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 * Home * Final Project Proposal **
 * Part One Overview - Page One **

__Topic: __ Middle School Math: Solving word problems with graphing
 * __Title: __ Messy Math: Solving Word Problems with Graphing
 * __Brief Description __ (for example 10-50 words)
 * Students choose are given a packet of 9 word problems and choose one of the problems to work on. The problem they choose must be one that they cannot do.
 * The class is then broken up into subgroups according to which problem they chose. Each student is given a graphing worksheet, a final video presentation sheet, and a grading rubric. Groups work together to figure out how to solve their problem using graphing. During this phase students fill out the various steps in the worksheet.
 * Once they know how to solve the problem, students fill out the final video presentations sheet. Since this sheet will be used in the video, it needs to be done carefully – clear writing and accurate calculating. Next, they create their Messy Math video students using the final video presentation sheet as a prop. One of their group-mates will do the camera work.
 * Once the video is complete, students take it off the camera, compress it, then put it up in a new post on their WordPress blogs. Below the video students write a reflection from the following prompt: “How did your performance in the video compare with what you actually know about solving problems with graphing?”

__Do you want your students to gain **knowledge how**? **about?** or **of?** __ My intent is that students learn __both__ “how” and “of”. That is, __how__ to solve a word problem using graphing, i.e., assign variables, create an x-y table, write equations, build a graph, and interpret the graph to write a solution. And, __knowledge of__ the information embedded in a graph; assimilating the title, axes labels, legend, data points and connecting lines in order to pull the solution from it. __<span style="color: #000000; font-family: 'Arial','sans-serif';">Who is this lesson for: __<span style="color: #000000; font-family: 'Arial','sans-serif';"> This lesson is for all seventh grade students at my middle school. __<span style="color: #000000; font-family: 'Arial','sans-serif';">Where will the learner be? __<span style="color: #000000; font-family: 'Arial','sans-serif';"> The learners will be in their regularly scheduled Computers class at our school. Students will be given the option of completing the video clip outside of class. So, some learners will be at home, or in the town library.

__<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Rationale __<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">: <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Currently the math program at my seventh and eighth grade middle school separates students into ability “tracks” in the 8th grade. This act of separation is inefficient: many students on both sides of the divide either are not sufficiently challenged, or are over challenged and struggle to keep up. In both cases learning takes a hit. <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">This lesson provides an example of how to design math lesson for a heterogeneous classroom so that all learners are sufficiently challenged all the time. If enough of these lessons can be created to cover a two-year curriculum, then my school can keep students in heterogeneous classrooms and improve the amount of learning for every student. <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">The basis of the approach is to design lessons that contain complex (messy) problems. Present these messy situations and provide supports to help students break down those situations. __<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Why is this course necessary or valuable for your learners, __ <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">In solving messy problems in math or science, students seldom choose a graph as a way to get to the solution. But, graphing data generated from a problem can quickly illuminate relationships between variables. This course will provide students the opportunity to solve a problem using a graph and see the value of that approach.

__<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Why do it online, __ <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Students will publish their results online in order to up the stakes for them. Having to present what they know to an audience is very engaging and challenging for middle school age students. <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">The product to be published is a video. First, students will narrate a video in which they explain the solution to the problems by interpreting the graph, then this video will be posted on each student’s WordPress web site. A short reflection will accompany the video on the post.

__<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Why did you choose the format you chose, __ <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Capturing a student’s assessment in video form creates a richer picture of what that student knows and can do. This video not only presents the student at the time of capture, but serves as a benchmark to measure future growth.

__<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">What is the learning theory (ies) you think you will employ: __ <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Constructivism is employed because students are being asked to construct their own solution to the problem. Cognitive Load theory and Knowledge Building are used in that students work in groups to share prior knowledge and discuss strategies, structured worksheets are be provided to lead them through the components of a graphic solution, and an already worked problem can be consulted to help guide them along.

__<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Learning objectives __<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> - <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">After completing this course, the learner will be able to:
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Construct a table, equations, and a graph from the information given in a word problem
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">solve a complex word problem by interpreting a graph

__<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Prerequisites __ <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Students must have access to a WordPress, or similar, web site on which to post their results.