusses the importance
of introducing new skills as methods for solving real problems (learning
in context) rather than teaching skills first and doing practice problems
to learn them. In addition, she outlines the necessary components of an
effective math program, including:
n
Present problems that interest and challenge
n
Encourage talking and sharing ideas about math
n
Ask students to explain and justify their methods and answers
n
se a range of representations: symbols, drawings, tables, graphs,
U
diagrams, etc.
n
ffer a choice of activities and the freedom to take problems in
O
new directions
Filled with practical strategies for success and solid research, What’s Math
Got to Do with It? is an excellent resource for teachers and parents who
want to encourage a stronger math foundation in their students.
Living Education, a publication of Oak Meadow
MATH AND SCIENCE
RESOURCES
Astronomy
Picture of the Day
NASA Astronomy Picture
of the Day is a great way to spark and
feed an interest in science. Check out
their website archives. Here are just a
few of our favorites:
wringing a towel in space
relative size
aurora borealis in Norway
Finding Strategies for Math
Learning Disabilities
From the National Center for Learning
Disabilities website:
“Dyscalculia refers to a wide range of
lifelong learning disabilities involving
math. There is no single type of
math disability. Dyscalculia can vary
from person to person, and it affects
people differently at different stages
of life. Work-around strategies and
accommodations help lessen the
obstacles that dyscalculia presents. And
just like in the area of reading, math
LD is not a prescription for failure.”
Their website is full of helpful
resources, information and tips.
The Beauty
and Art of
Mathematics
“Math is the beautiful, rich, joyful,
playful, surprising,
frustrating, humbling and creative art that
speaks to something transcendental.
It is worthy of much exploration and
examination because it is intrinsically
beautiful, nothing more to say. Why
play the violin? Because it is beautiful!
Why engage in math? Because it too is
beautiful!” ~ James Tanton,
Thinking Mathematics
Don’t yet see the beauty in math?
Watch this video.
21
Fun with
PATTERN PUZZLES
Pattern recognition is an essential skill in higher
math and can be encouraged from a very early
age. Even preschoolers start to recognize patterns
and enjoy playing with them (numerical patterns
as well as patterns with colors, shapes, words, etc.).
Numerical pattern puzzles can progress from the
very simple to the highly complex and are a fun brain challenge.
Pattern puzzles give a short sequence of numbers that follow a specific pattern and then you have to
figure out which numbers would come next in the sequence. First present the pattern by asking if
your students can name the next three numbers in the sequence. If help is needed in the beginning,
give the pattern rule and then see if they can come up with the next numbers.
Give these a try. The patterns are explained below so no one gets stumped forever, but try not to peek! List the next three
numbers in each sequence:
1, 3, 6, 10, 15, 21…
(Pattern: add 2, then 3, then 4, and so on)
2, 4, 8, 48…
(Pattern: multiply each number with the one to its left to find the next in the sequence)
1, 6, 12, 17, 34…
(Pattern: alternate +5 with times 2)
Once your children understand how pattern puzzles work, see if they can stump you with a pattern. It’s okay if they give a
faulty pattern at first (random numbers rather than a logical numeric sequence) because then you have a great opportunity to
explain the difference between patterns and random sequences. Let them try again, and if they still have trouble with creating
a logical pattern, give them a pattern to follow (for instance, starting with 1, skip every other odd number) and see if they can
create the sequence.
Taking it to the Next Level
Sometimes it is useful (or just plain fun) to know what the tenth term in a particular sequence will be, or the 100th term,
but you don’t want to have to write out ten or 100 individual problems. There is a shortcut that takes pattern puzzles to the
next level. It adds new skills in charting, analyzing and identifying a relationship, and describing the pattern with an algebraic
sentence. This is a great way to challenge older students. For our purposes, we’ll use very straightforward patterns
(not ones with multiple or progressive variables as in the examples above).
Here’s how you find the formula for an arithmetic sequence:
Step 1: Create a table. Shortcuts always start with a table! Create a table that shows the “term” (the order in the sequence,
e.g. first, second, third, etc.) and the numbers you already know (the known values). Fill in the known values (usually the first
three or four terms in the sequence), like this:
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Living Education, a publication of Oak Meadow
Pattern: 1, 5, 9, 13…
Term in
sequence
Known values
1
2
3
4
1
5
9
13
10
100
Step 2: Identify the pattern. It’s easy to see that the numbers in this sequence come in intervals of four (not multiples of
four, because it didn’t start with 4); each number is four more than the previous number. Even knowing this, however, we can’t
easily figure out what the 10th or 100th term will be. That’s why we look for a pattern. We find the two parts of the pattern that
are changing (the two variables) and then establish a relationship between them. The first variable is the term in the sequence—
we might want to know the 50th term or the 23rd term or the 501st term. The second variable is the number or value.
Step 3: Translate the pattern into an algebraic formula. Using letters to stand for the variables, try to describe the pattern
or relationship. Because we want to know numbers very far along in the sequence, we can’t just describe the relationship
as +4—that only works if we know the previous number so we can add four to it! We need another way to describe the
relationship, based on the term (the order in the sequence) and the known values. For instance, if x is the value and T is the
term, we can describe this pattern as x=4T -3.
Step 4: Test your formula. Using your known values (the ones already in your table), see if your formula works:
Term in
sequence
Known values
x=4T -3
1
2
3
4
1
4(1)-3=
4-3=1
5
4(2)-3=
8-3=5
9
4(3)-3=
12-3=9
13
4(4)-3=
16-3=13
10
100
If your formula works, you can do a little happy dance! If the formula doesn’t work, adjust it until it does work. For instance,
suppose we thought the formula was x=4T -4. A quick test would show that this formula doesn’t work (if it did, the first term
would be 0, the second term would be 4, and so on), so we’d have to adjust until we found a formula that applied to each of
the known values. Adjust, re-test, and then do your happy dance.
Step 5: Solve for your unknown values. This is the fun part! Once you have successfully translated your pattern into an
algebraic sentence, it’s easy to find out what any term in the sequence will be:
Term in
sequence
Known values
x=4T -3
1
2
3
4
10
100
1
4(1)-3=
4-3=1
5
4(2)-3=
8-3=5
9
4(3)-3=
12-3=9
13
4(4)-3=
16-3=13
37
4(10)-3=
40-3=37
397
4(100)-3=
400-3=397
If that doesn’t quite make sense yet, or you’d like to see a visual presentation of finding the formula for arithmetic sequences,
here is a great video.
Once you understand how it works, you can amaze your friends and relatives by asking them to give you a term and you’ll
tell them the value in just a few seconds. You can also do a puzzle challenge with your friends or parents: using the formula,
someone calls out a term and everyone scrambles to solve it.
Now It’s Your Turn
Once you have the hang of it, it is time to make up pattern puzzles of your own. Keep it simple in the beginning—write
the formula first to make sure you have a solid pattern and not just a random sequence of numbers. Begin by using relatively
straightforward patterns (for instance, x=5T +3). Try writing an incomplete table of values and let your student fill in the
blanks and then write an algebraic equation to describe the pattern. You can create a Pattern Puzzle of the Day for a family
challenge and to keep math skills sharp. Encourage your students to make up their own sequences and/or partial tables to
test and trick you!
Living Education, a publication of Oak Meadow
23
MATH AND SCIENCE RESOURCES
Great Books for Kids
Eat Your Math Homework: Recipes for Hungry Minds
by Ann McCallum
Navigating Early by Clare Vanderpool
(an adventure story with a bit of math)
Mystery Math: A First Book of Algebra
by David A. Adler
Robotics: Discover the Science and
Technology of the Future with 20
Projects by Kathy Ceceri
Edgar Allan Poe’s Pie: Math Puzzlers in
Classic Poems by J. Patrick Lewis
Science, Medicine, and Math in the Early Islamic World
by Trudee Romanek
The Wing Wing Brothers Math Spectacular! by Ethan Long
The Wing Wing Brothers: Carnival de Math by Ethan Long
Sports Illustrated KIDS. Sports math series:
Football: The Math of the Game by Shane Frederick
Baseball: The Math of the Game by Thomas K. Adamson
Basketball: The Math of the Game by Thomas K. Adamson
Hockey: The Math of the Game by Shane Frederick
Two Favorite Links
Check out these great simple experiments from the folks at 3M.
If you haven’t yet discovered the math doodling of Vi Hart,
you are in for a treat.
Pinterest for Every Interest
Oak Meadow’s fabulous Pinterest boards provide
an ever-changing source of inspiration and
delight. Don’t miss these excellent math and
science resources:
Explorations in Math and Science
Over the summer, many
homeschooling teens
connected with college
faculty members and
other students who
are passionate about
learning through
Marlboro College’s
summer programs for
teens. Here are just
two of the great summer
programs that were offered
this year:
n DNA: Barcode of Life
Just like the “universal product code” used at the grocery
store, DNA provides scientists with a kind of “barcode of
life.” An organism’s DNA contains an enormous amount
of information, including details about its evolutionary
relationship with other organisms. In this workshop students
are introduced to basic molecular genetics and guided in
extensive hands-on laboratory activities, as well discussions
on the implications and limits of genetic testing.
n Finding the Key
Do you wish you knew the math to design your own Suduku,
or to solve a Rubik’s cube? Perhaps you think you’ve got
what it takes to find the elusive treasure on a daylong team
expedition? This workshop is an exploration of puzzles of all
sorts and the math that makes them work. Students will solve
a variety of puzzles from across the globe—using math and
techniques for problem solving—and creating their own.
All Oak Meadow students are eligible for an automatic
10 percent discount for any Marlboro College summer
program for teens. In addition, students enrolled in Oak
Meadow High School are eligible to receive Life Experience
Elective Credit for their participation in Marlboro’s programs. Next year, consider how you can use these great Marlboro College summer programs to extend your interests and
inspire your learning!
United Nations Windows on the World
Many of the UN websites are excellent sources for all kinds
of science and social studies information and research. Here
are just a few to get you started:
UN Water Statistics UN Environment Programme Towards a Green Economy
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Living Education, a publication of Oak Meadow
• Oak Meadow News
OM Launches new blog “In the Meadow”
Oak Meadow’s blog, “In the Meadow,” provides a warm, engaging and supportive gathering spot in the cyberhood for all
Oak Meadow families and homeschoolers around the world. In the Meadow is a place where we can explore great resources,
ideas, and sources of inspiration that can enhance the overall homeschooling experience. Reader responses allow for more
dynamic community interaction and sharing of wisdom, experience, and ideas. Individual K-4, 5-8, and High School blogs
are in the works, which will create new forums for our enrolled students and families to connect, collaborate, and engage in
dialogue with one another and with their teachers. In the Meadow is designed to encourage a cross-pollination of ideas from
homeschoolers, unschoolers, educators, parents, lifelong learners, and everyone interested in pursuing an education that
inspires, delights, and creates a better world. Join us In the Meadow!
OM Welcomes New Faculty and Staff
We are pleased to announce several additions to our
dedicated and dynamic team. Oak Meadow families will
probably come into contact with one or more of these
wonderful individuals in the months to come. Each of them
will be happy to help you!
Alan Fortescue, High School Program Director
It is with great pleasure that we announce our
new High School Director, Alan Fortescue.
Alan comes to us from The Earthwatch
Institute. He holds a Ph.D. in Education
and Leadership from UVA, and earned
his undergraduate and master’s degrees in
literature. In addition to his extensive experience in teaching
and leadership in higher and experiential education, Alan
has served as a consultant for UNESCO, The Discovery
Channel, and WGBH. He is also an award winning painter
and skilled mountaineer. Alan looks forward to working with
our Oak Meadow faculty, staff, and parents, and guiding
our high school program forward into new and exciting
directions as we continue to explore ways to empower
students to discover their own inspired path to learning
Deb Holman, Director of Marketing
We are pleased to welcome Deb Holman
to the Oak Meadow team. She comes to
us after spending ten years as Director of
Communications at Northfield Mount
Hermon, a private independent high school
in Massachusetts. Deb has lived in the
Brattleboro area for almost four decades and is very active
in the local community, volunteering and doing public
relations for several nonprofits including Boys & Girls
Club, Brattleboro Outing Club, St. Brigid’s Kitchen, and
Living Education, a publication of Oak Meadow
a Tropical Storm Irene recovery group. She is thrilled to
become part of Oak Meadow as we expand our horizons,
and is looking forward to finding more ways to let the
world know about our exceptional curriculum and the
many exciting learning opportunities we offer to students
in K-12. Deb enjoys visiting her two daughters, who live
in Baltimore and Austin, and playing tennis, cycling, cross
country skiing, hiking, and swimming.
Eden Terrell, Registrar
Eden Terrell is Oak Meadow’s Registrar, and
she’s taken on her myriad responsibilities with
efficiency, professionalism and good humor.
She notes, “I like working at Oak Meadow
because it is an energetic, collaborative
environment focused on providing families
and students with options to reach their goals.” Outside the
office, Eden’s life revolves around her husband and fouryear-old twin son and daughter. She enjoys swimming,
biking and knitting (though not all at the same time) and
loves to catch a movie or concert every now and then.
Biz Dana, Executive Assistant
Biz Dana, Oak Meadow’s new Executive
Assistant, has quickly learned her way around
the office and is now the go-to person when
anyone has a question or needs help. She
enjoys working in such a busy, lively office
and appreciates that “Oak Meadow’s mission
of education is heartwarming and important.” Biz loves to
tap dance, tent camp, cook, garden and play with her two
dogs. She and her husband also enjoy spending time with
his 12 grandchildren.
continued
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• Oak Meadow News continued
Kiqe Bosch, Purchasing and Shipping Coordinator
Kiqe Bosch, our Purchasing and Shipping
Coordinator, has lived in the New England
area for the past ten years. Before joining the
Oak Meadow team, he held a variety of jobs,
including teaching Spanish in the public school
system. Kiqe is a master craftsman who raises woodworking
to an art form. He is also an excellent photographer--you’ll be
seeing some of his work on our website.
Andrea Kilroy, K-8 Faculty
Andrea Kilroy taught middle school history
and English for thirty years at a private school
in Massachusetts. Concerned that children are
often underserved by mainstream institutions,
she turned her attention to helping each child
get the best educational support possible.
Andrea is currently completing a customized hybrid B.A./M.
Ed. degree in Educational Advocacy at the University of
Massachusetts, Amherst. She believes that parents often lack
the confidence and guidance to embark on an alternative
educational path that would better serve their children’s
needs. She feels Oak Meadow’s mission of instilling a love of
education in its students while gently guiding both student
and parent provides the best of all possible worlds: a teacher
(the parent) who is 100% committed to the student’s success
paired with a curriculum that is solidly grounded in good
pedagogical research and practice. Andrea is the mother of
five and the grandmother of five. She loves teaching, reading,
cooking, needlepoint, and being with her grandchildren.
Michelle Menegaz, K-8 Faculty
Michelle Menegaz holds a BA in Psychology
and Biology from Middlebury College,
and a Masters in Environmental Science
and Elementary Education from Antioch
University New England. Michelle taught at
Academy School in Brattleboro for 13 years and
relished incorporating nature studies, gardening, movement,
knitting and song into the curriculum. John Muir’s insight
carries special significance for Michelle: “When we try to
pick out anything by itself, we find it hitched to everything
else in the universe.” Michelle homeschools her daughter and
runs a camp called Girls on the Farm from her home. These
endeavors have strengthened her belief that relationship is an
essential piece of learning. Michelle lives in Southern Vermont
on a “farmette” with her husband and daughter along with a
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mixed menagerie of goats, sheep, ducks, chickens and one old
demanding cat. In between gardening, homeschooling and
animal care she enjoys singing, knitting, hiking, and biking.
Tara Sullivan, High School Art Teacher
Tara Sullivan received her BFA from the
University of New Hampshire, her MFA
from Southern Illinois University, and K-12
certification from Franklin Pierce College.
Tara has taught art to students ranging in age
from preschool to elders, and in a variety of
settings from formal classrooms to camp sites. In addition
to receiving a grant from the Andy Warhol Foundation,
she has done artist residencies at The Atlantic Center for
the Arts in Florida, Haystack Mountain School of Crafts,
and The Vermont Studio Center. Tara feels that her role
is to share her knowledge of art and to facilitate students’
discovery of the creative process. Learning to express one’s
self visually is both an adventure and a thoughtful process
of discovery. Tara engages in the creative process in many
ways, including drawing and painting, sewing, gardening,
cooking and parenting. In the spirit of adventure, Tara has
traveled extensively, lived in Alaska and Ireland, and now
calls Brattleboro home, where she lives the adventurous life
of a creative mom.
OM Science Teacher Heads Back to Alaska
to Learn about Teaching Climate Change
Julie West headed back to
Alaska this summer for a
workshop at Denali National
Park about how to integrate
climate change studies into
the teaching of science. In
the summer of 2012, Julie
traveled by bicycle along
the Alaskan highway for
four weeks to study the local
ecology. For this year’s trip
to Alaska, Julie worked on a
series of teaching segments in
conjunction with Polartrec,
an organization she is involved with that provides resources
and support to help teachers and researchers collaborate. Julie
West has been teaching science and health at Oak Meadow
for 21 years, and her students and colleagues are always eager
to see where her work and interests will take her next.
Living Education, a publication of Oak Meadow
Oak Meadow Advisory Board
Meets
Oak Meadow’s advisory board met this
spring for the first time. The advisory
board supports Oak Meadow by providing
guidance and thought leadership to our
growing organization. We are grateful that
nearly all of the new board members were
able to attend the inaugural meeting. The
day-long session provided great insights,
conversation and exciting directions for
Oak Meadow to consider in the year ahead.
Advisory board members are:
Eric Jones: Head of School, Community
Partnership School; Philadelphia, PA
Yuan-Hsiu Lien: World Language
Department Chair, Eaglebrook School;
Deerfield, MA
Steve Lorenz: Head of School, The Grammar
School; Putney, VT
John Pandelaki: Senior Analyst, IT
Development, Northfield Mount Hermon
School; Gill, MA
Rainbow Rosenbloom, founder Live
Education!, Aptos, California
Amory Rowe: Founder, In the Arena;
Cambridge, MA
David Sobel: Antioch New England
professor, author, Childhood and Nature;
Keene, NH
Adam Weinberg: President, Denison
University, former President, World
Learning; Granville; OH
Nikhil Goyal: Student activist, author, One
Size Does Not Fit All: A Students’ Assessment
of School; New York, NY
Bruce Hallett: Former CEO of Time
Magazine and Sports Illustrated; VT
Ellen McCulloch-Lovell :President,
Marlboro College; Marlboro, VT
Facebook Rewind: Taking a second look at
great Oak Meadow community discussions.
“Hi, I am looking for
Lego alternatives. No preconceived
kits, but building blocks that my 5
and 8 year old can use to build with
their imaginations. Any ideas?”
JENNIFER ASKS:
• My 7yo is most happy with duct tape and cardboard. Every other toy is
ignored if he has access to those.
• 3-D puzzles are great, and some are basic, and some are of famous places, so
there’s a geography lesson in there too.
• When my 7 year old turned 7, he specifically asked for “just Legos, no kits”—
he looked them up on Ebay with Dad, found a mixed lot at a great price,
made and won a bid, and waited patiently for them to arrive. We’ve been
gifted many mixed sets over the years, but this was all his own. He and his
brothers can spend hours, together and apart, building their own creations.
• I get the “ew, a set” feeling, but the reality is that most children will make
the sets and then just PLAY. My son has a ton of Lego sets, and he makes
so much stuff from the pieces, he comes up with amazing things! I resisted
the *set* but once I saw how he played with the sets, my mind was at ease.
And the learning he has done while following the instructions for the sets
is amazing! It’s tangible learning; I still remember having to help him every
step of the way with his first big Lego projects, and now he’s a pro. And he
remembers how things went together, how they got that whatever to move
in THAT way, and he’ll redo that for other creations.
• My son loves the irregular shaped wooden blocks from Myriad. They have
so many different blocks, great for imaginations and problem solving.
• My great-grandpa used to have a wooden crate that had many different
sizes of colored scraps of wood. We would play for hours over them. He
also had some scrap wooden dowels that he had painted to put in there.
Square, rectangle, triangles, thin long pieces that looked like width of pop
cycle sticks, half circles cut on some of the ends so we could act like the
dowels where tires.
More great suggestions:
• Keva planks
• Lincoln logs
• Tinker toys
• K’Nex
• Citiblocs
• Tegu
• Magna-Tiles
• Ball of Whacks
• Zoob
• Kapla blocks
• Jenga
• Magformers
• Quadrilla
• Wedgits
Peggy O’Mara: Editor, Mothering Magazine,
founder Mothering.com; Santa Fe, NM
Living Education, a publication of Oak Meadow
27
Leaf Print Tiles
Leaf print tiles are a wonderful way to preserve, study, and enjoy the beauty
of nature. This simple craft, found in Oak Meadow’s First Book of Crafts
(part of our kindergarten curriculum), lets children of all ages create
beautiful keepsakes and gifts.
WHAT YOU NEED:
• Air-dry clay (found in any art supply store)
• Waxed paper
• Plastic tablecloth or laminated cotton
• Two pieces of wood, 18 inches long by 1/2 inch thick
• Rolling pin
• Assortment of leaves with interesting shapes and
vein patterns (geraniums, ferns, and reedy grasses
work well)
• Ruler
• Knife or pizza cutter
• Spatula
• Cardboard covered with foil (use as a drying tray)
WHAT TO DO:
1. Cover the table with the plastic tablecloth.
2.Take four or five handfuls of moist clay and throw the lump down on the table several times to squeeze
out air bubbles.
3. Lay the pieces of wood about eight inches apart on either side of the clay lump.
4. Roll the lump into a flat slab with a rolling pin.
5. Arrange the leaves and grasses on the slab, leaving plenty of room for a border around each tile.
6. Lay the sheet of waxed paper on top. Run the rolling pin over this to press the leaves into the clay.
7. Using a ruler for a straightedge, cut out the tiles with the knife.
8. Carefully lift each tile with a spatula and place it on cardboard covered with aluminum foil to dry.
9. As the leaves begin to dry, they will curl up and you can easily pick them off.
10. Allow clay to dry thoroughly. When dry, paint if you wish. You can glue a magnet to the back, or hang
it on the wall (you might want to poke small holes in the clay before it dries if you want to hang up
your tiles).
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Living Education, a publication of Oak Meadow