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# CERA saad chahine 2013 fuzzy clusters

## on Jun 02, 2013

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Research paper on Fuzzy Cluster Analysis presented at the Canadian Education Research Association

Research paper on Fuzzy Cluster Analysis presented at the Canadian Education Research Association

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• Before we can begin to answer that question – we actually need to understand the thought processes of educators in two main areas 1. Statistical Literacy & 2. Score Report Interpretation. Together I describe these as data habit of mind
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## CERA saad chahine 2013 fuzzy clustersPresentation Transcript

• Embrace the Fuzz ofDifferentiated InstructionSaad Chahine, PhDJune 2, 2013CERA | Victoria, BC13-04-30
• Differentiated Instruction• Huge push for teachers to provide DifferentiatedInstruction (DI)• Many publications are oriented to different ways ofattempting to “do” DI in the classroom• There is a great deal of speculation on the ways inwhich you do “DI” in the classroom• In practice, the attempt to be more differentiated isoften intuitive rather than evidence-based
• Purpose- It is almost impossible for teachers to provide studentswith individualized attention for prolonged periodsduring the day- It is possible to create smaller groups of student froma pedagogical perspectiveBig Questions:Can we use mathematical algorithms to identify groupsfrom students response patterns?ππ33
• Fuzzy Logic• Introduced in 1965 by Lotfi A. Zadeh• Questions the crisp boundaries thatwe form that may be artificial• Is becoming more widely used inengineering, computer science andmachine learning etc…ππ44
• Some Interesting Applicationsππ55
• Algorithm1. K “means” are randomly generatedbased on the data2. Clusters are created with data pointsclosest to these means3. The centroid of each clusterbecomes the new mean4. Repeat steps 2 & 3 until convergenceFUZZY C-Means:For each point, calculate theCoefficient of being in the clusterhttp://home.deib.polimi.it/matteucc/Clustering/tutorial_html/cmeans.htmlππ66MountSaintVincentUniversityMountSaintVincentUniversity
• Fuzzy GroupingGroup 1BobSallyJimRobinStudentsBobSallyJimRobinGroup 2BobSallyJimRobin40% 60%20%80%25%80%75%20%
• Methods• TIMSS 2011 Math Number -Reasoning Items - Book 1• Random selection of 30 students• Items coded:– “2” for correct– “1” for partially correct– “0” for incorrect• Analysis conducted using R“fannyx” ππ99