The M.In.E.R.Va Project Statistical Analysis and Rasch Model Other Tables A Rasch Analysis of Math Tests using M.In.E.R.Va. Platform Grazia Messineo - Salvatore Vassallo ICETC2014 Messineo - Vassallo Rasch Analysis in Minerva Platform 1/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables The problem Students must achieve some automatism in each discipline to succeed Many students have difficulties in Mathematics (see Ocse-Pisa reports) Traditional ways (courses) to help students are difficult to implement, also because of their costs Messineo - Vassallo Rasch Analysis in Minerva Platform 2/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables Goals To help students to recover their deficiencies in a discipline To provide teachers a tool to assign common or personalized tasks to students To provide teachers a tool to automatically verify students’ achievements Messineo - Vassallo Rasch Analysis in Minerva Platform 3/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables The structure: contents Theoretical schemes to strengthen or create knowledge Guided exercises to illustrate the correct way for solving the problems Consolidation and self-assessment exercises Performance assessment exercises Messineo - Vassallo Rasch Analysis in Minerva Platform 4/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables The structure: feedback Assignment of a score Automatic answers correction Hint to get a solution References to theoretical content Solution (complete or in partial form) Messineo - Vassallo Rasch Analysis in Minerva Platform 5/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables How it works The software consists of some L A T X files: The E package minerva , the master files, and the files of the exercises Each file of exercises contains one or more variants of a basic exercise The output is a pdf file with interactive content managed by Javascript Messineo - Vassallo Rasch Analysis in Minerva Platform 6/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables Advantages Possibility of being used offline Wide range of exercises: Multiple choice tests Open questions (with powerful automatic computation) Multiple answers questions (with different marks for any question) Messineo - Vassallo Rasch Analysis in Minerva Platform 7/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables Advantages Use without installing any additional application Excellent display of mathematical text Independence from operating system Ability to use the same tool in different situations and disciplines Messineo - Vassallo Rasch Analysis in Minerva Platform 8/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables The generation of a test A variant is randomly chosen Variants are randomly scrambled Answers are shuffled Values are assigned to random parameters A test is produced (PDF file) Messineo - Vassallo Rasch Analysis in Minerva Platform 9/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables The url: http://progettominerva.unicatt.it Messineo - Vassallo Rasch Analysis in Minerva Platform 10/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables Students’ interface - 1 Messineo - Vassallo Rasch Analysis in Minerva Platform 11/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables Students’ interface - 2 Messineo - Vassallo Rasch Analysis in Minerva Platform 12/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables Teachers’ interface - 1 Messineo - Vassallo Rasch Analysis in Minerva Platform 13/37
The M.In.E.R.Va Project General frame Statistical Analysis and Rasch Model The Web Platform Other Tables Results Messineo - Vassallo Rasch Analysis in Minerva Platform 14/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Secondary Schools Trial has been going on since school year 2011-12 Results before and after the use of the tool Messineo - Vassallo Rasch Analysis in Minerva Platform 15/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis University Trial started in February 2014 Students can perform exercises and study theoretical material online A group gives a part of the final exam online: figure shows positive marks. Messineo - Vassallo Rasch Analysis in Minerva Platform 16/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Rasch model Mathematical model to compute the probability p ij that the subject i with ability „ i answers correctly to question j with difficulty ˛ j Rasch measure based on the difference „ i ` ˛ j Data collected in a raw score matrix: n rows (subjects) and m columns (items) Conversion of values of measures of ability and difficulty into a common scale ( logit ) Messineo - Vassallo Rasch Analysis in Minerva Platform 17/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis The analysis performed in 2014 Data collected from a test of Mathematics Two sets of students: 20 of Catholic University and 16 of a Secondary School Questionnaire with 16 multiple choice questions, 8 on derivatives and 8 on domains Messineo - Vassallo Rasch Analysis in Minerva Platform 18/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Summary Statistics Messineo - Vassallo Rasch Analysis in Minerva Platform 19/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Summary Statistics interpretation For students: separation index lower than 2 and reliability index lower than 0 : 8 Messineo - Vassallo Rasch Analysis in Minerva Platform 20/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Summary Statistics interpretation For students: separation index lower than 2 and reliability index lower than 0 : 8 ! more items may be needed for a better separation of ability levels (actually we can divide the sample into 3 levels) Messineo - Vassallo Rasch Analysis in Minerva Platform 20/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Summary Statistics interpretation For students: separation index lower than 2 and reliability index lower than 0 : 8 ! more items may be needed for a better separation of ability levels (actually we can divide the sample into 3 levels) For items: separation index lower 3 and reliability index lower than 0 : 9 Messineo - Vassallo Rasch Analysis in Minerva Platform 20/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Summary Statistics interpretation For students: separation index lower than 2 and reliability index lower than 0 : 8 ! more items may be needed for a better separation of ability levels (actually we can divide the sample into 3 levels) For items: separation index lower 3 and reliability index lower than 0 : 9 ! the students’ sample is not large enough to confirm the item difficulty scale. Messineo - Vassallo Rasch Analysis in Minerva Platform 20/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Person-Item Distribution Map Messineo - Vassallo Rasch Analysis in Minerva Platform 21/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Person-Item Distribution Map Messineo - Vassallo Rasch Analysis in Minerva Platform 21/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Person-Item Distribution Map Messineo - Vassallo Rasch Analysis in Minerva Platform 21/37
The M.In.E.R.Va Project Initial data Statistical Analysis and Rasch Model Individual Analysis Other Tables Differential Analysis Person-Item Distribution Map Messineo - Vassallo Rasch Analysis in Minerva Platform 21/37
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