History: In March of 2005, the New York State Regents issued a new set of performance indicators that revised the sequencing of courses at the high school level. The first high school math class would now revert to the more traditional Algebra that most students take around the country. A group of teachers in the Arlington Central School District took this as an opportunity to design a robust Algebra course that utilized graphing calculator technology without sacrificing essential skills. Arlington is a large school district located just outside of Poughkeepsie, New York. Using careful curriculum design methods, twenty-five high school and middle school teachers designed twelve units of study. For each unit, the essential knowledge that we wanted our students to acquire was debated and designed. The result was an e-text comprised of note-template lessons that could be distributed to students each day along with an associated homework. These lessons are designed to allow the teacher to direct a mathematically enriching conversation with students while at the same time delivering essential algebraic skills. There are approximately 120 lessons and associated homework assignments on this e-text. We hope that they allow teachers the time to create enrichment activities and high quality assessments while being assured that working through the curriculum exceeds all state performance indicators.
Lesson and Homework Format: Most lessons are driven by the Socratic method of teacher directed discussion. These discussions lead students to fundamental understanding of core algebraic principles while having them explore relationships graphically and numerically as well. Each introductory exercise helps the students understand the core concepts within each lesson, while additional problems at the end give teachers the flexibility to assign more practice. Most lessons are designed for a single 45 minute period. Some of them extend to multiple days. We have found that some lessons include more exercises than can be covered in a single 45 minute span. We feel this allows teachers to pick and choose the exercises they would like to emphasize. Homework assignments are broken into three categories: Skills, Application and Reasoning. Not all assignments have all three sections, but most do. The homework assignments are intended to be completely done by all students in one night, although some are long enough to be broken up into two assignments. Many times the Reasoning section includes exercises that self-teach a student an important concept that is within the performance indicators.
Calculator Usage: The authors of the Algebra e-text debated how to effectively use the graphing calculator to reinforce fundamental algebraic concepts without sacrificing necessary skills for future courses. We decided to use only a few primary features on the calculator:
(1) Tables of Values - We used the graphing calculator to generate traditional xy-tables for a variety of purposes: graphing curves (primarily quadratics), for solving equations numerically, for solving systems numerically, and for checking solutions to equations. For the most part, we did not use the calculator to generate graphs all that much because we felt that it continues to be important for students to plot points by hand.
(2) The STORE Feature - We used the STORE feature on the graphing calculator quite often in order to check equations and evaluate functions. This feature allows a user to store a value in a particular variable and then type an expression containing this variable in order to determine the value of the expression. This was particularly useful, as noted, in checking solutions to equations.
(3) Data Manipulation - The graphing calculator was also used for some basic data manipulation including finding equations of best fit lines, finding the five number summary for a data set, and finding measures of central tendency for a data set.
Please contact the Arlington High School Math Coordinator, Jean Fox, if you have any comments, questions or suggestions regarding the Algebra Project via email at jfox@acsdny.org .