Sunday, October 19, 2014

Rethinking math in the Kindergarten

The intention

After spending years hosting a math circle and workshop in the Kindergarten each afternoon, we decided to make a concerted effort to embed literacy and math into our morning and afternoon experiences this year.

The Reasoning

Young children have a curiosity that is contagious. They are intrigued by problems in their environment and enjoy solving these problems with their peers. As the co-construct meaning together, they propel the inquiry process forward. We always seek best practice that engages and motivates the Kindergarten children.

The environment and routines are  equally important to the effort of embedding literacy and math and provoking inquiry. Story Workshop emphasizes the studio languages of expression and story development. We are looking for similar experiences that consistently stretch strategic, logical and mathematical thinking.

How does this intention translate to practice?
                       Gabriel  loves nature and notices the daily evidence of the Fall season. He has been collecting acorns. He filled a jar with acorns and presented his classmates with the challenge of estimating the number of acorns in the jar.  We later read the recorded estimates, counted the acorns and decided which estimate was the closest. C. is estimating our second challenge. This time Gabriel has filled a larger glass container.                                                    
Reed estimated 54 acorns in the jar.

Counting has many perils. Remembering the sequence of numbers is one such obstacle. We also try to assign only one number to each object counted and avoid skipping objects. Our class has developed several strategies to support counting. O. and G. were counting the floors in a skyscraper they built. They disagreed regarding the number of stories. 

They both counted separately several times. O. noticed that G. skipped a floor and G. noticed that O. counted out of sequence. Finally they decided to count together and agreed that there were 16 stories in their skyscraper.

The sensory experiences of a rice table inspired thinking regarding measurement. Tucker noticed that there were markings on one of the cups. When he put a "teeny" bit more in the cup and the rice rose to the number one but when he put more rice in the cup it moved to ten. Cole said that he filled all of the containers up to the top. The biggest container was the heaviest. Carter suggested that we get a scale and weigh the containers to see which container was the heaviest.

The next day....

Tucker: I kept scooping until they were the same size. This side is holding the other side down even though it has more rice.

We compared the size of the containers. Cole felt that the containers that were wider would hold more rice but Oliver disagreed. "If we filled both containers one would be way heavier because it is made of glass."

A week later we are still recording discoveries.
S. works meticulously to measure equal amounts of rice into the same containers achieving balance between the scale.

N: This is weighing the scale down because it is the tallest container.
S: It is because it is tall and made of glass.

S., N. and O. decide to use containers made from the same material to try to achieve a balanced scale. They realize through trial and error that they must continue to add rice and then weigh the containers.


The Scaffolding
We to meet in small groups during the morning and afternoon, as we have done in previous years, to consider the skills that support mathematical thinking and literacy. Mary and I notice the  challenges that exist for each child as they solve problems mathematically . Small groups provide an opportunity to tailor an experience to fit the needs of a particular student or group of students.

Working this way does require an understanding of the development of mathematical thinking of five and six year olds. This process also demands a vigilant level of listening and documenting. The questions that we choose to ask are also crucial.

One questions leads to another....
On Friday, a large noisy crowd gathered at the estimation jar. The children noticed that one of the acorns was sprouting.

Evan: Gabriel, look what is coming out of the acorn. It has a tail and is growing.

Monday, October 13, 2014

Do You Live in the City?

We listen for the space that exists between understanding and confusion. The space that lives between agreement and conflict. This space was defined by Vygotsky,  a well respected Soviet psychologist,  as the zone of proximal development (ZPD). We see potential in this space (or zone) for learning and discovery.

We returned from our field trip with new knowledge regarding the word "city". We saw skyscrapers, new city hall, old city hall, roads, a river, a circular coliseum, the baseball diamond, apartment buildings and parks. Several classmates expressed their vision of the city using blocks and then labeled the parts of the city.  

 As the children were building  I documented a conversation. I included the things I notes while listening in blue.

L: O, you live in the city.

B:  No, you live near me and I don't live in the city. I live in a neighborhood.
(using landmarks in close proximity to determine location)

L: Just ask your mom. (authority source)

B: You live close to me and it is definitely not the city. (sorting attributes)

L: I live more far away and the city is far from my house. You live close to my brother's school. (more sorting and identifying landmarks and proximity)

G: I live in the place where there are no buildings and just lots of houses. There are lots of vines, morning glories and flowers. (defining attributes) 

I asked the children what was needed when creating a city.

O: It needs to have lots of buildings and there are schools. I don't live in one.

L: You live on the side of a city. (attaching a visual representation)

O: I have gotten in my yard and looked over my fence. I do not see anything that looks like a city. (offering proof)

Dy: If you live in the city it has to be Virginia but I don't live in the city because there are not any hotels.

El: I live on the border of the city.  I live in a tall tall building. I can see a little bit of Sabot and a little bit of the city. (provided a word for the idea of a "side of the city".)

Len: I live in Virginia and I live right next to Sabot.

We brought the thinking from the block table  to our Project Circle. In their mind's eye where do the children see their house in relation to the city? Where do they see the school? Do the children think that they live in the city of Richmond or do they consider the city an urban environment with a city hall, buses, tall buildings and many hotels? 

Where do you live? Do you live in the city of Richmond? We added the visual of the yarn and beads to support the conversation and offer a representation of the conversation.

SR: I live no where near the city.

Do you live near Sabot school?

SR: Yes.

Li: I don’t live near the city. I am not close to Sabot.

Dy: Sabot is really close to me though and I don’t live near the City. I live in Virginia near my school.

N: I live close to Tavish. Yeah, you can ride a bike to his house. I don’t know why I am not next to Miles because my dad said that I live near Miles.

T: I live near Nathan’s tower. 

The conversation continued as children determined where to place their bead in relation to the tall buildings in the center of the circle (City Hall).

Elina shared her map of Richmond completed at home with her family. The map spanned a large region but offered a perspective of the city because Elina lives in the city. 

Anna asked the children to raise their hand if they live near Cartwheels and Coffee or raise their hand if they go to Sabot. Raise your hand if you live near the Diamond. 

The children also noticed the river running throughout Elina's map.


Together with the teachers the children hung for awhile in the ZPD and felt some disequilibrium. What does the path to the city look like for each child? Do their paths overlap with each other? What parts of their paths are similar and what parts are different?