Place Value, Fractions, and Algebra: Improving Content Learning through the Practice Standards

CONTENTS OF CURRICULUM UNIT 14.05.03

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Content
  4. Sample Lessons
  5. Standards
  6. Appendices:
  7. Bibliography
  8. Notes

Defending a Fractions Position

Patricia Lee

Published September 2014

Tools for this Unit:

Introduction

"Hey! Mrs. Lee, why did you want to be a teacher?" According to Dictionary.com, a teacher is: "a person who provides education for students, one who imparts the knowledge, and/or to instruct by precept or example." 1 None of these words came to mind, as I mustered to find the true reason why I keep coming back year after year. As a fifth grade math teacher, for the Pittsburgh Public Schools, more specifically, Miller African Centered Academy (A.C.A.), located in what is referred to as the Hill District of Pittsburgh; I take my job seriously, and more often than not, I enjoy it. The school is a Title I school, where 96% of its students receive free or reduced lunch. 99 % of its students are African American and 1% Caucasian. All students are American citizens and their primary language is English.

Over the past century, the Hill District has gone through several metamorphoses. From the 1920's to the 1950's it was a booming cultural center for African American Music. Famous jazz players such as: Billy Eckstine, Stanley Turrentine, and George Benson, to name a few, were born, raised and had their careers take off in "the Hill." "During the 1940's the Hill District was considered an ethnic melting pot with 25 various nationalities." 2 In the 1980's and 1990's it turned to a neighborhood that struggled with gun violence, drugs and poor housing conditions. For the past 20 years, the Hill District has undergone several stages of revitalizations, renovations and gentrification. Crowded and dilapidated buildings of the past, are now new individual homes, some non- and government subsidized housing and apartments. The students who attend Miller A.C.A. more often than not live in subsidized housing. The majority of the students come from single parent households, headed primarily by mothers, but occasionally a father, a grandmother or foster care family. Many of our students have experienced homelessness at one point or another. Each one comes to us with his or her own story; some hardship is the loss of a parent due to health reasons, violence, imprisonment or abandonment. Others may be residing with an adult who suffers from a mental health disorder, alcoholism or a drug addiction. It is important to note that Miller A.C.A. also has hard working parents who struggle to make ends meet; single moms who have returned to school to further their own education and some two parent households.

For students living in less fortunate situations and/or who are experiencing a family crisis, the school offers therapy. Grief and anger management therapy are two of the more predominantly prescribed. Four of my students receive these services once a week. Within my class of twenty-four, five students are receiving daily medication therapy for either bi-polar or attention deficit disorder. It is necessary to begin each morning by taking the pulse of the classroom to determine if we move forward first with academics or open a group forum to express concerns. The pulse check increases the chances of reaching our intended learning goals.

The school has morphed right along with the neighborhood. It has been relocated, a popular occurrence here in Pittsburgh. The changes are often hard to keep up with. For clarity, during conversation, one might state the name of the school then state its previous name. For example, I work at Miller A.C.A., the old McKelvy building. Initially Miller A.C.A served students in pre- kindergarten through fifth grade. It was converted to a pre-kindergarten through eighth grade school and several years later, back to a pre-kindergarten to fifth grade. The consistency within the school has been its leadership; having only three principals over the past 20 years. Over the past three years, recent changes within the district created a 60% teacher turnover within the building. As in any district, openings are not always filled as expeditiously as one would like, leaving classrooms of students to be maintained by day to day or permanent substitutes. The students I will be teaching, for the 2014-2015 school year, have received instruction from a certified, permanent, teacher for two out of their last five years of schooling. This occurred during their second and fourth grade. I, being their fourth grade teacher, will continue next year as their fifth grade teacher.

Needless to say, due to circumstances beyond their control, my students came to me below the expected level of proficiency. Their math concepts were frail; they solved problems only through procedural methods. The goal was to get it done, not to know if they had done it well or with precision. They had accrued many misconceptions. These were exposed during lessons when students attempted to add, subtract, tell time, answer questions concerning place value, make change and round. The class as a whole possessed little fact fluency. Initially, 16 percent of the students knew their multiplication facts. With hard work, we now boast a 78 percent fact knowledge base. The first month and a half of school was spent strengthening number sense through various place value activities and exercises. Merely reading numbers into the thousands was a struggle. Less than half of the students could correctly read an analog clock and only two could consistently solve elapsed time problems. One third of the class pronounced four o`clock, as four twelve.

Not only were there substantial academic concerns, but compounding the situation, the class had a strong mistrust of adult educators. The students had established a hierarchy among themselves and had unwritten class rules. The many years of teacher turnover and multiple substitutes left them with what resembled abandonment issues. At the start of the year, I sensed a feeling of, them against me. A look in their eyes said, "Lady, you won't be around long either, so don't expect us to listen to you." This was understandable, since during their third grade school year, they were under the care of three different substitute teachers. They learned not to get too close or comfortable with any one of them in particular. They also became disheartened by the idea of learning yet another set of systems for procedures and classroom rules, as another new teacher took them on. Our fourth grade year was spent building strong relationships and discovering the fundamentals of math.

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