My Visit to the Earth School

Today I visited the Earth School. The Earth School was founded in 1992. It is located in Manhattan's East Village. The dream of the Earth School is "to create a peaceful, nurturing place to stimulate learning in all realms of child development–intellectual, social, emotional and physical" (from http://www.theearthschool.org). The Earth School incorporates "hands-on exploration and interaction, an arts-rich curriculum, responsible stewardship of the earth’s resources, harmonious resolution of conflicts, and parent-teacher partnership". They strive to use curriculum which is active, playful, socially-conscious, and rigorous.

The focus of my visit was to observe math classrooms. I am in New York City for a math conference hosted by radicalmath.org. The conference is titled Creating Balance in an Unjust World: Conference on Math Education and Social Justice. The objective of the conference is to explore links between the fields of math education and social justice/social justice education. The conference coordinated our visit to the Earth School.

The classrooms at the Earth School are all multi-age, with two grades in the same class together. They are broken down into Pre-kindergarten and kindergarten, 1st and 2nd, 3rd grade and 4th and 5th (3rd grade, of course, being the exception). The students stay with the same teacher for two years. This facilitates students acting as teachers and helping one another. The teachers I met said they work with the students to help them self-identify their strengths and weaknesses so that they feel more comfortable offering help and asking for help.

The first math class that I observed was in the 1st and 2nd grade classroom. The room was set up with a circle rug area, and several small round and square tables with 4 to 6 chairs. The classroom exhibited a lot of constructivist pedagogical attributes that I was aware of. The whole lesson was about alternative approaches to addition. The teacher facilitated a discussion of how using doubles facts (i.e. 2 x 3 = 6, 2 x 4 = 8) can be used to help solve addition problems. They talked about how 2 x 3 + 1 = 7 gets the same answer as 3 + 4 = 7 (a.k.a. 3 + (3 + 1) = 7. Therefore, if you are able to see 3 + 4 as one more than 3 plus 3 or 2 times 3, then you could possibly more quickly arrive at the solution than if you counted on your fingers or used some other strategy. This part of the lesson also incorporated constructivist approaches in that it was a student-centered facilitated discussion and not a teacher-centered lecture.

In the next part of the lesson the students broke up into groups. The teacher gave instructions for an activity, then asked if there were any students who were still confused. She asked for any specific clarifying questions. She then asked students who felt confident going into the activity and thought they could assist another student to pair with students who still felt confused. The activity used 3 resources: number cards between 0 and 9 with counting dots on them, a "game board" listing "doubles facts" (any multiple of 2) up to 18, and two-sided colored foam circles. The instructions were to draw three cards from the deck with a partner. The students were to pick two cards of the three, which they could use a doubles fact to solve ( although the students discovered this might not always be possible to find two cards which were one away from each other and therefore this alternative addition process wasn't helpful for). Once they solved the addition of the two values, they wrote it down on a slip of paper, citing the doubles fact they used. After that, they used a foam circle to cover whichever double fact they used. They repeated this process, trying to cover every single double fact on the sheet. The slips of paper were placed in a white basket for class work.

The final element of the lesson was when the students came back together. The teacher brought forth the white basket and she went through the math facts placed inside one by one. She read the math fact aloud and the doubles fact which helped in solving it. She asked the students if the answer and doubles fact made sense together and why. If there was a name on the slip she asked the student who wrote it to explain how they came to the answer. Another element of constructivist teaching which was demonstrated in this part of the lesson was that no matter if the teacher knew the math fact to be correct or wrong, she asked the class or a particular student to explain how it was reached and if any changes needed to be made.

The students seemed to enjoy and be engaged by this lesson. It allowed flexibility in the process for students who understood the concept and for those who were developing understanding to both interact with the concept. The teacher gave students time when they got there materials to figure out the activity on their own without rushing in and micromanaging each group. It is helpful to understand the process of the activity if you are going to construct understanding.

This school has an integrated approach to special education. They have a special resource teacher who comes in to the regular classroom during math lessons (or any other designated lessons) and supports the lead teacher in the schoolwork. She is aware of special needs of the students. She works with all the students, but focuses on those with formally identified special needs. Sometimes, the class breaks into two groups (decided on by the teacher) and they learn the concepts in those separate groups. The lesson on this particular day was with the entire group together. They also have another special education teacher who sometimes pulls students from the regular classroom to work on special skills outside of the regular classroom.

The second classroom I visited was a 4th/5th grade classroom. The classroom had a stage-type area in the front, with a square rug in front of the stage. The desks were set up along both sides of the classroom in groups of four. The math class started with the teacher giving the students a page of 80 multiplication problems. The teacher gave the students approximately 5 minutes to finish as many problems as they could in that time period. This part of the lesson was for speed skill building. It struck me as extremely traditional, which isn't bad, it just wasn't what I expected. I wonder if there is a way to build that skill without engendering the competition that this activity did?

The next part of the lesson the teacher asked the students to review what strategies they had been exploring to solve multiplication and division in different ways. The students listed all the skills they had tried which included clustering, the "traditional algorithm" (which is the common way students learn to multiply and divide in mathematics), as well as a few others. For this lesson the students practiced using both clustering and the traditional algorithm. They were given one problem and asked to show solutions to the problem using both strategies. They were split into groups of two and three. Clustering was a new concept for me. In this strategy you break each multiplier into the place value numbers it is composed of. For example, if you were multiplying 645 x 137, you would think of it as multiplying 600 and 40 and 5 by 100 and 30 and 7, then you list all possible combinations. One way to start the cluster is by clustering combinations with the same total number of place values, starting with the largest: 600 x 100, 600 x 30, 100 x 40, 100 x 5, 600 x 7, 30 x 40, 40 x 7, 30 x 5, and 5 x 7. You list all of the individual totals and then add them together.

After about 10 minutes of group time, the teacher called the students back together, by having them meet on the square rug. The first thing the teacher asked the students was to indicate how their groups worked together by either giving a thumbs up, a neutral thumb, or a thumbs down. This allowed the teacher to make a mental note of the perceived success of the group pairings for future group work. Any groups where a member gave a thumbs down, the teacher asked them to share why. After they shared their problem, the teacher asked other students if they had any advice on how the group could work better together in the future. I really liked this process because it helped the class problem solve on good strategies for group cooperation and success.

Then the teacher had students volunteer to present how they found a solution using each multiplication strategy. Then the students discussed which strategy was more helpful for them and why.

I think this lesson was hard to evaluate on a one-time basis. It seemed like the unit was probably helpful for many students, but I still noticed students who seemed to be making it by, by hiding behind the work of other students without real understanding of the concepts. In this particular lesson it wasn't apparent that the teacher was aware of it, or any strategies she was using to solve that problem. I think I would have used the strategy of the 1st and 2nd grade teacher in pairing students who had understanding of the process and those who were confused. One instance that I saw where a student didn't understand and that wasn't being addressed was where a student who understood and was proficient at both multiplication strategies completed the entire problem without input from the struggling student or sufficient attempts to help them understand.

Overall, the identity of the Earth School as an environmentally conscious school was not at all evident in their math classrooms. There were elements that were observable throughout the school, such as a recycling program, but it was not integrated into the math program on those days. Most of the insights I gained were on seeing constructivist teaching strategies implemented in a classroom, and not on integrating math and social justice.

Harriet Tubman Free School

The Harriet Tubman Free School (http://www.tubmanfreeschool.org) is an offshoot of the Albany Free School. It is in its second year of operation and has 30 high school students, 3 full-time staff, and 2 interns. The school has 5 students that grew up going to the Albany Free School, but the rest are students that came from public school. There is a wide variety of reasons that the students have for going there and a wide variety of goals that they have. Some students were otherwise facing dropping out of school, and others hoped to graduate high school faster. The goals of the students vary: some want to graduate in 2 years and go to trade school and some want to take the regents exam and go to college.

The school day is scheduled loosely, but there are classes offered every day. However, the classes are not mandatory. The students meet with their advisor throughout the week to set goals and maintain them. The students are divided among the 3 teachers for advising, with each teacher taking a certain age range. The students are all working on building portfolio’s while they are attending.

I have spent quite a bit of time at the Harriet Tubman Free School. I teach math there once a week. I am one of two math teachers. I have a group of 3 students that regularly show up to my classes. They are all ninth graders and so far we have been working on percents, long division, multiplication, fractions and algebra. I have been pulling interactive mathematics activities off of the internet to do them with my class. My favorite so far was “How to win at Wheel of Fortune” which found the probability that letters will occur.

Another reason why I often go over to the high school is that they regularly host games of kickball, capture the flag, and whiffle ball. Many of the older students at my school like to go over and join the games there. The high schoolers are really great about including the younger students.

Brooklyn Free School

This week I went on a full day trip with the 4th through 8th graders from our school to the Brooklyn Free School (the website is really cool, check it out: http://brooklynfreeschool.org/). The school has been operating for 3 years, and is already at capacity in their current building. We went to the school to attend the convergence of northeastern democratic schools that was being held there. There were several different democratic schools that were represented including the Brooklyn Free School, the Albany Free School, the Harriet Tubman Free School, and the Hudson Valley Sudbury School. Each school had between 20 to 40 students and 5 to 10 teachers. In the morning there was a meeting of everyone in attendance. Each school gave a report of news from there school, talked about upcoming events, and then the students proposed events for after lunch.

After lunch there were many different activities offered. There were 3 different walking trips to parks and walkways in the area. There was a discussion on schools and pedagogy. I decided to go to the room designated for board games and I played Scrabble with students for a few hours.

All in all the day was very Free School-esque. There weren’t any required activities; people chose what they wanted to do. The Brooklyn Free School is a little smaller than the Albany Free School. The Brooklyn school is housed in a church that still holds services on weekends. The student population is more diverse than the Albany Free School. A majority of the students at the Albany Free School are white, but at the Brooklyn Free School there was more racial diversity. That is a very interesting fact because the Albany Free School is housed in a neighborhood that has a very high population of black residents, but the school population does not reflect that. The Brooklyn Free School must be more rooted in its neighborhood, or perhaps the idea is more widely accepted in New York City.

The interactions between the students and teachers at the Brooklyn Free School seemed relaxed.