Estimation

Overview

Ask a child what 'zero' is and they will either say "a number" or "nothing". But there is a lot more to zero than being "a number" and "nothing." This unit, " The Amazing Zero Starring in Place Value, Estimation and Order of Magnitude " will show the children how important the number zero is in mathematics. It will especially focus on the use of zero in our base ten place value system for writing numbers. It will also delve into how numbers with lots of zeros, round numbers, help us with estimation by concentrating our attention on the relative sizes of numbers, rather than being mesmerized by their digits. The unit will begin with the importance of zero in place value and then finish with the importance of zero in order of magnitude in real life situations such as adding and subtracting. The main objective for this unit is to build a strong foundation of the concept of Order of Magnitude. Within order of magnitude falls the concepts of place value, place holder, with zero being the main character in the scenario.

In the Pittsburgh Public Schools, we believe that all students are capable of making sense of mathematics. Classroom environments are respectful of all ideas; students are invited to take risks as problems are posed and students wrestle with solutions. The focus is on students figuring things out, testing ideas and making conjectures, developing reasons and offering solutions. Students share and discuss in groups, in pairs and individually. Reasoning and hard work is celebrated, as students defend their methods and justify solutions. In Pittsburgh Public schools students build understanding and develop skills from their own experience. Mathematics is more meaningful when it is rooted in real life contexts and situations. Children begin school with more mathematical knowledge and intuition than previously believed. Our program builds on this, and gradually moves children from a concrete to an abstract and symbolic understanding. Mastery of mathematics concepts and skills comes with repeated exposure and practice, not after one lesson. This enables students to make new connections and build on the mathematical content they already know while gradually learning more difficult and challenging content. All students in the Pittsburgh Public Schools have the capability to be empowered mathematically, or become mathematically literate. In providing opportunities for improvement of quality of life, it widens choices for personal and professional life pathways. Our goal is to provide a high quality curriculum that empowers students to cope with the mathematical demands they will face in the future. ¹

My school is located in one of the highest crime and poverty areas in Pittsburgh. There is a lot of instability in the neighborhood and most of the families are non-traditional families. Many of the children come to school for stability, hot meals, and social interactions. My school is a kindergarten through eighth grade center where the average student body is 250 students with 99.2% African American. Discipline within the building is very strict and requires that each child wears a uniform. Class size ranges from fifteen to twenty-five children. The current elementary math curriculum is the Everyday Math Series. The Everyday Math curriculum is based on hands-on-activities. The lessons are taught through the spiral method in which the children learn a little bit about a topic each year. The children are learning a lot of important ideas but I have found as a middle school math teacher the children come to sixth grade with big holes in their prior knowledge of basic math skills. Their concepts get mixed up and they do not have a solid foundation in math facts. It is my job as a third grade teacher to give the children the solid foundation needed for a successful education. The children need to be given a safe and nurturing environment in which they are able to focus on their education. I need to give them the foundation that will be ever-lasting.

My third grade classroom is based on positive self-image and mutual respect for anyone that steps through the door. Rules, procedures, consequences and rewards are all part of my classroom management. Many of the children come into school with negativisms and issues that effect not only their education but all of their peers' education as well. This unit needs to be started the very first day of school so as to begin the classroom atmosphere immediately. Built into the unit is a positive self-image and support of classmates. To get the children coming to school and learning they have to be happy and feel protected from outside influences. I need to have the dual responsibility of planning situations and activities to facilitate their math development while being flexible enough to capitalize on opportunities as they arise incidentally during the day to capture the 'teachable moments'. One of my aims is to help my children become independent learners. This can only happen if I allow the children to make decisions and take responsibility for their learning. By involving my children in daily decisions about evaluating their work and encouraging them to set and review personal goals, I can help my class to become avid learners. Self-evaluation encourages them to think about what they are doing and what they need to do.

Students in the primary grades are capable of learning the skills of estimation, and they need instruction to do so. We will all agree that there is a great need for activities that will lead students into an awareness and understanding of estimation. It seems very apparent that children can only be successful estimators of computational solutions if they first have a sense of number to form the basis for problem solving and logical reasoning skills. Estimation plays such a pervasive role in out-of-school settings that children must have a wide variety of experiences with the skill. Over 80% of out-of-school problem solving situations involves estimation. I believe that a topic with such wide uses in later life should not be studied as spiral activities. If a child does not have a firm foundation with estimation at a very young age I feel that they will be playing catch up throughout their education. Spiraling will not have the immediate effect that is needed to build the desired foundation.

The Final Report of the National Mathematics Advisory Panel 2008 also state: "A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided. By the end of Grade 6, children should have a robust sense of number. This sense of number must include an understanding of place value and the ability to compose and decompose whole numbers. A strong sense of number also includes the ability to estimate the results of computations and thereby to estimate order of magnitude, for example: How many people fit into a stadium or how many gallons of water are needed to fill a pool?"

It is my opinion that a complete understanding of estimation needs to be given full attention not just an "oh by the way" kind of lesson. Many of the curriculums I have seen uses estimation as a secondary way to solve the problem. For example: an open-ended problem is taught by having the children show their work, explain their work, and check their work using estimation. With estimation being so important in everyday life it should be taught to estimate the answer first then solve the problem using the usual steps. If the answer is similar to the estimation then the problem should be right. Finding the ball park figure first helps the child understand reasonableness of their answer. This strong conviction brings me to the conclusion that every lesson given here needs to be continued until it is mastered.