Overview
I teach 3rd grade at Wexler-Grant Community School in New Haven, Connecticut. We are a school that begins with Headstart and ends with 8th grade. We have an interesting history. We were two separate schools at one time, Helene W. Grant and Isadore Wexler. Due to the close proximity of both schools and the remodeling of all of the schools in New Haven, we were scheduled to merge, as many schools in New Haven have, and add 6th - 8th grades. Our population of students is approximately 90% African-American and the remaining 10% is made up of White and Hispanic. Many of our students in our school have never left the state of Connecticut. Many of them have never even been out of the city of New Haven. Teaching in New Haven can certainly be tough because some students seem to come to school for reasons other than learning. You certainly have to have a thick skin to work in our school. You also have to bring enough enthusiasm for the whole class as well as yourself.
Math always was a subject that I had difficulty with while growing up. The teacher would present the problem and I just did not get it. I could not "see" how to do the problem. Everything would be a mess of jumbled numbers that I could not put into the appropriate places. At the same time, I didn't understand why we were doing what we were doing in math. To put it more clearly, I would try to follow the "rules" but I didn't know who made up the "rules" and I didn't understand how and why they worked. For example, if we were learning how to add two digit numbers and regroup, the teacher would typically say, "27 + 19, we start in the one's place and add 7 + 9 which is 16. We then carry the 1 and put it in the ten's place on top of the 2 and then add 1 + 2 + 1 to get a sum of 46." I'm left scratching my head. I carry the 1? Why? What does this all mean? What's going on with the 1 that I have to put it over the 2? I was always told, "That's the rules. Follow the rules and you'll always get the right answer." I learned to follow the "rules," but I never understood how or why the "rules" worked. I realize now that I did not have a good number sense. As I got older and more mature and had a better understanding of numbers, it began to make sense. It actually wasn't until I began the accelerated teachers Masters Program at the University of New Haven that my number sense came in focus. My class in elementary math with Dr. Shirley Wakin was truly an eye-opening experience. Dr. Wakin taught us that there were many different ways to solve math problems. She exposed the class to manipulatives and visual aids that helped me "see" how numbers work and fit together. I realized that math is the science of patterns. Though math has language that tells the reader what must be done, math is also a language unto itself. It is a language that I am trying to become fluent in so that my students will become fluent in turn. Teaching math and having to explain to my students new math concepts has developed my number sense even more.
In the past, our school was recognized as one of the "good" elementary schools in New Haven. This applied to everything, including math. In 1999 we struck out on our own (against the Math department's wishes) and began a math program that was different from the district's. The New Haven District uses the Saxon math program for Kindergarten through 4th grade. Our school decided to use a program called Investigations developed at TERC (formerly Technical Education Research Centers). At the time, our school was smaller, we only went to 5th grade and we had a dynamic staff that was handpicked by the administration and the staff collaboratively. Investigations seemed to be a breath of fresh air because it presented a whole new way to teach math to our students. Investigations had four major goals. It wanted to offer students meaningful mathematical problems and emphasize depth in mathematical thinking rather than superficial exposure to a series of fragmented topics. Investigations also wanted to communicate mathematics content and pedagogy to teachers and to substantially expand the pool of mathematically literate students. For someone like me, this was better than the invention of sliced bread. The features of Investigations were new and innovative. It was extremely different from Saxon math which focused on learning math from lots of repetition. Students would sit at their desks and the class would do side A together. Side B would be done for homework. Saxon would add new concepts while still providing problems from previous lessons. Although this is a highly effective pedagogical device, there was no creativity from the children to develop their own ways to solve mathematical problems. Investigations provided a curriculum that would ensure that all students are included in mathematics learning. Investigations follows a model of cooperative learning where students move around the classroom exploring math in their environment and talk with their classmates. The students work in groups or in pairs where they try to find various solutions to problems. Students are encouraged to invent their own strategies and approaches to problems rather than depending on memorized procedures. Finally the students express their mathematical thinking through drawing, writing, and discussion.
Investigations also has some very good math games that the students can play to help them develop a good number sense. Though this program seemed like a dream come true, it had its drawbacks. We were always told that Investigations was meant to be a supplemental program, not a stand-alone program. Investigations requires a lot of reading beforehand and a lot of copying for the various games and activities. It required a lot of time to prepare for the lessons. Due to various circumstances such as teacher turnover, loss of supplies, and lack of training, Investigations has not fully met the needs of our students. Many teachers now just rely on the math mini-workbooks that are given to us from the Math department. Many of our staff have watched the math scores start off well and consistently drop as the year progresses. We have met and discussed the results and have attributed it to the fact that we do not have a solid math program in our school.
Most of the resources and teachers' time in New Haven is devoted to literacy. The Reading Department does a great job with providing teachers with training and materials to increase the scores in reading. They push their teachers to become well versed in the various reading strategies so that we can better equip our students with skills to improve their reading. Our students are inundated with various reading strategies to help them become better readers. Those strategies are drilled into our students so that it becomes second nature to them to know the strategies. It doesn't mean that our students always use the strategies, but they are at least familiar with them. This unit will take those same reading strategies and apply them to math. Those strategies are making connections with the text. This includes making connections to yourself, making connections to the world, and making connections to other texts. Another strategy is asking questions about what you are reading. Visualizing is a strategy that allows you to "see" the picture the author is trying to paint by imagining in your mind or sketching on paper what is happening in the story. Making predictions allows you to think about what will happen next. Determining what is important is a multi-faceted strategy in that the purpose for reading means that there are number of variables that must be taken into account such as are you reading to learn new information? What is important versus what is interesting? Also, is the author trying to entertain, inform or persuade?(1) Students also have to distinguish in a story the difference between major events and details. They also have to infer which is reading between the lines and possibly determine the author's intent or purpose. The last two strategies are synthesizing and metacognitive monitoring. Synthesizing is taking information you have read that is new and combining it with information that you already know to create something new.(2) Metacognitive monitoring is the monitoring of one's own thought process that they go through based on one's current thoughts and knowledge.(3) Though these strategies have been identified as reading strategies, they are excellent strategies that can be used in all areas of study, especially math. For the purpose of this unit, metacognitive will not be explored further at this time. The emphasis for the final strategy will be synthesis.
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