Helping Teachers Generate Exercises with random coefficients

Denis Bouhineau, Hamid Chaachoua, Jean-Francois Nicaud & Camille Douine

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What’s next ?

Introduction : about Aplusix What is working ? For real ? Two taxonomies

Teacher’s place and role in TEL* environments Activities foreseen and provided by TEL environments

Patterns of exercises Pedagogical Web Standard approach Specifically Math web approach with CAS (Our) Teacher-friendly approach

Perspectives

(TEL*: Technology Enhanced Learning)

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Introduction : Aplusix

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Aplusix – Learning by doing elementary algebra A microworld and an exerciser for doing algebra Students freely write algebraic expressions Natural representation and editing of algebraic expressions Two fundamental feedbacks

Semantic equivalence between successive steps Syntax of the final expression

Introduction to Computer Algebra Systems (via commands)

Introduction : Aplusix

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Students Gain autonomy Learn algebra Feel happy

Teachers Specific tools (replay system, statistics, exercises editor, …)

Experiments Available

for research, http://aplusix.imag.fr/Dir-Vers-Rech or see publishers : Chartwell&Yorke (uk), Les éditions

Archimède (fr), MediaDirect (it)

What is working ? For real ?

Mediappro (7393 students aged 12-18, from 9 contries in EC) 50~70% of family have computer with internet access, ~100% of

college have computer with internet access Internet (everyday/several time a week): 67 % at home, 26 % at

school, in france 70 % at home, 10 % at school, (65% never) one-to-one computing programs (NY State)

Many schools have given up No evidence it had any impact on student achievement It’s cost prohibitive Laptops have been abused by students

Questions Tel are good enough? Teacher are happy to use TEL?

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Teacher’s place and role in TEL environments

TEL environments that simply ignore teachers (5/21*) TEL environments that supposes the presence of a teacher TEL environments that incorporates an electronic teacher

TEL environments that give feedbacks to teachers (4/21) TEL environment showing externally the internal representation of

the students TEL environments dedicated to competencies diagnosis

TEL environments with teacher’s interface to manage classes (5/21) TEL environments with teacher’s interface to manage classes and edit

activities (7/21)

21* : 21 rich TEL environments

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Activities foreseen and provided by TEL environments

What are the added-value introduce with the use of computer ?

Lessons most of the work (fill the content) is done by mathematicians,

didacticians, teachers activities analogous with/without computer

Training activities link to Computer Algebra Systems (as mathematical expert) or simple / multiple choice questions

Test activities mathematical difficulties major didactics and pedagogy difficulties

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Patterns of exercises

TEL with teachers to edit training activities

Pedagogical Web Standard approach IMS-QTI, IMS-SS, IMS-LD, IMS-CP, LOM IMS-MathQTI

Specifically Math web approach with CAS Wims, AIM, … Web expert (+ script expert) + CAS expert (+ teacher)

(Our) Teacher-friendly approach based on our model of pattern no web, no script, no cas integrated to the standard system instanciated examples + feedbacks

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Patterns of exercises

Model of patterns Name, Comment, Heritage, Time, Frequency, PostProcessing

Pattern, Domains and Constraints. First work

2 didacticians, 9 files, 650 patterns, 157 Ko

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Patterns of exercises

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Perspectives

Generic Pattern editor and Exercises generator Web-based Pattern editor and Exercises generator

Exercises generator based on didactical variables

Think about usage

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