1. Intelligent tutoring goes to school ITS- Sept 30, 2004

2. 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

3. 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.

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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!