synopsis

SYNOPSIS

Mary Giacomarro & Joel V. Thornton

Council of Curriculum Development

Proposed Curriculum Change

The council of curriculum development is a group of administrators and teachers working together to promote success. The council’s responsibility is to review current curriculums and locate areas of improvement that should be made to promote student achievement. This year the council focused on the improvement plan to “UNLEARN” the passive learner in the mathematics classroom. It will also focus on one of the Five Theories of Learning, which is the experimentalist theory. Here students learn “by” doing or hands-on.

The first step of the council was to develop a three-stage learning curve that included the following: CONCRETE à ICONIC à SYMBOLIC. We identified these three characteristics based on the current curriculum. The current curriculum in place, teaches our students from the CONCRETE to SYMBOLIC stage. This means that our students are only memorizing the material. They truly never learn or understand the material to apply that knowledge to higher-order-thinking problems. The proposed curriculum will teach from the CONCRETE to ICONIC then SYMBOLIC. Through this sequence, students learn to make the connection and understand why they are solving the problem. With the connection, students are able to apply their knowledge and solve higher-order-thinking problems or real-life problems.

The proposed curriculum will also focus on three aspects: “UNLEARN” traditional assessment methods, improve technology and promote success for the 21^st Century learner. The proposed curriculum will have teachers grading their students through projects, presentations, tests, quizzes, homework, research papers and bi-weekly blogs where students solve real-life problems and respond to team members. Teachers will also have a classroom set of graphing calculators that are connected to a computer that projectors their answers and individual screen. Here the teacher has a virtual classroom where everyone is interactive. Smart boards will be provided in each classroom with projectors and a mobile cart of laptops provided with mathematics features. The 21^st Century learner must be able to adapt and reason. The world is forever changing and the successful student will be prepared for the rigorous road ahead. I would like to end with a quote by Nelson Mandela “Education is the most powerful weapon which you can use to change the world.”

Memo to Superintendent

Life Long Learners Institute

3.14 Aim High Lane

Motion, New Jersey 02468

Mary Giacomarro & Joel V. Thornton Telephone: (201) 527-4961

Council of Curriculum Development Fax: (201) 301-2546

MEMO

Date: December 4, 2008

To: Barry A. Bachenheimer, Superintendent

From: Mary Giacomarro, Principal

Joel V. Thornton, Vice-Principal

Re: Proposed Curriculum Change

Education is the key element for success in our student’s lives. The future of our society rests in the hands of our students. To prepare our students for their roles in the current society and future we have proposed the following. We need to “UNLEARN” the passive learner in the mathematics classroom. We will apply a three-stage learning curve: CONCRETE à ICONCI à SYMBOLIC. Here our students will make the connection and understanding to the material being taught and apply that knowledge in the 21^st Century.

The reason for the proposed curriculum change came from the following data. The Passing Rate for students in our school taking the HSPA Mathematics is 63.3% proficient and 16.6% advanced proficient. The state average for advanced proficient is 23.2%. The Passing Rate for students in our school taking the GEPA Mathematics is 61.5% proficient and 13.5% advanced proficient. The state average for advanced proficient is 22.5%. Our scores in the advanced proficient are below average. Our student’s performance is based on the CONCRETE and SYMBOLIC stages. Students never learn to make the connection of material learned and apply that knowledge to higher-order-thinking problems and real-life problems. Our current curriculum does not apply the ICONIC stage where the connection is made. Schools that applied the three-stage learning curve have improved advanced proficient on the GEPA Mathematics from 12.4% to 32.1%. The data clearly shows students who learn from CONCRETE TO ICONIC THEN SYMOBLIC have a meaningful understanding of knowledge that promotes success. When students make the connection, they are able to see the larger picture “The key to success is to risk thinking unconventional thoughts. Convention is the enemy of progress. As long as you’ve got slightly more perception than the average loaf, you could invent something” (Pink, 2005).

The three-stage learning curve: CONCRETE à ICONIC à SYMBOLIC will offer the teachers involved with an abundance of Professional Development. Each Professional Development session will focus on a different aspect. Such as team teaching, use of technology, alternate assessment methods and teaching to the 21^st century classroom. Team teaching is one factor that assists the three-stage learning curve through teacher consistency. It is stated in a quote by James Surowiecki “A successful face-to-face team is more than just collectively intelligent. It makes everyone work harder, think smarter and reach better conclusions than they would have on their own.” We have received a grant through the Mathematics Association of Growth, to purchase textbooks, supplies, materials, professional development, laptops, smart boards and projectors. Also through the Mathematics Association of Growth grant, we will have a math tutor to help students with their homework and answer any questions for an hour after school each day of the week for the school year. Our student’s achievement will come from the connection made in the ICONIC stage. When our students make the connection, their success in life has endless possibilities.

Curriculum Change

Results NOW!

I am acting as a Principal of a Middle School…

…isolation ensures that highly unprofessional practices are tolerated and thus proliferate in the name of…professionalism…”what works” morphs easily into what feels good, or keeps kids occupied or, “what I’ve always done and gotten good evaluations for.”

Upon completing my first round of observations, I have noticed that there an exceeding amount of unprofessional practices going on throughout our school. I have met with several teachers within our school in order to gain input as to how to resolve this problem. Collectively, we have decided to put our teachers/students into teams in order to force us out of the isolation that is our classrooms. Students and teachers, within each grade level, will be divided into teams. Each team will consist of four primary teachers, Language Arts, Mathematics, Science, and Social Studies. These teachers of each team will meet weekly in order to discuss students, concerns, and best practice. These teachers will also conduct parent meetings as a unit. Five times a year, each teacher is to video record themselves teaching in their classrooms. With that video, each teacher will work with their team counterpart (a math teacher from team A of the 8th grade will meet with a math teacher from team B of the 8th grade) in order to evaluate each other and adjust lesson designs accordingly, possibly implementing an alternate lesson plan template. This will force teachers to not remain in isolation and work together for the best interest of the students.

Taken from page 108, paragraph 4
“We have relied far too much, with miserable results, on a failed model for improving instructional practice: training, in the form of workshops or staff development.”

Continuing with the idea that a teacher should not teach in isolation, a teacher should not assume to improve the quality of their teaching by attending workshops alone. We can make significant strides if we pool our knowledge, utilize our best practices and refine them. We have teachers within our school that have endless capabilities. We can bring out the best in our own faculty if we focus on instructional practice within our school, with our teachers and team-based learning communities. By doing so, we encourage teachers to rely on the expertise within our school, as well as empower our faculty.

Taken from page 15, second paragraph
Over the years, I have persuaded teachers and administrators into doing something most don’t do very often of with a clear focus: tour classrooms.

As part of our new initiative, I encourage teachers within our school to tour other classrooms at least four times a year. When doing so, please make yourself aware of what is taking place in our school. Are you witnessing students learning? Can they articulate what they are learning? Can the teacher? Are the students actively engaged? If there wasn’t a “buffer”, what do you think parents might not agree with that is going on in our classrooms? Where can we improve? Where are we exceptional? How can we share those ideas?

UbD-comments

Writing my lesson plan in this manner was difficult for me to do. Even though I have written many lesson plans, I believe that this took more time and effort than previous lesson plans. Essentially, I thought about every single second of my 42 minute period. I believe it is a great tool to use for a weekly plan, but seems unrealistic to do for every individual lesson plan.

UbD

Understanding By Design Lesson Template

Title of Lesson	Developing Patterns in Linear Equations		Grade Level	8
Curriculum Area	Algebra and Patterns		Time Frame	Five Days
Developed By	Mary Giacomarro
Identify Desired Results (Stage 1)
Content Standards
4.3.2.A.1 Patterns - Recognize describe and extend patterns 4.3.2 B.1 Functions and Relationships -Use concrete and pictorial models of function machines to explore the basic concept of a function. 4.3.3 B. Functions and Relationships 1. Use concrete and pictorial models to explore the basic concept of a function. Input/output tables, T-charts
Understandings			Essential Question(s)
Overarching Understanding			Overarching		Topical
To recognize linear patterns from using square tiles, tables and graphs. To use data patterns to make predictions. To be able to create linear equations			*What are linear equations? *How do you represent linear equations using concrete models?		*How is slope represented concretely across each stage of various patterns? *How is the y-intercept determined once patterns are developed and represented in tables?
Related Misconceptions
Students may not see the pattern initially. A student may find it difficult to make predictions when the constant is changed from a number to a variable. Students may also have trouble with graphing these patterns.
Knowledge Students will know…			Skills Students will be able to…
*What is slope? *What is the y-intercept? *Where do they appear in patterns? What are different ways to represent patterms?			Take a domain and range chart and develop linear equations Compare graphs and understand how the input/output effect the slope and y-intercept of the graph
Assessment Evidence (Stage 2)
Performance Task Description
Goal	SWBAT use patterns to develop linear equations.
Role
Audience	8th grade students
Situation	Period 4 Algebra Class
Product/Performance
Standards
Other Evidence
Read chapter 4.1 Coordinate systems and plotting points on a coordinate plane. Do 2-20 even. Check answers in the back of book.
Learning Plan (Stage 3)
Where are your students headed? Where have they been? How will you make sure the students know where they are going?		Students will be able to develop the ability to examine graphs and explain the relationship to the data provided.
How will you hook students at the beginning of the unit?		Creating the models using square tiles (concrete manipulatives).
What events will help students experience and explore the big idea and questions in the unit? How will you equip them with needed skills and knowledge?		The students will be able to explore and experience a variety of patterns and determine equations from them. After the students have had a chance to use the manipulatives, they will be able to explain what their findings are.
How will you cause students to reflect and rethink? How will you guide them in rehearsing, revising, and refining their work?		The students will have the opportunity to reflect and rethink using a Kagan cooperative learning strategy called “Sage and Scribe.” The students will be set in pairs. One student explains and shows, while the other listens. Then, they switch.
How will you help students to exhibit and self-evaluate their growing skills, knowledge, and understanding throughout the unit?		The students will be able to use “Two Stars and a Wish.” Students will write down two things they learned from the lesson, and one thing they hope to learn during the next lesson.
How will you tailor and otherwise personalize the learning plan to optimize the engagement and effectiveness of ALL students, without compromising the goals of the unit?		During class, I will use communicators in order to be able to keep the students actively engaged. This will enable me to see that ALL students are on task.
How will you organize and sequence the learning activities to optimize the engagement and achievement of ALL students?		All manipulatives are ready on their tables, in baggies. The baggies are located in a box. Each table has a group box, which includes everything that the students will need in order to move from one activity to the next. The box includes pencils, calculators, manipulatives, and communicators .

From: Wiggins, Grant and J. Mc Tighe. (1998). Understanding by Design, Association for Supervision and Curriculum Development

I believe...through the eyes of an eighth grader

I took "I believe" into my classroom of 8th graders. One of my students wrote this in under 10 minutes. Had I not had that extra few minutes in class...I never would have known what this student was capable of. Let's face it, I teach Mathematics...we rarely get to see this side of the students. So, I decided to put it to music and surprise her with a video of her writing. This video was shown to my entire school (grades 6-8) during a school-wide assembly. It will also be shown at our next faculty meeting. I must say that I am pretty excited for my student.

Do You Know?

Shift Happens

What was your initial reaction to the video?
I must admit that my initial response to the video was fear. Not crazy over the top fear, but a slow churning gut feeling of fear. I am not sure if I felt this way more for myself or more because I have two small children. What will their future be like? My son (who is almost six) has an I-Pod, knows what a podcast is (because we watch space related podcasts), and hears me talking about my blog. He already plays on the computer on occasion and he is very aware of Google. My daughter (who is almost 3) knows that if I press a few keys, we can get “Dora” to help us with our ABC’s. It’s amazing what they know already. On the flip side, both of my children enjoy “reading” and the library. Neither of them have video games or a tv’s in their rooms. A parent is usually split on this decision. One day research says video games are bad, then the next you hear hat it is great for their hand-eye coordination. Which is correct? Let’s face it, technology is not going away. It is everywhere. It is incorporated in classrooms via blogging, podcasts, wikis, calculators, computers, “Elmo’s”, etc. Therefore, my fear is not necessarily of the fact that the world will not be as it is now, but fear of the unknown. What will it be like for our children? Will they be happy? Will their need for immediate gratification alter the way our society reacts to each other? Will our interpersonal skills come to a screeching halt because we are attached to texting and not talking? Is this flat world going to create such a place where children are almost communicating robotically?

What challenges must we overcome as we move forward?
The challenges we must overcome are far too numerous to state them all. However, I believe that the first step towards teaching the 21st century student is to be aware. Be aware of what new technology is out there. Be aware of the latest technologies that interest your students. Be aware when it is all too much. There will be times when a student is tired of looking at a power-point. There will be times when a student wants more interaction with humans. Be aware of when that is. Be aware of that they are not learning the way the way students did when we were younger.


Is it possible for a teacher to be an excellent teacher if he/she doesn’t use technology?
Well, I don’t really know the right or wrong answer to this. I know of an excellent teacher who barely integrates technology at all. She teaches World History. She incorporates a variety of classroom management techniques. She uses differentiated instruction…name the catch phrase of the week, she does it. She brings in artifacts from around the world, because she is a world traveler herself. She is passionate about her content area (and has visited most of the countries herself). However, she barely uses email. She barely goes on the internet. She doesn’t get her facts about the Mayan civilization from “Google”, she got it from visiting Central America. Yes, a teacher can be amazing without using technology.

Symphony

Picture this...I (as many of us did) had the day off of work today. My children did not. So, I had the television on, and I was listening to the news. Yes, listening, because I was multi-tasking, as many of us are doing these days. (This was actually a treat for me as I do not watch much of anything when my children are home.) I was listening to Mr. Obama speak about what he would potentially do for our country. He began to speak about education. Naturally, I began to focus a little more on what he was saying. He spoke about not teaching to the test, getting and keeping the best educators out there...and then he said (along with many other things) that he would keep art in our schools. He made a clear point to say that our future depends on developing the whole child. I then began thinking about what Pink wrote and how he said that symphony is about seeing relationships. At that moment, I connected what I read in Pink's book to Mr. Obama...and decided...

I couldn't agree more.

Unfortunately, as a math person, I am most likely considered a left-brainer. Although, I understand the importance of putting the pieces together, people would probably assume that I am more logical than anything else. However, even as a "left-brainer" I still believe that symphony should play a role in everyones classroom. Yes, it is the ability to see the "big picture." This ability goes way beyond an art classroom. In my classroom, students have the ability to share their thoughts on the content I am teaching. I have students telling me they learned the same material in different ways...others tell me that they have never seen it all. (Mind you, they are coming from the same classes!) However, when I take the math lingo out of the conversation, that is when they understand it most. I had students not understand what variables were...then I changed the variables for objects and magically they understood. Some of the students did not welcome the symbolism, they wanted more. When they have the opportunity to have manipulatives in hand, or figure out for themselves what I am asking from them...all of a sudden, they make a connection. They are able to see the relationships to real life situations, and why the "stuff" I am teaching is actually worth something! SYMPHONY! Math is not just about numbers and signs! If you allow it, math can be like music. There can be many different steps necessary to get to that end result, but we don't have to all dance the same way to get there. My students know that they do not have to do it my way, as long as it's mathematically legitimate. I encourage them to see the big picture. Telling them stories and relating them to math. Allowing them to draw and explain their answers...I do not try to squash that right brain...I encourage it!

I have a student who is a true artist. She is constantly drawing. She takes my notes in artistic form. It is amazing to see her write notes (that only she usually understands)! Most of her notes are sketches, but she understands her relation to what I am teaching. She can write a logical two-column proof with pictures. Many of her teachers complain about her doodling...I tell them that I allow it. They, in turn, think I am completely wrong. This student just took one of the most difficult tests that I will give in this marking period, and she got every question correct! She is artistic, why would I squander that? As long as she is listening and contributing, and understands what I am trying to teach...I have no problem with her "doodling." The mere fact that she has the ability to work with both sides of her brain and excel should be applauded.

E.D. Hirsch

Dear Mr. Hirsch,

I absolutely agree that there is certain content knowledge that all students need to learn. I also agree that it should be uniformly paced within our nation, so that all students across our nation can have the same educational opportunities. I also agree that having this core curriculum will provide students, who frequently move, with many more opportunities to be successful. Imagine how much easier a transition for a student would be to go from one district to the next? These are wonderful thoughts Mr. Hirsch! However, there are some aspects of what you discuss that I do not agree with.

What I think your discussions lack most is the discussion of pedagogy. Pedagogy is most frequently described as the art of teaching. Your descriptions make me think of a classroom as an on-going drill. A classroom should look more like a laboratory, where students are questioning, responding and searching for answers. Inquiry based learning helps students learn the why of what they are learning, rather than simply the what. Students in a math class will understand why the denominator in a fraction is what it is, rather than just repeat 2/4=1/2 because of rote memorization.

While I understand that over the years your views have changed slightly, I continue to believe (as you do) that there should be a core curriculum in place. It doesn't have to be yours, just one that is similar in comparison.

Thank you for being so passionate about your prescription for school reform. I look forward to reading your most recent work

Sincerely,
Mary Giacomarro

This I believe...

I believe in people giving back to people through a variety of means.

My father immigrated to America when he was sixteen. He had nothing but the clothes on his back, and some spare change. He was born in Macedonia. He left there because he wanted "to save his family." After the war, people in his village had to start over. Red Cross had to bring them meals, farms had to be regrown, houses had to be rebuilt...not to mention, spirits had to be lifted. So, my father thought that he had to come to "land of opportunity" in order to make money to send to his family. So, at 16, he and two of his friends left. The night was dark and rainy. He had to cross borders illegally (it was a Communist government then) in the dead of the night, in the pouring rain, with the fear of being shot by guards. Luckily the guards remained in watch towers when it rained, so it was difficult to be seen. He then migrated across some of Europe and made it to Italy, where he began his journey to the "land of the free." My dad immediately began working when he arrived to the USA. He continuously sent money to his father in Macedonia. He played soccer, very well I might add, and was offered a scholarship at Montclair State. What a dream come true?! My father always wanted to be a physical education teacher. However, he knew that as a student, he couldn't continue to work full time and send money to his family. So, he refused the scholarship. He instead went on to Passaic County Vocational School (at night) and became a certified Machinist. He also became a citizen of the United States. He was a proud American...He did it!

During this time, my father was introduced to my mother, via pictures and letters. They wrote letters back and forth. My father went back to Macedonia in order to marry her. He brought her here, along with four of her siblings and brought his brother here. They all have become very successful US citizens.

Here I stand today...deciding that I would be a teacher, just like my dad always wanted to be. How fortunate for me to have these opportunities to give back to my students everyday all that I have learned from my daddy.

I believe that all students need someone to ignite the fire inside them, someone to make them want to be successful...someone who is there to hold your hand through it all...yet know the exact time to let go...I hope to, at the very least, be that someone to at least one of my students every year for the rest of my career.

Standards...We all have them...

Although some view using the New Jersey Mathematics Core Curriculum Content Standards (NJMCCCS) as a daunting task, they really are an invaluable tool. These standards reveal a common goal for all Mathematics teachers in New Jersey. If utilized properly, the NJMCCCS can help guide a teacher (novice or master) in deciding how and what to teach. As part of the Mathematics NJMCCCS, there are numerous ways that teachers can help students cover all of the clusters and strands. I believe that the standards are most helpful to new teachers because they have the least experience on what the students need to accomplish. The NJMCCCS help guide and give examples that can clarify what is expected of the teacher and the students. However, I say this because I know and understand them. If I did not know my content area, I may not understand how to utilize the standards in my classroom. What I like best about the standards is that I know I can always look back and check what my students should have learned from previous years. It guides me. If the NJMCCCS are utilized in daily lesson planning, there is a better chance that your students will do better on standardized tests as well.

My Introduction

My name is Mary Giacomarro. I work in Wayne, NJ as an 8th Grade Mathematics teacher. This is my third year in this district and I love it. My background is pretty diverse. My undergraduate degree is in Mathematics from Seton Hall University. After SHU, I went to New York Law School for one year. I did well there. However, during my summer hiatus, I decided that my calling was in education. After some agonizing discussions with my family, I left NYL and got my first job as a Math and Science teacher in a Catholic Middle School. Soon after, I earned my Teaching Certificate via Alternate Route and began teaching Mathematics at the high school level in my hometown. After about two years, I took a break in teaching in order to have my children. Then, decided to go back to work and have been in Wayne ever since. My career goals involve completing my Masters in 2009, and becoming a Mathematics Supervisor. Eventually, I would like to be a Principal or Vice Principal. I am taking this course not only to fill a requirement, but to also gain knowledge from the various professionals that I am taking this class with.

I am a Blessed single mother of two delightful children, my son who is five, and my daughter who is 2. They are the loves of my life. My son is in Kindergarten and my daughter just began Pre-K 3 (early). On her first day, I (as most parent's are) was feeling so anxious about sending her to school for a full day. My beautiful daughter turned to me and said, "Mommy, I independent, I a good girl." My heart melted and I left knowing that she was more than ready to be there. My son is involved in Sil Jun Do (a mixed Martial Art), hip-hop dancing in an all boys group of dancers, and swimming. He reminds me daily that he wants to be a scientist for NASA, and that we are going to move to Texas when he gets a job. He also reminds me that he does not want to be an astronaut, his interest is in the possibilities of life on Mars. We are contants on the NASA website (I have learned a whole lot too!) All of that from a five year old!