Algebra has long been taught in the same way. This usually means teachers rely heavily on the textbook. Though some textbooks have changed in recent years, the central focus is till on paper and pencil, memorization of rules, and use of algorithms. The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) asks mathematics teachers to seek activities that “model real-world phenomena with a variety of function” and “represent and analyze relationships using tables, verbal rules, equations, and graphs”. The standards also urge teachers to give students the opportunity to be actively involved in math through data analysis and statistics that are integrated into the curriculum. My hope is to show that these types of activities can be incorporated into an algebra I course as a way of teaching slope, y-intercept, and linear equations. I plan to teach a unit on linear equations during the third nine weeks of an eighth grade algebra I course next semester. The project will begin with one class learning the material typically covered in most algebra textbooks. I do not plan to pretest the students because this is new material for them. This class will also go to the computer lab and complete a lesson on the computer covering linear equations. In addition, they will work in pairs using T1-82 graphing calculator to explore slope and y-intercept. All of these methods are what I have typically taught over the past 5 years. Another eighth grade class will be given several data collection activities as a unit of study for linear equations. The primary resource for this class will be Algebra Experiments I by Mary Jean Winter and Ronald J. Carlson. My focus will begin with a whole class participation data collection activity. The class will perform “the wave” in small sections at a time until the entire class has completed it. As a group will record the number of seconds it takes (for example) 3, 5, 8, 13, 15, 20, etc. to complete the wave. Students will then use a prepared activity sheet that requires them to draw a diagram of the experiment, describe the procedure, identify the independent and dependent variables, create a table of data, graph data, choose two representative points to connect and create a “line of best fit”, find the slope and y-intercept of this line and describe it algebraically and verbally, then interpret the data through certain questions designed to create understanding of the purpose of the data and using the data to make predictions. This same format will be used for all subsequent activities during the unit of study. The authors of the book say “Algebra Experiments I reflects the basic philosophy of the NCTM standards for learning, teaching, and assessment. Students have an opportunity to work collaboratively, to interact, and to develop communication skill.” The whole idea is to “bring the real world into your algebra classroom.” I plan to require the class that does the experiments to keep a daily journal. It will include hot they felt about the daily activities, a description of any specific new topic or topics they learned and a list of questions they still have. Each day the class will address any concerns from the previous day's activity. After several activities have been done by hand, I will instruct the class on how to analyze the data on the T1-82 graphing calculator. They will then be given the opportunity to use the calculator on another experiment. This class will also do the same graphing calculator activity on slope and y-intercept that the other class will do. I will give each class the same test and compare scores. I will also give each class a survey to compare attitudes, interest and understanding of the use of the material in a real-world application. My hope is that the students in the experiment class will have grasped the basic concepts of linear equations as well if not better than the other class and be able to relate this...
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