Estimation

Rationale

The responsibility of each elementary school mathematics teacher is to use effectively the required math curricula, ultimately guiding their students through a sequential path of concepts and practice. The choice of "concept paths" is decided and formatted by the authors and publishers of each curriculum. We, as professionals, are given some resources to guide us. These take the form of teacher manuals, professional development, team meetings and planning sessions. These resources are essential to the success of the teaching year for each of us and the learning year for the students. The particular teaching strategies and mathematics concepts within the scope and sequence of a curriculum need to be digested and fully understood by the teachers using it.

As a result of the No Child Left Behind law, states are looking to increase performance in mathematics to then improve scores on the state testing that must occur each year from third to eighth grade. Because of the pressure to be successful in this goal, school districts are turning to new texts, increasing technology and finding ways to prepare the students to achieve higher scores. Currently, many schools and teachers are experiencing what our district is - trying out several options. The variable that is being overlooked is the teachers themselves. Good teachers must be at the core of a solid mathematics education.

Teaching mathematics effectively depends on a solid understanding of the material. Teachers must be able to do the mathematics they are teaching, but that is not sufficient knowledge for teaching. Effective teaching requires an understanding of the underlying meaning and justifications for the ideas and procedures to be taught, and the ability to make connections among topics. Pedagogical content knowledge, the knowledge of how to teach a concept or subject, must be aligned with subject matter knowledge to create a productive learning experience for the student. Together these allow for understanding student's responses and determining the goal of the lesson.

An article by Hill, Ball and Schilling on pedagogical content knowledge suggests that although teachers' knowledge of content and students is not necessarily easy to measure, it appears from initial study that the news is good. Teachers in this study demonstrated a familiarity of students' mathematical thinking, for example, predicting common student errors. Understanding how students think is distinct from pure content or pedagogical knowledge and shows teacher skills and insight needed for successful student learning and growth. Because teachers see student work, hear student statements and see students solving problems, they are constantly considering what students are doing and how they are thinking. Designing instruction and motivating students to learn are the potential positive results of this unique knowledge. ¹

My intent and goal for writing this curriculum unit is twofold. Initially the unit will focus on increasing conceptual knowledge of place value and order of magnitude. This first objective will allow a more successful outcome for the second objective, which is to then have the first graders develop through mathematics activities the concept of place value. This unit covers 2 digit numbers and ends with the first 3 digit number in our number system, 100. The key goal for these students is to learn that a two-digit number is made of a certain number of tens and a certain number of ones. The key estimation principle to learn is that the tens are bigger than the ones, and most specifically, given two numbers, the one with the larger tens digit is larger. The core idea of this concept is what a digit at a certain place stands for. This will lead to the next level of instruction which is adding and subtracting of two digit numbers.

This unit will use the months before the 100 ^th day of the school year to prepare for the celebration of that day. It has become a standard practice in primary classrooms across the country to celebrate the 100 ^th day of school. Certainly this is monumental not only as a number but as a benchmark for teachers and students as the general school spans 180 days. This of course this can become a fun, exciting, anticipated day of activity, practice, and reinforcement.

To be successful with this, subject knowledge of place value for the teacher will help to ensure a deeper understanding for the students. Place value appears to be a simple enough concept and is certainly found in our first grade textbooks or workbooks with guides for teacher language. So it must be that we are prepared and ready to teach. However, it is not enough to know how, one must know why. As a teacher of very young children, my task is to give them a strong and complete foundation to use in their mathematics classes and throughout their learning. It is in fact too important to overlook and breeze through quickly and unprepared.