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E NHANCED D ISCOVERY L EARNING H OLTVILLE H IGH S CHOOL WALTER L EWIS www.lewisinmath.wikispaces.com

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A comparison of 360 comparisons of “enhanced” discovery learning with other forms of instruction showed that enhanced discovery learning was superior to other approaches. (Robert J. Marzano) Projects engage students in applications of mathematics, which may help them to transfer their mathematical skills to other disciplines and to real-world problems. Using significant problems often increases student motivation, in turn promoting learning. Research has shown that a well organized project coupled with direct instruction is more effective than either pedagogy by itself. R EASONS TO U SE P ROJECT B ASED L EARNING

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T HE NCTM P RINCIPLES AND S TANDARDS … support inquiry, or discovery based learning, which is an important component of project-based learning. In addition, projects address the NCTM Principles and Standards process standards better than many other teaching strategies. Students gain valuable skills in problem solving, reasoning, and communicating mathematics, while learning how to conduct research, manage resources, and collaborate with others, important skills for the workplace of today.

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D AN M EYER : M ATH C LASS N EEDS A M AKEOVER Use project based learning to replace textbook content not in addition to textbook content.

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D AN M EYER : M ATH C LASS N EEDS A M AKEOVER

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E XAMPLES OF P ROJECT -B ASED L EARNING IN M ATHEMATICS In a high school geometry class, students take the role of an architect and design a state of the art high school. Students research the design of high schools and the feasible plans for various types of stores.

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E XAMPLES OF P ROJECT -B ASED L EARNING IN M ATHEMATICS Engage and interact!

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I N A HIGH SCHOOL ALGEBRA OR TRIGONOMETRY CLASS, students take the role of historian by researching the life of a mathematician of the past. Students present an important contribution of the person, in addition to his or her life story. The end product can be a PowerPoint® presentation about the mathematician presented to interested students or adults.

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I N A HIGH SCHOOL ALGEBRA CLASS, students take the role of an investment planner. They research various forms of investments and formulas for calculating interest on savings. The end product can be a written report or investment plan with relevant formulas defined, and graphs as appropriate.

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I N A HIGH SCHOOL ALGEBRA CLASS, Make Math Class Real

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I N AN ADVANCED HIGH SCHOOL MATHEMATICS CLASS, students explore the literature of Edgar Allen Poe’s Pit and the Pendulum.

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I N AN ADVANCED HIGH SCHOOL MATHEMATICS CLASS, G ET R EAL ! C ONNECT A CROSS D ISCIPLINES.

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I N ANY MATHEMATICS CLASSROOM, students take the role of a statistician researching population trends for a state, country, or the world. The level of sophistication of the project will depend upon the mathematical level of the students. The end product can be a presentation, written report with appropriate graphs, or webpage of the findings. You may want to team with a social studies teacher for this project.

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G ETTING S TARTED Start small. Begin with a project lasting only one period or a few class periods. Plan for part of the project during class time and part outside of class. Do the project over a longer period of time using part of the period each day.

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D EFINE THE PROJECT … and the objectives carefully and clearly. Have the objectives align with both process and content standards for your school or state.

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G IVE STUDENTS A TIMELINE so that they know exactly what is expected and when the project is due. Insist on progress reports, assigning points for the reports.

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L OOK FOR PROJECTS … that are already written. Check newer textbooks, ancillary materials, or the Internet.

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D ESIGN YOUR ASSESSMENT PLAN … in advance. Share the rubric you will use with the students before they begin the project. If possible, show students samples of what you expect, including project documentation and the end product itself. Or, you may simply grade the project for completion. Or, you may grade it as a presentation.

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I NTERVENTION AND F ACILITATION If students need a particular skill for the project, such as graphing data, front load mini-lessons along the way. Have appropriate resources for the students: Web sites, books, people (parents are great for this) available to answer questions, computer software, including various programs for helping students present their project. Give students class time to complete some of the steps necessary, such as brainstorming, writing an outline, and drafting a report while some work can be done outside of class. Consider using Google Docs so that students may all access their work from their homes or any computer lab.

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C ONSIDER THE POWER OF … teaming-up with teachers in other subject areas.

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1 M AKE A M ODELING A CTIVITY FOR A S ECONDARY C LASSROOM M ODELING P ROJECT G UIDELINES M ATH 5329, F ALL 2011, WITH J OE C HAMPION OVERVIEW Y OUR M ODELING COURSE includes many activities that are designed for teachers to develop applied modeling skills. This project asks you to explore a modeling problem and develop an activity to use in a secondary classroom. The assignment counts for 30% of the overall course grade. 10 STEPS TO A SUCCESSFUL PROJECT Soft Deadline 1. Decide whether you want to work by yourself or with a classmate. 9/26 2. Choose a modeling problem with applications to secondary math content. 9/26 3. Solve the modeling problem, type-up the problem and solution. 10/10 4. Explore extensions and generalizations of your modeling problem. 10/31 5. Create a stand-alone activity (or lesson plan) to introduce your problem in a secondary math class. 1/7 6. Create a 1-page Guide for Teachers to accompany your activity. 11/7 7. Share your project with a peer, trade constructive feedback. 11/14 8. Review the grading criteria, adjust and clean-up your project. 11/21 9. Publish your activity and 1-page guide to the web in a modifiable format. 11/21 10. Give a brief informal presentation on your project to the class. 11/21 or 11/28

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K ATHY S CHROCK ’ S G UIDE FOR E DUCATORS A link to rubrics and rubric links Student Web Page Rubrics Group Project Web Page Rubric Rubric for Evaluating WebQuests Rubric for Classroom Web Pages Rubric for Student Web Pages Student Web Page Rubric Subject-Specific and General Rubrics Large Rubric Collections and Information Chicago Public Schools: Rubric Bank Ideas and Rubrics Make Room for Rubrics Required Benchmark Assessment Rubrics (K-12) Rubric to Assess a Rubric Rubric Gallery Rubric Tutorial Rubrics from Read, Write, and Think Teacher Created Rubrics for Assessment Understanding Rubrics

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S OME P ROJECT B ASED L INKS National Library of Virtual Manipulatives Illuminations: Welcome to Illuminations

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A P ROJECT E XPLORING S LOPE U SING G EOGEBRA

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K EY C URRICULUM P RESS GSP B OOKS Sketchpad® 5 Curriculum

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