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Intelligent tutoring goes to school ITS- Sept 30, 2004

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PAT PUMP or Practical Algebra Tutor Real world problem situations Use modern algebraic tools Spreadsheets, graphers, calculators In use in real schools PAT students +15% on standardized tests +100% on real world type tests PUMP or Practical Algebra Tutor Real world problem situations Use modern algebraic tools Spreadsheets, graphers, calculators In use in real schools PAT students +15% on standardized tests +100% on real world type tests

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New NCTM standards Real-world problems Computer tools Mathematical communication Making connections Downplay: Traditional word problems, factoring, etc. Real-world problems Computer tools Mathematical communication Making connections Downplay: Traditional word problems, factoring, etc.

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Example problem Comparing current qty. & growth of old growth forest in the US to the harvest rate Addressing questions like: When will the old forest be gone? Create tables to see relationships Scaling, graphing, id. intersection points Algebraic notation to rep. structure Using notation to compute solutions Comparing current qty. & growth of old growth forest in the US to the harvest rate Addressing questions like: When will the old forest be gone? Create tables to see relationships Scaling, graphing, id. intersection points Algebraic notation to rep. structure Using notation to compute solutions

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Inductive support Students often perform better in certain contextual problems in comparison with the algebraic representations Immediate feedback: Outline font for numerical mistakes Gray points on plots for incorrect placement Motivation Less social stigma assoc. with errors Students often perform better in certain contextual problems in comparison with the algebraic representations Immediate feedback: Outline font for numerical mistakes Gray points on plots for incorrect placement Motivation Less social stigma assoc. with errors

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Help on request Use production system to ID next activity Student’s focus of activity Overall status of solution Internal knowledge of interdependencies Multiple levels of detail Reduce student frustration Provide sense of accomplishment Use production system to ID next activity Student’s focus of activity Overall status of solution Internal knowledge of interdependencies Multiple levels of detail Reduce student frustration Provide sense of accomplishment

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Knowledge tracing Could be used for self-pacing Was not used because of classroom issues Also needed more student data to fully develop production rules Could be used for self-pacing Was not used because of classroom issues Also needed more student data to fully develop production rules

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In the PUMP classroom Students work in groups Emphasis on transfer to pen-paper skills All answers in complete sentences Written reports Presentations of findings Alternate forms of assessment Mini-scoring conference for grading Students work in groups Emphasis on transfer to pen-paper skills All answers in complete sentences Written reports Presentations of findings Alternate forms of assessment Mini-scoring conference for grading

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Large-scale experiment Change curriculum & add tutor Standardized test comparison Learning gains on new NCTM tests Slightly better on standardized tests Program expanded, self-pacing added Change curriculum & add tutor Standardized test comparison Learning gains on new NCTM tests Slightly better on standardized tests Program expanded, self-pacing added

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Implications? Understanding of learning (inductive) led to design of program that still supports standardized test performance but increases skills in other, very important areas Feedback & motivation? Students in experimental group would have been placed in general math, not algebra! Understanding of learning (inductive) led to design of program that still supports standardized test performance but increases skills in other, very important areas Feedback & motivation? Students in experimental group would have been placed in general math, not algebra!

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