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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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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
Nov 2001
22
2
Overview
IntroductionMain ongoing project : Lingot
PepiteEducational foundations (Grugeon 95)Pepite software (Jean 2000)Pepite testings
Results and questions
Nov 2001
33
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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
Nov 2001
44
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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)
Nov 2001
55
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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
Nov 2001
66
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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
Nov 2001
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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
Nov 2001
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Pépite software
PÉPITEST PÉPIPROFIL
Transversal analysis
PÉPIDIAG
Interpretation of the data
End-users: Students
Teachers Students ?
Nov 2001
99
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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
Nov 2001
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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)?
Nov 2001
1111
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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
Nov 2001
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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
Nov 2001
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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
Nov 2001
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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
Nov 2001
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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
Nov 2001
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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
Nov 2001
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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 ?
Nov 2001
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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
Nov 2001
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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)
Nov 2001
2020
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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
Nov 2001
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Thanks for attention
Questions?