CREATING OPEN-ENDED Think of an essential topic you will PROJECTS - PowerPoint PPT Presentation

Creating Open-Ended Projects in Middle School Mathematics 4/27/2012 Prelude CREATING OPEN-ENDED  Think of an essential topic you will PROJECTS IN MIDDLE SCHOOL cover in your classroom next year MATHEMATICS  Keep that topic in mind as we talk about ways to develop engaging projects Heather Gramberg Carmody hcarmody@parktudor.org hgramber@purdue.edu Beginning Presentation  Projects began as an assignment with Thanks Structure Dr. Nancy Hertzog, University of Illinois  Description of Open-ended Projects  Structure for Creating Open-ended  Several teachers have collaborated on Projects these projects. They include:  Theoretical Backgrounds  Doug Stotts  Examples of Open-ended Projects in  Serra Nicollette Mathematics  Liz McHenry  Practical Considerations  Jennifer Kuntz  Trenna Thomas hcarmody@parktudor.org 1

Creating Open-Ended Projects in Middle School Mathematics 4/27/2012 Reference for Related Article What are Open-ended Projects? Carmody, H. G. (2010). Water bottle designs and measures.  Ill-structured assignments that require creativity Mathematics Teaching in the Middle School, 16 (5), 272-277. to finish  A form of learning activities and authentic assessment  A way to build differentiation into a general assignment What is the purpose of an Open-ended Where have they been used? Project? Application of academic concepts to real life   Seventh grade classrooms situations  Large public schools with ≈30 students per class  Small private school with ≈15 students per class Movement beyond basic skills and to explore   Wide range of abilities meaningful applications  Culturally and linguistically diverse settings  Other settings (rural, urban and suburban) by  Encourage independence and autonomy other teachers  Require students to reflect upon and refine their work hcarmody@parktudor.org 2

Creating Open-Ended Projects in Middle School Mathematics 4/27/2012 How do they fit with school curriculum? Structure for Creating  Designed to complement daily lessons OMPs  Seven Design Components  Content Components  Students work in class and at home  Supportive Instructional Components  Questions to Develop New OMPs  Projects typically take 2 to 3 weeks to complete Content Components Supportive Instructional Components Extensive mathematical computation 1. 5. Project proposal 2. Algebraic notation 6. Peer collaboration 3. Written expression 7. Reflection and self-evaluation 4. Visual or graphic representation (Carmody, 2010) (Carmody, 2010) hcarmody@parktudor.org 3

Creating Open-Ended Projects in Middle School Mathematics 4/27/2012 Questions to Create an OMP Questions to Create an OMP  What choices can I offer in terms of content or  What topic is essential to the curriculum? product?  What resources will students need for the project?  What are some meaningful and real world applications of this topic?  What amount of time will students need to produce quality work? How can I structure a timeline that allows for creativity and rigor?  What applications are appropriate for students of this age and level of mastery?  Are there adequate opportunities for differentiation to accommodate various student needs?  How can I include the different components?  Does this project encourage a deeper understanding of mathematics than students would otherwise have? Recommendations for Students (gifted and beyond) Justification from  Depth of application (Hirsch and Weinhold, 1999) Educational  Recommendations for Students Research  Recommendations for Classrooms  Opportunities to reflect upon and refine their  Recommendations for Teachers work (Koshy, 2001)  Recommendations for Assessment  Opportunity to discuss their thinking with peers and adults (Hirsch and Weinhold, 1999)  Differentiation in terms of content, process and product (VanTassel-Baska, & Stambaugh, 2006) hcarmody@parktudor.org 4

Creating Open-Ended Projects in Middle School Mathematics 4/27/2012 Recommendations for the Classroom Recommendations for Teachers  Provide time to let ideas develop and form  “Challenge students with rich problems that (Hadamard, 1945) encourage deep exploration” ( Warshauer et al., 2010)  Provide the chance for “responsible risk taking” (Costa, 2001)  Provide opportunities to demonstrate giftedness (Koshy, 2001)  Emphasize independence, and favor flexibility over structure or chaos (Wheatley, 1999)  Move past “unimportant knowledge” ( Renzulli,  Provide students support to move beyond the familiar 1982) into areas of challenge and creativity (Mann, 2006) Recommendations for Assessment  “assessment [should] be an integral part of  Rate and Ratio Project teaching” ( Zemelman, Daniels and Hyde, 1998, pg. Examples  Water Bottle Project 105)  Project “flops”  A few warnings  Assessment can have “a significant role in the learning process” (Taylor, 2009) hcarmody@parktudor.org 5

Creating Open-Ended Projects in Middle School Mathematics 4/27/2012 Rate and Ratio OMP Rate and Ratio OMP Student Materials Targeted Concepts Required Components  Project Assignment  Rates  Researched starting  Grading Rubric fact  Unit Rates  Seven equivalencies  Ratios with at least two  Proportions visualizations  Dimensional Analysis  Poster or PowerPoint Rate and Ratio OMP Examples Water Bottle OMP  Amanda – Gasoline Consumption Targeted Concepts Required Components  Volume  Table with three  Sean – Professional Athlete’s Salary proposals  Surface Area  Flat pattern or  Solving for Unknown  Caven – Chewing Gum prototype of favorite Quantities design  Relationship between  Writing to persuade 2-D patterns and 3-D others that their design objects is best hcarmody@parktudor.org 6

Creating Open-Ended Projects in Middle School Mathematics 4/27/2012 Water Bottle OMP Student Material Water Bottle OMP Examples  Assignment Sheet  Grid for 3 proposals  Grading Rubric OMPs that Did Not Work Small Warnings  Start small – a goal of 4 Open-ended Projects per year is very reasonable  Story Project  Construct your grading rubric ahead of time  Menu Project took a few years to refine  After completing the project, ask for student opinions. My projects are always evolving. hcarmody@parktudor.org 7

Creating Open-Ended Projects in Middle School Mathematics 4/27/2012 Resources Contact Information Through NCTM resources By email request Heather Gramberg Carmody  OMPs  Bibliography hcarmody@parktudor.org  Water Bottle  OMP Components  Rate and Ratio  Questions to Develop  Spreadsheet Or OMP  Integer Game  Presentation Slides  Menu  Transformations hgramber@purdue.edu  Surveys  Examples of student work hcarmody@parktudor.org 8