1. Lesson Study: Word Problems with Systems of Linear Equations Michael Hinder and Kathryn Spoke Mentors: Ruth Whitmore and Joan Stamm University of Wisconsin – Whitewater, Department of Mathematics Introduction This lesson study is designed to teach an Intermediate Algebra course with realistic applications. These applications will be based on the typical college and local lifestyle. The study is designed to teach students how to translate a real world setting into algebraic language and solve it as a system of two equations. We will focus on immediate and long term retention along with student engagement. Primary data collection will be done by giving students questions to establish a baseline for content knowledge before the lesson is taught. Immediate retention will be shown by their answers given on a worksheet following the lesson. A few weeks later, students will be given more questions to test for long term retention. The expected results is that students will understand and retain the methods when given in a realistic way. Conclusion The students we worked with in the Algebra 141 class did not know much about how to solve a word problem involving systems of linear equations. After we taught the lesson, the data showed that the students retained the information better as time progressed. Results Methods To create our Lesson, we…  Identified a weakness in the Algebra 141 curriculum. We chose to work with solving a system of linear equations in word problems.  Researched common word problems associated with textbooks and decided that we needed relevant word problems that would intrigue the students.  Created unique word problems to solve by a system of two linear equations. We each created a problem that met this criteria.  Wrote a lesson script to plan each part of lecture. This script detailed each problem and accounted for each minute of the fifty minute period.  Made three worksheets to collect data from the lesson. There was a pre-lecture homework sheet, an in class handout, and a post lecture homework sheet. The second round of long term retention data was provided by an actual class quiz given by Professor Stamm.  Taught the lesson.  Collected and analyzed the data. Student Improvement Average Pre-Lesson Knowledge 45.5% Average Retention 1 Day Later 70.8% Average Retention 21 Days Later 88.7% The pre-lesson handout included a minimal amount of real world application. The post lesson homework included all real world application. The retention test showed that many students were able to retain almost all of the information needed to solve these problems. Therefore the conclusion can be drawn that algebra lessons taught with real world applications is very helpful for student understanding. Acknowledgements Thanks to the University of Wisconsin-Whitewater Undergraduate Research Program. We would also like to thank the Algebra 141 class we used in our research. A big thanks to Professor Stamm and Professor Whitmore for their guidance. Process of a Lesson Study We gave the Algebra 141 students this before we taught the lesson. We used these questions to test for immediate retention of the material. We used these question to test for long term retention. Form a Team Develop Goals Plan Lesson Gather Data Analyze Data Revise and Repeat Lesson Future Lessons For future lessons we would include more real world problems based on the high percentage of knowledge retention shown by the students. However based on questions from the retention quiz, more time would be spent on translating problems to equations.