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Pepite : software to help teachers diagnose students’ algebra competencies Élisabeth DELOZANNE Brigitte GRUGEON IUFM de Créteil IUFM d’Amiens LIUM (Le Mans) DIDIREM (Paris) France 1 1 Déc. 2001

Pepite : software to help teachers diagnose students ’ algebra competencies

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1. 1. Déc. 2001. Pepite : software to help teachers diagnose students ’ algebra competencies. Élisabeth DELOZANNE Brigitte GRUGEON IUFM de Créteil IUFM d’Amiens LIUM (Le Mans) DIDIREM (Paris) France. Overview. Introduction Main ongoing project : Lingot Pepite - PowerPoint PPT Presentation

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Page 1: Pepite :  software to help teachers diagnose students ’  algebra competencies

Pepite :

software to help teachers diagnose

students’ algebra competencies

Élisabeth DELOZANNE Brigitte GRUGEONIUFM de Créteil IUFM d’Amiens LIUM (Le Mans) DIDIREM (Paris)

France

1 11

Déc.2001

Déc.2001

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Overview

IntroductionMain ongoing project : Lingot

PepiteEducational foundations (Grugeon 95)Pepite software (Jean 2000)Pepite testings

Results and questions

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Pedagogical Basic Assumptions

Students’ answers show coherences in their reasoning

It is possible to analyse their answers to identify the competences the students have built (correct, partial, inappropriate)

Identifying those competences would help teachers to give appropriate tasks to destabilize them (if inappropriate) and to make them evolve

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Design assumptions Computers can help teachers both

in identifying competences “Pépites” (nuggets)

in giving appropriate tasks to enhance learning and understanding

building “Lingot”, (ingot) Two classes of end users

Students usual user-centred design techniques (Human Computer

Interaction) task analysis based on educational research

Teachers new usage patterns to be invented participatory design (researchers and teachers)

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Lingot project Objectives

To instrument teacher’s activity with systems to enhance algebra learning and teaching

Pepite : Assessing assistant Stephanie Jean Free download :

Pepite.univ-lemans.fr Demo in English

Amico : Learning environment Dorothée Rasseneur Interaction with virtual peers

To promote algebra as a proving tool To develop links between different representation modes

Natural language, algebraic, graphical, numerical Demo in French

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Pépite Objective

To help teachers diagnose student's competence in algebra

Multidisciplinary projectEducational research in mathematics (DIDIREM)

basis: a multidimensional model of algebraic competence result: a paper and pencil diagnostic tool

Computer science research (LIUM) (partial) automation of this paper and pencil diagnostic tool

Together Developing awareness about diagnosis algebra competencies Modifying teaching approach to algebra Watching teachers using Pépite in classrooms Spreading research results

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A diagnosis tool (Brigitte Grugeon 1995)

A multidimensional model of competence Mastered skills, meaning of letters, processing algebraic expressions,

translation between representations, type of rationality A set of Paper & pencil exercises and an analysis grid

Technical (generational and transformational), modelling, interpreting skills

Analysis grid derived from the model of competence Students’ profiles

quantitative description Success rates on mastered skills

qualitative description Meaning of letters, processing algebraic expressions, translation between

representations, type of rationality description of flexibility between representations

Diagram

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Pépite software

PÉPITEST PÉPIPROFIL

Transversal analysis

PÉPIDIAG

Interpretation of the data

End-users: Students

Teachers Students ?

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PÉPITEST: the students’ software

proposes 22 exercisesLarge sample of algebraic activities

gathers the student's answersdata collector for the diagnosisquality of data and quality of the diagnosis

are linkedHCI issues to obtain better results

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PÉPITEST: Main Issues

Can PÉPITEST collect informative enough data to build a student profile ?

To what extent does the software change students' answers ?Does PÉPITEST reduce the variety of proposed

answers?What are the differences between answers with

paper & pencil and answers with PÉPITEST

(especially for algebraic expressions)?

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PÉPIDIAG: the analysis module interprets and codes the student's answers

data collected by PÉPITEST

applies the analysis grid MCQ Open answers

algebraic expressions, natural language, mixed (“mathural” language)

fills a matrix for each student 55 questions 35 items in the model of competence

gives very fine description of the student's behaviour

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PÉPIPROFIL: the teachers’ software

Two tasks for the teacherTo scrutinize student’s profile

To understand it, to complete it, to correct it To ways

By student’s answers By profile items

To have an overview on student’s profile

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PÉPIPROFIL: the teacher software

Two tasks for the system to establish the profiles

by transversal analysis of the filled matrixto highlight consistency in the student's way of

functioning to present them to teachers

with different levels of description overall view of the profile / all available information

with different modes of representation Graphical, textual, values

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Pepite testings PépiTest

Lab testing and 2 hours videotape 100 students (grade 9 and 10) in 4 differents schools

PepiDiag Comparing the matrix filled by Pepite and by teachers or

researchers PepiProfil

10 Case studies in personalised help sessions Uses of Pepite

40 downloading Training sessions for math teachers

5 sessions : Teachers trainers inside Pepite team Outside ?

Pilot sessions personalised help for students with difficulties auto-assessment and revision before examination introduction of a notion from a debate with data show learning activities

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Results PÉPITEST

Limits :difficulties to enter algebraic expressions

Supplies reliable data finding every kind of answers expected by the didactical analysisshowing competences or fragilities that usual tests do notcorresponding to students' usual functioning ?

Cases studies show that teachers recognize their students

Used by some teachers Used by teachers trainers

Larger sample of exercises, more different competences involved

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Results PÉPIDIAG

Analyses 75% of the answerssimple methods to analyse answers

Does not analyze expressions on several lines mixed language

On averageexperts correct 10 % of Pepite’s analysis

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Results PÉPIPROFIL

The teacher completes and corrects PepiDiag’s diagnostic when trained : ½ H first time : 1 H 1/2

PepiProfil automatically builds detailled profiles abstract of the profiles

Evaluation profiles correspond to experts ones to teachers’ ones ?

Teachers involved in the project Experienced teachers, teacher trainers

Depends on how they consider teaching algebra Beginners (pre-service)

matching student's knowledge ?

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Usable by teachers? What they like:

shows competences that they were not aware of makes them more confident with their poor students helps them to install new relationship with their students’ errors helps them to understand the new official program in mathematics

What they dislike: difficulties with using computers didactical jargon time consuming (1 H1/2 test, ½ H analysis) distorting mirror of their teaching mistrust of their understanding of algebra teaching

What they ask for: remediation proposals according to student’s profile a feedback for the students given by the software possibility to modify the test training in using the model of competence

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Ongoing and future work

Correcting bugs and “jargon” Suggesting activities adapted to each

profile Making a diagnostic for students and

discuss it with themLater Enhancing the diagnosis Make a more reusable software in an other

domain (statistics)

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Key elements in Pépite

An iterative methodology which enables usto work in a pluridisciplinary context and in

classroomsto build an “instrument” for teachers (Rabardel)

Intrumentalisation (artefact evolution) Instrumentation (teacher evolution)

to spread research results

A diagnostic assistant that can help teachers improving their teaching of algebra

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Thanks for attention

Questions?