Monica Marshall RSC – Art of Teaching 2nd grade - MATH 6/26/2012
MATH
In Practical Advice for teachers Steiner
says a lot about math.
Rudolf Steiner curriculum for Waldorf
Students – The divided I speech
GOALS for 1st grade –
Introduction
to qualities of numbers 1-12 ---Feeling of the whole and whole to the part
Intro
of #’s 1-12 up to 100-200
Introduce
concept of 0 – nothing
Strong
understanding of the story of the = sign and that it also means is
Counting
Story
Develop
familiarity with counting backward
Introduce
four processes
A lot of people used gnomes, knitted
gnomes, gnomes with capes, it can make it really alive.
# Patterns – developing
sense of estimation
Roman Numerals 1-12
Using manipulatives – rocks, river
stones, acorns, wooden beads
Sensory math – blindfold – smell things
Geometry curriculum imprinting
Jot things down so you can bring it back
(in 2nd)
Through the Curriculum can use remember
in 1st, especially if you set up the foundation
Division – Rudolf Steiner says it is
like multiplication, no difference; children connect and move to multiplication
easily. If child is a choleric then will
like division because they are demanding everything get broken up.
1st division need to do both
It’s
basically factoring 
AND ALSO
The way a # can be divided into
even groups
Need to SEE what difference is
Strategies for children that are
not there
They just work with the others in
the class. Don’t pull them out to have them
remediate yet, pair them with other students so they can help each other and
just keep bringing them along with the group.
Math is subject that can’t go to
sleep. She would have had children do
summer math work with parents and will have them do something like cooking with
the parents at home. Summer work should
be counting objects around the house, not drilling or written math – fun.
Mental math – wonderful especially
for the child that can do so but not on paper – really delight in them
The children LOVE having a long
problem that goes all the way across the board.
Come in the morning and there is an easy multiplication on the
board. Want to go from the whole to the
parts
Whole
|
Equals
|
3 groups of 2
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When write use strong rhythm!!!
Umbrella Story – solidifies and
carries the year, meets developmental style of class and can get pedagogical
stories into it. Monica uses the book Indian tales and uses the same
characters. The book itself is not for 2nd
grade and should not be read verbatim, but using the outline of the character
is perfect for the second grade mood. So
you can take a culture, she did Native American because she felt it was
important to honor the culture from where we live – POMO. You can use African, Japanese, chose
somewhere that you want to bring the culture and are interested in.
So her protagonist is
fox-boy. In Monica’s mind he is 8 years
old, and she never tells the children if he is an animal or a human. She talks about his beautiful bushy tail and when
children ask if he is a boy or a fox she says, well you will just have to
listen, never tell! It can bring in the
children that might drift when they think oh she might tell us this time if he
is a fox or a boy. Fox boy develops the
entire math curriculum story. She
developed his home, where he lives and brought glass from glass beach and used
the imagery of glass beach in her story as jewels that were traded. The other characters can be developed,
antelope mama, father bear…
So fox boy has tantrums and when
he does he gets the hahas and he can’t stop kicking his leg. Grandfather coyote is another character that
visits foxboy. He tells stories like a
true American tale, story within a story, real folktale of Native American and
all the math comes from these stories.
So how to introduce times tables
Fox boy had a great relationship
with Grandfather coyote….build up the story…and tells how he can talk to the
animals by teaching him to sing the secret songs.
One night he heard an owl hooting
– owl two-feather. Fox-boy was in his
grass hut (or wikiup –but pomos lived in grass huts) and heard owl
hooting……..continue embellish…found owl and he sang the song of owl, the song
of 1 1 is 1x2 this leads them to talking and he shows fox
boy where he can find the sticks.
At end of the lesson can say, “And I have some of
those sticks right here for you – OHHHHHH!!!!”
They will be SO excited, (Rhythm sticks) can paint bottom of the
branches/sticks. One time Monica had her
class go out into the Robin Hood forest and gather sticks – they didn’t last so
well, but you could make rhythm sticks and put them around the forest – would
have to make sure there were no branches they would want to use – or get crafty
about it. Could maybe throw them around
the forest and tell them owl left them for them and they will need to find.
Fox boy meets other animals in the forest – mouse 10
ton, otter 4 splash. The word spreads
about fox boy and that he could learn the song of the animal. Each animal is associated with a
multiplication table.
Rhythm of #’s – change it up from 1st,
bring it in all different ways. Don’t
buy into the FEAR of them not knowing their times tables – make it fun – living
loving pictures.
2nd grade characters
should NOT be anything like 1st grade characters – they are no
longer 1st graders and they need to know that YOU know and
understand this. When the children ask
is …(from 1st grade) coming to 2nd grade – OH NO…that is
a 1st grade thing. So NO
carrying the fabulous gnomes forward, so tempting but no – that is a 1st
grade thing, we are in 2nd grade.
Though you can refer back to say a story in 1st, it something
that they can hold on to when bringing new ideas.
Can do a chalkboard drawing of an
owl in the tree and animals in the forest and the inhabitants, or could do owl
in the tree and then add the inhabitants a bit a time.
MENTAL MATH
Write a mental math story for 1st 6 weeks
Need to do narrative, not the 10+3 is - you can do this practice but not at mental
math time.
The narrative builds critical thinking skills and
independent and creative thought.
Make sure you mix up the difficulty of the
questions. If you start to easy the
smart ones won’t listen if you start too hard the ones that struggle will check
out, start with medium to hard.
As I was walking to school today I saw 50 squirrels
in Tehlias’ yard (use a bigger number than in 1st), 20 squirrels
went in one direction and 15 went in another, how many were left? Use RIDICULOUS things. There were 150 ducks in the pond, in 1st
grade they would want to go to the pond and see them but in 2nd they
just think it’s funny. Don’t want to
give too much to story – downfall if so – just 3 minutes, it will deaden if you
go on to long, just thinking it is an exercise and make it humouous. The pace should vary and it takes time to
build it up when you stop doing the math your skills deteriorate, even for the
teacher, can do an everyday story with 5’s in it. Should be doing mental math every-day in main
lesson.
When you call on a student whose hand isn’t up and
they say, but my hands not up, then you can say, “Oh I know but this question
is for you.”
Child that can’t visualize they can use their hands –
10 left – 5 went away.
Mental math (from Antje)
A jellyfish knocked on my door yesterday
He was selling butter cookies and marmalade
There were 25 cookies upon the plate
I ate 4 and Tehlias ate 8
How many were left? 13
Just then Cooper my dog past by
He jumped on the jellyfish and did the plate fly
The puppie ate up another two
How many cookies were left for you? 11
Monica marshall Art of teaching 2nd con’d (came in late –
traffic accident)
Place value
For children there needs to be a
reason why we go from 9 to 10
Children get it – reason WHY we don’t stay in the 1’s
So story of skunk she made up and foxboy about bag where he cant hold
10 in his hand at one time. So he needed
a bag to but them in whenever he had more than 9. So the bag is named 10. Can do other ideas like eggs in a nest.
YOU JUST WANT TO CREATE A PIX AND MOOD OF WHAT TO BRING
 |
Fox
boy collected 4 in the morning
 |
He
collected 11 by the afternoon
Do you think fox boy got the hahas?
So what did he have to do?
He put 10 in his bag.
So he had 1 left.
Do you think he could gold one in his hand? YES
Can make the pouches out of leather and then can
say…..and I have a pouch right her for you!!!
They will give OHHHHHHH…if they are living into the story and then can
have the children blanket stitch them up.
So then (want to say all different ways)
We can draw 2 bags on the board and 3 jewels
And say This is what fox boy had in the morning
 |
|||
 |
|||
) 0
0 0
3.)How
many here
1.)So how many in this pouch
2.)
How many in this one
How many is that? 23
Then add bags
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0 0 0
0 0 0
Count 10 20 30
Remember the 1st day when he could only
hold 9 in his hand?
No can add together
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0 0 0
0 0 0
_________________________________________________________
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|||||||||
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0 0 0
0 0 0
So how many did he have all together? Lets count
10 20 30 40 50
and how many in the hand-6
Now there is another way to do this – introduce
vertical
23
+33
5 bags – 6 in the hand
Ask the children – can my hand hold more than 9??? NO
So all of that could be 1st weeks work
So the 1st thing is making the 10 around
the pouch, then do it with the pouches counting, then doing it vertical, should
be a progression. Then can use
manipulatives with the bag, whatever you used in 1st you can use in
2nd.
Good to use manipulatives too so that they realize
things come in different sizes and colors
So now next week
Fox boy getting so puffed up, thinking he’s all that
and Grandfather (give visual description of him) cam over to talk to him.
Fox boy learned about the song of the owl and fox boy
needed to teach the song to the people of his village. Fox boy didn’t like that.. (Build in lots of
drama within the words of the story)
Fox boy taught the song of the owl to the other
children of the village so they could all be safe when they walked
through. Now fox boy all puffed up and
grandfather coyote says you look like a porcupine – fox boy is humbled. He collects pouches – all the way up to 99
So need to have some way of character holding 99
things
He has more than 99 so he drops them all to the ground - go to 100
So fox boy looked at all those jewels on the ground
and what do you think happened??
He got the hahas – and his leg begin to shake and he
was howling
The mama came by and said I haven’t seen the hahas in
a while…I have a basket that I have been weaving and I would like you to
have. So he picked up the basket and
wouldn’t you know all 100 pouches fit perfectly in the basket
Draw a basket and put a 100 on it
If students understand correctly they can go on with
baskets, if not you will have to work there.
So now you can draw baskets and pouches and in the
hand on the board (always use the same terminology – children will get lost
easily if you skip from calling it pouches and then bags)
So
Bag bag 000
Bag
bag bag 000
Basket basket bag
bag bag bag
bag 6
Then next adding
23
233+
256
So this is all in 1 color of stone
Don’t normally have the same amount of bags as in the
hand so…
Bags don’t necessarily have to line up either.
If you set up really well this – they will all get it
REALLY have to think out place value and story
because if you do it confusing – they will be totally lost and confused.
So for each place
Mama comes and rescues fox boy and gives him
something else he needs
Backpack etc…
THEN –
Grandfather coyote sees that Foxboy has so many
jewels. Foxboy is stronger and standing
taller and says Grandfather coyote to Foxboy I want you to come with me
somewhere. And grandfather goes into the
story of his Great great great great great great great great grandfather that
told him of this place and (foxboy has a best friend by this time – badger
girl) and coyote squatted in the soil and drew a map on the ground to show fox
boy how to get there.
Fox boy and badger girl go on the quest all the way
to the beach – glass beach
Fox boy and badger girl gathered as many as they
could gather of the green stones
Grandfather coyote said no we must not give them out
yet because we have far less of the green than of the purple (this is when we
use stones or beans or glass)
Grandfather Coyote goes into a deep deep sleep and
his ancestors tell him that you may trade.
You may trade 10 purple stones for 1 green stone and yadayada – Tell me
what fox boy would have if he had 25 stones
So high level will count out 2 green and 5 purple,
others that didn’t make the leap will count out 25 purple stones.
So then the stories of going to toehr beaches and
collecting other gems or stones and each one being more valuable.
Good to do manipulatives at end of class on floor in
a circle so you can see your feet and everyone elses.
It’s a balance – you don’t want to stay too long in
1’s and 10’s but don’t want to go on if some don’t understand it
well.
When you go to the #’s you might lose children but
that is ok – just keep bringing them along.
1st do the math horizontal.
Doing math left to right is setting a plain for language arts
2nd –
The children lose intuitive sense and gain more
imaginative forces – practice both horizontal and vertical math – but solidfy
it and then you will be able to go back to it and recall.
So can have a felt piece for each child
Fox boy gave 4 jewels to tribe …..
Bring down 4
So now take 10 and move it over into the pouch
Make sure it is set up so the 10’s are on the left –
then throw in fox boy needed some porridge and some…
Then fox boy came back and gathered another whole
pouch worth of stones
What do we have now?
2 pouches and 2 in the hand
This is not
recall or mental math this is arithmetic in main lesson, during Math block – do
this 2x a week.
So now how many pouches do you have? How many in the hand?
It is best to do this at the end of circle because
once set up don’t want to go on till everything is put away. Can call on children to set up – give felt –
jewels etc…
Picture of felt
Pouch pouch
00 so now have another
color because can only go so far if the stones are the same color
Person in charge of trading gives the beans/jewels
White bean -
100
Balck – 10
Brown – 1
Monica had enough different colors of jewels all the
way to the millionth. The millionth was
a dragon tear with a color inside the color (of course most valuable)
So have felt piece with jewels like this
100
10 1
1st block – no carrying and no borrowing –
just addition, towards the end can do the following type of example
Father Bear was always needing jewels to share with
the other people of the village. One day
Father bear came to fox boy and said I need 1 pouch and 3 jewels for ….
So he had pouch pouch 000
He gave pouch 000
He had
pouch and 0 in the hand
So subtraction do that 1st than can do 23
-13
10
Then father bear needed jewels for turtle girl and
Monica says he had (always start with the hand(
3 in the hand
3 pouches
2 baskets
How many did he have?
233
How many baskets? 2
How many pouches in the basket? 20
Jewels are very tactile and will help to activate
their thinking. Knitting activates the nerve endings in the brain (Swedish
study)
So the story lasts all year and at the same time fox
boy is learning new songs to go with the multiplication tables
20 pouches
Then he would have to hold 200 jewels
So now back to the 233 – let’s read that again - how
many jewels in the pouch? 30
Now fox boy
found 3 more jewels –
So now how many in the hand? 6
They are doing this on the felt with their jewels
Now he gathers 5 more black beans (5 more pouches)
Do we have enough to trade for a basket?
Then Fox boy gathered five more in the hand – is he
going to have the hahas? What do we
need to do? Trade
Oh no do we
have enough to trade for a basket? How
many more would he need?
Are we even close (estimation)
Build in the estimation, most children won’t be able
to answer, some can and some can without even knowing they can.
Can keep this active all year long and can work with
the stories.
Monica talks about being a chemist and having to take
a test. She was in upper math classes
and failed the foundations of math test.
She didn’t get these foundations in school - it is vital for students to understand this!
Manipulatives are really good for children that live
in their heads. Can tell them, pick up
the green stone, how does it feel? It
was laying on the beach getting tossed in the surf and it was rubbed smooth by
the sand – build up the living picture so they live into it – this creates
reverence.
At the end you can let them make a picture with the
jewels on the felt (just few minutes) and not everyone will finish the pix,
then you can go around the circle and show them. If
they didn’t finish they can say oh I was going to make…
Monica then had us go outside and had us do
jumprope. If children can’t do the over
then can do snake or evy ivy back and forth.
She said – jump over the rope if you have 10 people, minus 5 in your
house. Then you have to say the # as you
jump over the rope. You can do this with
breakfast (helps you find out who is eating healthy) – If you had 3 things for
breakfast jump over the rope – and name them.
Jump over the rope if you are 20 – 11+1+1 = They jump over the rope and say 9. You
can do the different ages.
Monica
Marshall – art of teaching grade 2 3rd class on
Math
2nd block
Use different felt colors for different things –
golden felt for recorder
Fox boy had 1253
(always have your own that you are working on – or you’ll prob. Get
lost)
How many baskets did he have?
Now fox boy has 2586
How many black beans does he have?
Does everyone have 8???
Give time for people to rejoin you if they are off
So how many pinto would we need for one garbanzo?
Shake things up – can ask a complicated thing and see
if anyone answers
Read the 1st and 3rd grade
indication – there is not a lot about 2nd
Book – examining the Waldorf curriculum from an
American viewpoint.
Children love accoutrements and being a scribe
Word “Weird” is a word not allowed in Monicas class – she’ll
say isn’t it odd and isn’t it a fun word we are so lucky we can speak it.
So we now have
Garbanzo beans in the 1000’s
Garbanzo Pinto BlackBeans Pintos
2000 500 80 6
Than Father Bear came by and needed to borrow 203 beans
Then can write this # on the board, helps children to learn visually
What was left
Use subtract sign
Last block take them into the millions (not millionth) just for fun
So if 203 two hundred three (not two hundred and three)
Saying “it’s just the way it is” instead of I say so
Bear now needed to borrow 200 more
Then came back 100 more (working the story into it)
What do you see now?
2083
As you go with the jewels or beans the children should point finger on
beans
So how many pintos are in the baskets?
In 2nd block talk to children about place value – can talk
about parents in the big world and how they use it
So taking away 1 basket and 2 in the hand
1081 left
So nothing in the basket place – what is that basket place? 100’s
Keep working with less than and equal than
There is lots of loss of common sense and so really bring in lots of
sayings
Early bird gets the worm etc…They are so very American (come up a lot
when study Rome)
In 4th there are lots of pioneer sayings
Now –
Quail girl came by which was so very unusual – and she borrowed 3 black
beans and then antelope came by and borrowed a garbanzo bean
What does that mean 51?
5 – 10’s
Then count 10’s on hands 10 20 30 40 50
Then Father Bear came by and asked for 21 more and did Dad take 21 No
He took 2 north and traded
By this time don’t need to say pouches and saying black beans
What is left 3 black beans
If I was drawing pouches/ beans, how many 1’s ??
Do I need to put that? Yes
To hold my place
Dorothy Herrer – book – Math lessons for Elementary grades
Commas in math – seashell to keep place
Secret relationship with children want to capitalize on
Bored – oh that’s good because when you think of something to do you’ll
be so excited
Academic part doesn’t always meet them
Develop the social realm and in 4th they
will be able to shine
Child will remember the one thing that was boring
They need to inwardly feel that you as the teacher
knew that they could answer and the idea that you gave that question just for
them to answer- just for me!!!
Don’t convince parents to stay can say – as a parent
I really trust your judgment and If you think that that he would be better off
Build relationship our of love and really work
through the temperments
Melancholic – “Oh I never get the answer right”
Always make sure the melancholic can answer something. But I just called on you yesterday and you
got it right away.
With Melancholic don’t respond of course your so
smart or oh that’s so sad or one day you’ll be able to get it right.
Can do the melancholic face, oh L, sometimes that is all
they need
Phlegmatic – inwardly a lot is going on – boy
nothing/ never gave any kind of sign even listeinging – they are on a different
rhythm but quite awake inside – The boy she tried to get him to answer but
wouldn’t – he was on a two day rhythm working through the info.
Monica doesn’t use columns or graphs because looking
for the inner column. Some children need
help – have vision of where want to go and the children to be
Example – Do main lesson book on Sunday so she takes
out all the childrens books and fixes the little things in them and then gives
whatever they need to be successful.
Children don’t like using crutches and will give them up when they feel
ready
Don’t say to children, oh no that is so beautiful,
when it is not your lying and they know
Nobody counts on their fingers if they don’t delight
in doing it or need to do it.
Love to have children collaborate
Remember – you go out and miss things during talks so
don’t be so on children when they do
Monica had us stand in a line of 5 or so and had 2nd person
write a number on the 1st person’s back. Wrote 25 and then next person did 35 than down
the line. Everytime you have to erase –
very crucial step (doing this actually helps with folk dancing???) Then had 2nd
person pic one of the #’s and they wrote and person had to guess.
The only time this was a problem is when the girls
started wearing bras – so when they got that age she stopped
Now
if someone does it wrong – 57 instead of 75 can say Oh lets try it again and
see if they start to do it right – if not can say 0h 5 first sweetie.
All the things in childhood normalize “of course
these things happen” That would be the gesture
In Steiners time prob not so many spatial issues.
Children did folk dancing from an early age, this creates less spatial
issues. Utilize as much as you can.
TIMES TABLES
2 is 1 x 2
Sticks - II x
(cross sticks together) II cross
sticks put on shouldersj
Hit on desk, hit on carpet – Each times table will
have it’s own pattern
24 is 12x2
Can do this times table backward
Can connect times tables and do them forward and
backwards or backwards and immediately forward
Also hitting the neighbors sticks on side if in a
circle – would have different rhythm or gesture for each times table. You don’t want to have the same rhythm it
will put them to sleep – you want to wake them up. And don’t only use sticks.
Can do in a circle and have stones for each different
clan – 4 groups – skunk, bear, coyote etc…
Fox boy crosses the country to visit the other tribes
Rocks carved into the animal shape – animal spirit in
the rocks – 1 for each clan
We teach to the imagination, public school children
say hate when they just can’t do it yet
Do it one way – then do it 5 other ways
Special basket
for the carved animals
Sitting
in a circle – those in the wolf clan, sing me the song of the owl 1 is 1x2….
Can of the ….sing me the song of the otter wolf
splash then they do the 4’s
There will sometimes be tension between the clans –
can have clans meeting each other in the
forest –
“Brash warrior we know the song of the ….better than
the other clan”
So then the 2 clans “battle” the other 2 clans
If one group is better – sounds like the bears and
skunks are tired
Can separate further to 1 clan on 1 clan and then
down to choosing 1 child from each clan so each child in clan doing there times
tables.
Can have someone step out of the circle and do on our
fingers
Have them make sticks – sand down and work them –be
careful with bamboo, splinters in it – so painful
Clans shift and change 0 no same stone get to be on
the floor in the center – the stones are a ceremonial thing. When bring out the stones they kow the clans
are here – and they live into the clan.
Luni stick is best for 4th
Chinese jumprope she thinks is better for 3rd
or 4th
Indonesian sticks 4th – dance movement
with them steeping over sticks shared at goetheum, finnish school, conference
in Dornach.
As move up the grades wouldn’t want to only do sticks
– don’t want to overstick them – so special thing a couple times a week – look
at gestures
Bean Bags
Partners move bean bag from hand to hand 2 is 1 x
2 hand hand hand throw can put students
in triplets or quad.
Timestables – counting stars – can use counting stars on each #
When create – not a clock - so do we have something between 2 and
3? Work with children to make the
numbers around the circle. Can have them
put stones 1st
Raccoon 3 legs, when he draws in the dirt he draw a
special seal and when fox boy is in trouble he needs to stop and draw the
special symbol (counting star needed) if he does anyone in the village will
come to his aid. Even’s go to the
highest will always end on evens.
Partial pix of owl two feather in a tree then on
other page mulitiples of 2’s
Children need help if just give them a pencil and say
write it they get squished. Do work in
crayons and nice and large . So does 4
times table on 1 page, equal sign should be directly below equal sign above it,
then groups of 1 group of 2 groups of
2 = 1 x 2
4 = 2 x 2
6 = 3 x 2
8 = 4 x 2
One color one
color groups This column
tells us how many per groups
Total the
same as
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