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RAPPSCEC08 - Teaching Ratio and Proportion Problem Solving...

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1 Teaching Ratio and Proportion Problem Solving Using Schema- based Instruction Asha K. Jitendra, 1 Jon Star, 2 Kristin Starosta, 3 Sheetal Sood, 3 Grace Caskie, 3 Jayne Leh, 3 Cheyenne Hughes, 3 Toshi Mack, 3 and Sarah Paskman 3 1 University of Minnesota 2 Harvard University 3 Lehigh University Paper Presented at the 2008 Annual CEC Convention, Boston, MA
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2 Thanks to … Research supported by Institute of Education Sciences (IES) Grant # R305K060075-06) All participating teachers and students (Shawnee Middle School, Easton, PA) April 4, 2008
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3 Mathematical word problems Represent “the most common form of problem solving” (Jonassen, 2003, p. 267) in school mathematics curricula. Present difficulties for special education students and low achieving students Cummins, Kintsch, Reusser, & Weimer, 1988; Mayer, Lewis, & Hegarty, 1992; Nathan, Long, & Alibali, 2002; Rittle-Johnson & McMullen, 2004). April 4, 2008
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4 Math Wars Math Wars April 4, 2008
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5 To solve word problems, Need to be able to recognize the underlying mathematical structure Schemas Domain or context specific knowledge structures that organize knowledge and help the learner categorize various problem types to determine the most appropriate actions needed to solve the problem Chen, 1999; Sweller, Chandler, Tierney, & Cooper, 1990 April 4, 2008
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6 Focus on math structure helps … • Allows for the organization of problems and  identification of strategies based on the  underlying mathematical similarity rather than  superficial features “This is a rate problem” – Rather than “This is a train problem”   April 4, 2008
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7 Prior research on SBI has focused on Schema priming (Chen, 1999; Quilici & Mayer, 1996; Tookey, 1994), Visual representations such as number line diagrams (e.g., Zawaiza & Gerber, 1993) or schematic diagrams (e.g., Fuson and Willis, 1989); Jitendra, Griffin, McGoey, Gardill, Bhat, & Riley, 1998; Xin, Jitendra, & Deatline-Buchman, 2005; Jitendra, Griffin, Haria, Leh, Adams, & Kaduvettoor, 2007; Willis and Fuson, 1988) Schema-broadening by focusing on similar problem types (e.g., Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, Hosp & Jancek, 2003; Fuchs, Seethaler, Powell, Fuchs, Hamlett, & Fletcher, 2008; ) April 4, 2008
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8 Our Approach S chema- B ased I nstruction with S elf- M onitoring Translate problem features into a coherent representation of the problem’s mathematical structure, using schematic diagrams Apply a problem-solving heuristic which guides both translation and solution processes April 4, 2008 Marshall (1990); Mayer (1999); Riley, Greeno, & Heller (1983)
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9 Teaching proportionality is critical … Challenging topic for many students (National Research Council, 2001) Current curricula typically do not focus on developing deep understanding of the mathematical problem structure and flexible solution strategies (NCES, 2003; NRC, 2001).
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