Dragonfly Newsletter 2012-13 Math Edition_1

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Amanda Janquart, Spruce Room
It is true that board games provide ample opportunity
to work on math skills. Pieces need to be moved a
correct number of spaces and dots on dice need to be
added-up. Throw in strategy and planning ahead,
and you can see how learning seems to multiply as a
child plays. I play board games with children because
they are fun. Sure, it isn’t always easy to introduce a
new game to a kid, but kids (and adults), can work on
patience as rules are read and the game is set-up.
Gaming with children can be frustrating. Neat piles of
cards might not stay neat and it is hard not to “help”
or to play for a young game player, but self-regulation
(for all) is an essential key to success throughout life.
Judy Ballweg, a Madison, Wisconsin teacher and
researcher writes the blog, Math at Play, and, back in
September of 2011, she posted a list of the benefits of
playing board games with kids. Take a look, and then
dust off some favorite old games from your own
childhood to share with the kids in your life.
• Using language (with adult
interaction)
• Counting with one-to-one
correspondence
• Subitizing ("seeing" a small number
of objects - like pips on a die without having to count them)
• Developing a spatial understanding
of numbers
• Estimation
• Performing simple operations (e.g.,
dividing cards evenly, adding one
more)
• Reasoning (mathematical
reasoning, and reasoning about
moral problems)
• Problem-solving
• Identifying patterns
• Identifying attributes (colors, shapes
and sizes)
• Directionality
• Predicting the outcome
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Reading symbols
Taking turns
Following rules
Planning
Patience, persistence, risk-taking
Fine motor development
THE DRAGONFLY
Dodge
Nature
Preschool
Special Issue 2012/2013
Board Games
Not, Bored Games!
A bi-annual
publication of
Dodge Nature
Preschool;
current
writings
& reflections
on
nature-based,
early
childhood
eduction from
the classroom
floor, and out
the door.
Preschool Wish List
How You Can Help
Washcloths (used or new)
Hand towels (used or new)
Peanut-free birdseed
Small couch for the Spruce Room
Immersion blender
Thanks for thinking of us!
The Math Issue
Thoughts About Children & Numbers
Marty Watson, Director, Dodge Nature Preschool
To read a little more about math and
young kids, visit my blog and find my,
Future Fibonaccis, post from Oct. 2012:
www.dodgecatalyst.blogspot.com
The focus of this newsletter, The Math Issue, is
appropriate shapes, to balance objects, to create
repetition, and to see the sum of the parts in a
whole desired representation.
children and number. Observing children is a
vital learning experience for adults. While in
“Lunch Bunch,” here at the Preschool, several
days ago, I noticed a child getting busy with a
little pile of blocks. I was busy myself, and when
I turned around again, just seconds later it
seemed, there stood a beautiful and complete
tower. The child had created a sturdy base and
stacked cubes to a height of about three feet.
Each block sat perfectly atop the next. At the
very pinnacle was perched a decorative triangle
that said, “Ta da! I am finished.”
Thanks for this opportunity to edit
The Dragonfly.
-Marlais Brand
Dodge Nature Preschool
1715 Charlton Street
West St. Paul, MN 55118
651-455-4555
www.dodgenaturecenter.org
In The Math Issue, teachers have identified
children sorting, organizing, repeating and
patterning objects inside and outside of the
classroom. Children use found natural materials
on the trail, sandbox materials on the playground
a n d a w i d e va r i e t y o f m at e r i a l s a n d
manipulatives in the classroom. The way that
children use these materials, inside and out, helps
develop a broad range of age-appropriate,
fundamental math skills.
The skills behind the creation of this structure
included the ability to differentiate and select
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fundamental math skills.
Teachers at Dodge, and elsewhere state-wide,
often refer to, The Minnesota Early Childhood
Indicators of Progress, as they evaluate a child’s
progress in his or her early childhood program.
The Indicators provide a straightforward outline of
general skill development by age; parents and
teachers use these indicators as a guideline or
measure for understanding how individual kids
are developing as compared to the general
standard. Dodge teachers also use The Indicators
in their “on the ground” research about naturebased teaching. In this issue, you will see just how
students are developing age-appropriate early
math skills, right in line with state guidelines.
One of my favorite “math moments” is this: A
child took a stack of wooden tree rounds and
lined them up. She then put one animal with its
own habitat on each round. This was clearly a
great example of a child’s understanding of what
educators call, “one-to-one correspondence,” but
it was also tied into caring for her animal friends
and it belied a greater understanding of how the
world works.
Number sense seems to evolve from something
deep inside of us. Maybe it begins with our own
rhythmic heartbeat. There are certainly wellproven theories of the strong connection between
number sense and music, and our human
musicality must ultimately be connected to our
own body rhythms.
My hope is that you will spend some time with
The Math Issue and ruminate with us about how
math skills develop in young children. Then I
hope that you will become an avid observer of
math development in your own children and
others around you. Watch how hard they work
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to make sense of their world. Look for where you
can support that concrete hands-on learning.
Enjoy!
11. Recognize objects can be measured by height, length, weight, and time
Weighing eggs
Measuring ice thickness
Finding a twelve-preschooler tree
12. Make comparisons
between at least two
groups of objects
Small sap buckets,
medium sap buckets, and
huge sap reservoirs
“I Found It. Two!”
Math Play
Kristenza Nelson, Willow Room
13. Use simple strategies to solve mathematical problems
In 2007, Dr. Kenneth Ginsberg wrote a clinical
study for The American Academy of Pediatrics.
He stated that children learn through play.
For young children, math skills, like other
cognitive skills, seem to be acquired through
concrete, hands-on, age-appropriate experiences.
In these early years, children seem to acquire
math skills naturally, through play. Sarah needs
four more blocks to complete the building of her
castle. Perhaps she needs a triangular block to
balance her tower. The blocks may not be
overtly counted, nevertheless she is selecting just
what she needs, understanding quantity through
necessity. Perhaps Sarah does not yet know the
word for the shape, but she has learned that
triangle is the shape she needs for success, and
understands its properties through hands-on
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18 children and only four tires.
Weʼll have to divide into smaller
groups and share tires.
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Did we build the wall tall
enough so the hermit
crabs can’t escape?
We’re running out
of long rectangle
blocks. We can
line up square
blocks to make
long rectangles.
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experience with the three dimensional shape. A
child rolls the dice and moves his pieces five
spaces in a game, not only practicing counting,
but understanding quantity and the relationship
between symbol and meaning too. Digging holes
in the sandbox side by side, two children practice
comparing and measuring:
“His hole is one shovel deep.
Mine is one shovel wide.”
Math skills are acquired each
and every day through play.
Math skill development seems
to require the mastery of one
concept before leaping to the
next; children build a
foundation of understanding
through hands-on experience
and then complicate and enrich
that understanding as they
begin to grasp more abstract
concepts later.
8. Order or sequence
several objects on the
basis of one
characteristic
Stacking blocks from wide to
narrow and lining up puzzle
pieces from short to long
9. Identify and name
common shapes
We encounter hexagonal
honeycomb, circular frozen
air bubbles, and create
spirals out of stones
10. Use words that
show
understanding of
order and position
of objects
Dictating stories in
journals often involves
talk of spatial
relationships
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The everyday world provides
many opportunities for teachers
and parents to foster
understanding and acquisition
of basic math skills; children
use math to make sense of the
world: Elsie is five, and Peter is
three. Both children know that
Elsie is older; they know that five is more than
three. Perhaps Elsie knows that five is two more
than three and can even ask, “What is five take
away three?” But age is never more important to
children than it is in the preschool years, and
they both know fundamentally that being five is
somehow larger than being three. Kids learn this
through conversation, experience and interaction
with peers, day in and day out.
“There was a banner that
said, ‘Michael.’ And there
was a lot of blobs shooting
towards it. And then there
was a 10 feet tall climbing
things with one X on top
and one X by it.”
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On a recent small group hike, a three-year-old
boy became quite excited when he found a piece
of wood that, to him, looked like “two.” Now, it
did not look like a numeral two, it looked instead
like the quantity of two, as if the wood was a
hand holding up two fingers, another symbol of
sorts, really.
The boy
heaved this rather large
piece of wood all the way
down the trail, back to
Dodge. He exercised his
problem-solving skills, by
the way, as he solicited
other children to help him
divide the labor and haul
the heavy load. As we
made our way back to
school, the excited boy
kept
pointing out his
discovery: “Hey, this is
two! I found it. Two!”
And so, we all talked about
two for the rest of the
hike. We discovered that
we have two eyes, two
ar ms, two feet, two
legs...We saw two sheep in
the pasture.
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Back at school, the boy
paints his found two,
claiming it and owning it in a new way. Here is a
child laying the foundations for abstract math
skill development in a very personal, concrete,
meaningful and developmentally appropriate
manner.
He is ready to build on his
understanding of quantity with concepts of
measurement and spatial relationships. His two
is pretty heavy after all, hmm...and how tall is that
two anyway?
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Using Tables
To View & Understand Information
5. Demonstrate beginning ability to combine and separate numbers of objects
Britney Stark, Willow Room
Throughout the early years of life, children
notice and explore math concepts in their world.
In their daily interactions, they discover patterns,
compare quantities and navigate through space.
As they make these discoveries, children begin to
compare information with each other too, taking
note of differences and similarities. It is often
helpful for teachers to gather information and
put it into a table with children, to help them
compare information or to find patterns that may
emerge.
In the Willow Room, our school year began with
the unexpected loss of our classroom chicken,
Pidge. The tragedy occurred on the second day
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of school and could not be ignored. Eventually,
some of the children joined Natalia on a visit to
the Dodge farm coop, to pick out a new chicken
for our room. The visit inspired an interest in
egg collecting among many of our students, and
so we began collecting eggs at the farm coop
every Tuesday.
Now, both morning and
afternoon classes stop and check for eggs. Each
time we do, we make a record of how many eggs
we find, and in which particular run of the coop
(our record-keeping is modeled on Farmer Don’s
official recording method at the farm). Children
have come to anticipate our visits, and we plan to
continue to collect the eggs for the rest of the
school year. Our hope is that by studying the
We frequently divide our classes into smaller
groups for hiking. Children often discuss ways
the small groups can be separated further, “We
have four girls and two boys in this group.” We
re-combine our separate groups when we
gather together back at school.
6. Recognize and
duplicate simple
patterns
7. Sort objects into subgroups by
one or two characteristics
information we collect, the children will find a
trend in numbers of eggs and determine when
the chickens lay eggs the most (hint: day length
and sunlight exposure is usually a strong
indicator of egg production).
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Baby pigs and grown-up pigs
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People tracks v. animal tracks
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There are many times throughout the year when
we may put together a table for viewing and
discussing information.
Many children are
focussed on their age, and the ages of their peers.
When this becomes a hot topic, we might create
a pictograph, using the kids’ photos, graphing the
ages across the class.
Interpreting The MN Early Childhood Indicators Of Progress:
Mathematical & Logical Thinking In Action At Dodge Nature Preschool
Joey Schoen, Assistant Director & Spruce Room
1. Demonstrate
increasing
interest in and
awareness of
numbers and
counting
We work to provide
materials and a
supportive
environment to foster
children’s developing
interest in numbers.
Graphs and diagrams are just some of the many
tools we use to help share and understand early
math concepts as they arise while we explore the
world around us.
2. Demonstrate an
understanding of
one-to-one
correspondence
between objects
and numbers.
Also, in our morning class, we have many
children who attend five days a week, and we’ve
found that creating a Venn diagram helps
children understand who among them attends
school on any given day of the week.
From setting the table
to standing in tires.
We offer many
chances to practice!
3. Demonstrate the ability
to count in sequence
4. Demonstrate the ability
to state the number
that comes next up to
9 or 10
Counting worms
Counting for hide-and-seek
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Finding Math in the Classroom
Moments of Meaningful Math Exploration
Melanie Grue & Lora Serafini, Oak Room
Some of the best moments of math
learning:
As a child (and to some extent an adult) I was
prone to what could be defined as, “math
anxiety.” Well, I graduated, went to college and
turned out to be a generally intelligent person.
However, I still look back and wonder when I
stopped seeing the beauty and possibility of the
mathematical sciences and started seeing a
meaningless avalanche of numbers.
Fortunately I work with preschoolers, whose very
existence embodies wonder at life’s possibilities.
At first I fretted over writing an article about
Math, with a capital “M.” Then I took a breath, started really looking at our classroom
moments and realized, as usual, my preschoolers were creating their own rich and meaningful
math experiences. These experiences have meaning because they are the natural unfolding of
curious minds.
--Melanie
Block-building and ramps...
Patterning and sorting...
Counting and measuring as we cook.
Sequencing & counting too!
Big to small,
right in a row!
Shorter
& taller.
“Three Cs”:
Color,
Counting &
Correction...
Which one is heavier?
Which number is the
worm hiding behind?
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Learning math concepts
through open-ended
experimentation with
toys, materials and
people...the
opportunities are
endless...
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