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Evaluating the Pépite Project: A Diagnostic System for School Algebra Performance

The Pépite project aims to design an online application to assist math teachers in managing cognitive diversity among students in 9th and 10th grade algebra classes. By utilizing a diagnostic system, it analyzes student responses to provide cognitive profiles and suggests tailored groupings and exercise sessions. This evaluation focuses on the system’s reliability and effectiveness in assessing answers, comparing expert evaluations with automated assessments, and ensuring quality results. Ultimately, Pépite seeks to enhance teaching strategies and save time for educators.

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Evaluating the Pépite Project: A Diagnostic System for School Algebra Performance

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  1. The Pépite project Evaluating the performance of a diagnostic system in School Algebra Naima El-Kechaï, Élisabeth Delozanne, D. Prévit, B. Grugeon, F. Chenevotot

  2. Outline • Why a cognitive diagnosis ? • The Pépite project • The diagnostic system • A simple example • PépiDiag • Evaluation • Conclusion

  3. The Pépite project • Objective • To design and implement a web-based application • To support math teachers • To manage the students’ cognitive diversity • Domain • Algebra class • 9th-10th grade (15-16 years old)

  4. A teaching scenario • Who ? • Mary is a Math teacher in 9th grade • Context • To bring all her class to the same level • Steps • Students have the online diagnostic test • Pépite • analyzes the students’ answers • displays a cognitive profile of each student and of the whole class • suggests 6 groups of students and a session of exercises adapted to their cognitive profiles • Mary can adjust the groups and the exercises • Students log in and do the exercises in their assigned session

  5. A cognitive profile of a class • Groupe A+ • Engage in algebraic thinking • Use algebraic calculation appropriately • Groupe B+ • Begin to use algebra to solve problems • Use sometimes mal-rules • Groupe C- • Stuck in arithmetical thinking • Algebra makes no sense

  6. A B+ student’s cognitive profile More More More More More More

  7. A differentiated session

  8. Pépite : Cognitive Diagnosis Process

  9. A simple example

  10. Answer assessment (local diagnosis) Type of answers : Recognition of sub-figures but turning a product into a sum

  11. PépiDiag general architecture Solves exercises Teacher’s interface Student’s answers StudentDatabase Student’s interface Student’sanswers Answerscoding + Student’s profile PépiDiag ExerciseDatabase Exercisecoding prescription file

  12. A coding prescription file (partial)

  13. PépiDiag • Global Diagnosis • Student’s profile

  14. Outline • Why a cognitive diagnosis ? • The Pépite project • The diagnostic system • A simple example • PépiDiag • Evaluation • Conclusion

  15. Evaluation • Quality requirements • No correct answer badly coded • Better no code than a wrong one • Minimal number of answers left unanalyzed • Method • Comparison between experts & system assessment • 3 experts assessed 360 answers of each exercise (one by one) • Experts worked separately and then agreed on some corrections to minor errors

  16. Unanalyzed answers • Data collected (on the exercise used as an example) • PépiDiag analyzes • More answers than the teacher • Less than the experienced researcher

  17. Correct answers • No correct answer is analyzed incorrectly • Unanalyzed answers • 5/13 : Using X instead of * • 8/13 : Mixing algebra and natural language : • « (a+b) times (3+a) » • Solutions • To prevent students from typing letters other than those relating to the exercise statement

  18. Incorrect answers • Incorrect coding • b+ axa +3 (parenthesis errors) • b + a² + 3 (gathering the figure items) • Both are incorrect (V3) distinct for human experts and the same for the CAS • Unanalyzed : incompleteness + interface

  19. Conclusion • Our approach to asses students’ open answers • Human experts • typify anticipated patterns of correct and incorrect solutions • code each type on several dimensions • PépiDiag, using a CAS, • matches the student’s solution with a pattern • PépiDiag is reliable • 100 % : closed answers • 80 % : answers with one algebraic expression • 70 % : answers with a multi-step reasoning [ITS 2008] • PépiDiag saves teachers’ time and tedious effort

  20. Current work • http://www.sesamath.net/ • Diagnosis • To evaluate the building of the student’s profile from the answer assessment • Comparing • Heuristic method (implemented) • Statistical building (being implemented) • Neural Networks (being implemented) • A differentiation support tool for teachers • To validate with teachers the different learning paths adapted to each (group of profile) • To build a tool to automatically • retrieve indexed exercises from a data base • suggest a session adapted to a student’s profile

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