The Use of Dynamic Geometry
Software by High School Teachers inVietnam: Analysis from Case Studies

Nguyen Chi Thanh
CICE Visiting Professor
Associate Professor at the Faculty of Teacher
Education,
University of Education,Vietnam NationalUniversity, Hanoi, Vietnam

Hiroshima University, the 8th Mars 2013

Plan
 Some remarks from the 1rst seminar Introduction DGS
 An institutional analyse: actual situation in Vietnam
 Teacher professional development

 Conclusion

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Some remarks from the 1rst seminar High school teacher (HST) training : 3 models

 No specific content in ICT use in pre-service teacher training No specific (or very little) in computer softweres in teaching andlearning

Pre-in service teacher are mostly weak in presentation skill, ICT use skill,repport elaboration skill and real life problem solving skill. (DinhQuang Bao, 2011) In despite of some positive modification recenly made,mathematics curriculum at high school remains accademic, formaland ‘’skillful’’ based orientation
 Very strong institutional recommendation in terms of ICT use andintegration in mathematic education
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Plan Some remarks from the 1rst seminar Introduction DGS
 An institutional analyse: actual situation in Vietnam
 Teacher professional development

 Conclusion

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What is expected from technology?
Must allow students
to master current mathpractices

Must help students to adapt
to the technological worldMust help to renew pedagogical practices,must provide new teaching tools,for visualising, communicating…

Must help to understandmathematical concepts,
must increase students’ math powerMust make teaching and learning easier and better
5157th CICE Open SeminarMust save teaching
and learning timeWhy Dynamic Geometry Software (DGS) ?

6157th CICE Open SeminarWhy Dynamic Geometry Software (DGS) ?
 Over the last two decades, DGS has become one of the mostwidely used pieces of software in schools and colleges all over theworld (there are versions of the software in French, German,Japanese, Spanish and Swedish etc.).
 In terms of research, Sträßer (2001) thinks that DGS may be oneof the best, if not the best, researched type of software withinmathematics education research. In respect of geometry insecondary schools, Hollebrands (2003) and colleagues consider
DGS research to be the sort of software research that offers mostinsight into its use in the classroom.
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A statistic figure about DGS(Wikipedia 2013)

2D DGS: 36
3D DGS: 98157th CICE Open Seminar

Plan Some remarks from the 1rst seminar Introduction DGS
 An institutional analyse: actual situation in Vietnam
 Teacher professional development

 Conclusion

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Introduction to DGS
 Interactive geometry software (or Interactive Geometry

Software IGS, or Dynamic Geometry environments, DGE) arecomputer programs which allow one to create and thenmanipulate geometric constructions, primarily in plane geometry.
In most DGS, one starts construction by putting a few points andusing them to define new objects such as lines, circles or otherpoints. After some construction is done, one can move the points
one started with and see how the construction changes.
 DGS provides a range of tools for constructing geometric objects
from a range of `primitive’ objects (such as points, segments, lines,circles etc.). The tools available in the software include ‘classical’constructions (midpoint, perpendicular, parallel, etc.) as well astransformations (reflect, rotate, translate, etc.).

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Generalities about a DGS: Cabri software

11157th CICE Open SeminarCabri: User interface

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157th CICE Open SeminarExample I

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157th CICE Open SeminarExample I

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157th CICE Open SeminarExample I

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157th CICE Open SeminarExample I

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157th CICE Open SeminarExample I

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157th CICE Open SeminarExample I

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157th CICE Open SeminarExample I

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157th CICE Open SeminarExample I

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157th CICE Open SeminarExample I

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157th CICE Open SeminarTo do now…

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The Euler line in a triangle
We will construct a general triangle ABC,- then its three medians (the lines that join a vertex to the midpoint ofthe opposite side)- Next the tree altitudes of the triangle (the lines through each vertex
in turn, perpendicular to the opposite side)- Finally the tree perpendicular bisectors (lines perpendicular to eachside, through the midpoint of the side
- The Euler line of the triangle

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The Euler line and…the Euler circle
Next, construct the nine-point
circle forthe triangle. This isthe circle whose centre
is at the midpoint of OH, andwhich passes through themidpoints of the sides: A’, B’
and C’ the foot of each
altitude, and the midpoint ofeach the line segments HA, HB,HC.

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157th CICE Open SeminarExample II27

157th CICE Open SeminarExample II28

157th CICE Open SeminarExample III

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and a number for theangle of ratation

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157th CICE Open SeminarExample V

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157th CICE Open SeminarExample V

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157th CICE Open SeminarExample VI

and a number…

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and a number…
and now enlarge
the quadrilateral
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Using the expression tool to create arectangle of constant area with Cabri 2 plus

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Let’s check by measuring
the area and the perimeterof this figure

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157th CICE Open SeminarCabri 3D: the unique 3D Interactive
geometry software Example 1

 Example 248

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Introduction to DGSWith a DGS in general, we can do followings:
 General geometric constructions
 Macros Loci Measurements and calculation
 Graphics Export Formats
 Object attributes
 Proof49

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Introduction to DGS: a historicalperspective
 End of 70s and in the 80s “significant” software started. They were

the result of university type research and spread throughpioneering teachers.
 Let us think in first place of Logo developed and spread underSeymour Papert’s impulse at Media Lab-MIT, USA.
 Later we have had soft ware like Geometric Supposer (MIT) andrather soon, authentic dynamic geometry software, came to live,say (historically):- Cabri (University of Grenoble –France) and- GSP (Swarthmore College – USA)50

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Introduction to DGS: a historicalperspective (Laborde J-M, 2010)

157th CICE Open SeminarFrom high perspective does DGS reallymatter?
 When participating in conferences on Computer in Education you

learn just (very often):- How wonderful the use of ICT is;- How much kids learn through technology;- How good my (i.e. presenter’s) DGS is good;-…
 Looking at actual data about the use of ICT shows that in fact, mostly
everywhere, ICT use is only marginal (even if in some country it isofficially part of the curriculum) - best cases 20%- (Laborde J-M,2010)
 Why such an apparent contradiction?

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Actually DGS matters
 In various countries some politicians claim that- the use of technology is a big mistake- one should come+come Back to Basics (USA);+ learn long division (GB);+ learn to extract square roots by hand (France).

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Plan Some remarks from the 1rst seminar Introduction DGS
 An institutional analyse: actual situation in Vietnam
 Teacher professional development

 Conclusion

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Shared research claims
 There are several technological environments very

promising in terms of learning The usual teaching practice does not take full advantageof these possibilities
 A critical element in the integration of technology into
usual teaching is the teacher (Artigue, Bottino andFuringhetti, Guin and Trouche, Monaghan, Ruthven,Sutherland…)

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157th CICE Open SeminarAn institutional analyse Teacher training programme Mathematic curriculum at high school: no or few activity with DGS
Textbook

Without others ICT(calculator, computer)With DGS

Edition 2000

50Edition 2005

150

 Teacher use- Example 1 (support of powerpoint presentation)- Example 2 (illustration of geometrical propeties)- Example 3 (exploring geometrical propeties)
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Reasons mentioned by teachers
 Benefit for teachers Facing the students
 More comfort (no pain in arms and back) Clean, precise and beautiful figures
 Saving construction and time Benefit for students
 Saving construction and time
 Multiplying cases
 Amplified Visualization

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How does a teacher usually designtasks?
 Duplication from pencil environment to DGSenvironment Adaptation from text book ‘’do-it-yourself’’ from the available resources
 Very few teachers design tasks from scratch

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How does a teacher usually designtasks?
 The most immediate use by teachers is just “showing”

geometrical theorems: teachers manipulate themselvesor the students are allowed to have a restricted
manipulation (dragging a point on a limited part of line)
 It would take a long time in order for them to master the package andI think the cost benefit does not pay there… And there is a huge
scope for them making mistakes and errors, especially at this level ofstudent… and the content of geometry at foundation andintermediate level does’nt require that degree of investigation » The student is a spectator of beautiful figures (showing the power ofthe software) or of properties part of the content of the curriculum(quoted by Laborde 2002)

 Sometimes the students must formulate the theorems
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157th CICE Open SeminarThree possibilities Three possibilities for the design of tasks
 using ready made tasks for technology
 adapting tasks designed for paper and pencil
 designing his/her own tasks

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Designing technology based tasks isproblematic Designing technology based tasks is out of the range ofthe ordinary activities of teachers Limited number of such tasks in textbooks
 Limited number of resources Including the new element “technology” is not justadding it but affecting all dimensions of the designactivity And introducing a hidden dimension: the instrumentaldimension
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Plan Some remarks from the 1rst seminar Introduction DGS
 An institutional analyse: actual situation in Vietnam
 Teacher professional development

 Conclusion

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Integration of ICT
Integrationof ICT

Use of ICT A change in depth in:- content presentation- forms of activity(Laborde C., 1998)

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Integration of ICT
Research in theintégration of ICT

Experimentalsituations

Take into account:- of research result-Reference situation

Teacher professional
developement in theintegration of ICT

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157th CICE Open SeminarAn litterature review on the field (Artigue, Lagrange,Laborde 2000)
Corpus : 662 publications
 E : Primery school C : Lower secondary school L : Uper secondary school

 S : Secondary school U : Higer Education
 FE : Teacher professional

developement 5%

12%
23%

0%

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E/C

14%

C

5%

1%

C/L

18%

17%
2%

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E8%

LS
L/UU

Dynamic geometry: major specificfeatures
 Dragging is one of the distinctive features of DG

 Geometric tools for constructing figures preserving theirproperties when dragged Three possible uses of dragging
 Dragging for seeing Dragging for conjecturing Dragging for validating/invalidating

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157th CICE Open SeminarImportance of tasks (1/2)

stressed by research in maths education: “importance oftasks in mediating the construction of students’ scientificknowledge” (Monaghan) Central role in several theoretical frameworks aboutteaching and learning processes even if they do not use the word “task” itself

 Constructivist and socio-constructivist approach:problematic tasks for the learners

 Problem is the source and criterion for knowledge (Vergnaud)
 Learning comes from adapting to a new situation creating aperturbation (Brousseau)

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157th CICE Open SeminarImportance of tasks (2/2)
In the praxeological approach (Chevallard) Knowledge used in an institution is characterized by asystem of tasks,

 techniques to solve the tasks,
 justifications of the techniques, and theories from which justifications may come68

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Activity of designing tasks
 Design activity is complex

 Requires to coordinate various types of knowledge aboutmaths, pupils, technology, learning As such it may be a tool for professional development
provided that some conditions are fulfilled

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Resorting to several types of knowledge(Laborde C., 2005)
 Three kinds of knowledge strongly intertwined in the designof tasks

 Mathematical knowledge
 Knowledge of DGS
 Pedagogical content knowledge
 about mathematics teaching and about the use of DGS for fostering learning

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The design of tasks taking full advantage of dynamic geometry:
What kinds of knowledge does it require from teachers? (HamidC., 2013)
Didactical knowledge

EducatorTeacher

Sm: mathematical knowledge

Si: artifact knowledge71

Sd-i: didactical knowledge relatied to the artifact implementation
in a learning situation
Sd-m: knowledge related to the implemetation of mathematical157th CICE Open Seminar
objects in a didactical situation

A professional activity
 Designing tasks is a teacher professional activity (Robert)
 It is a complex activity involving several dimensions
 Epistemological dimension: choosing features of mathematical knowledge how to use them Cognitive dimension: what kind of learning does promote thetask?
 Didactic and institutional dimensions: How does the task fit

 the constraints and needs of the teaching system, of the curriculum, of the specific class and of its didactic past?

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Key points in the anthropologicalapproach (Chevallard Y., 1998)
 Mathematical objects are nothing absolute; they arise

from institutional practices : « praxeologies » Praxeologies can be seen as complexes of tasks-techniques-technology-theory
 Knowing = ideoneity with institutional relationships
 The advance of knowledge goes along with theroutinisation of tasks and techniques, the naturalizationof knowledge
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Instrumental dimension
 A tool affects the way of solving a task

 A tool is not transparent but must be appropriated by theuser
 The user constructs schemes of utilization of the tool toperform tasks with the tool Construction process of these schemes: instrumental
genesis (Rabardel) Using a tool shapes the way to do mathematics andconsequently may affect mathematical knowledge
constructed by the user
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Instrumental dimension (Trouche2003)

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Instrumental dimension (Trouche 2003)

From the artifact

To the instrument

Instrumental
genesisInstrumentalisation

Constraints
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Instrumentation

New potentialDidactical situation
Knowledge

Teacher

Student"Milieu"
A-didactical situation

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Didacticalsituation

Example of analysis of “milieu” (Laborde, 2005)• Teaching goal:make the students learn the theorem according to which an angle inscribed in asemi-circle is a right angle

Task with dynamic geometry software:
Create a circle with center O and a point A on thiscircle. Construct B such that [AB] is a diameter of thecircle. Create a point M on the circle and thesegments [AM] and [MB]. Measure the angle AMB.
Drag M on the circle. What do you observe?

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157th CICE Open SeminarExample of analysis of “milieu”• “Milieu”:
Geometric figure (robust construction)
 Feedback:• Invariance of the measure of theangle AMB• Contribution to identification ofelements of the theorem:
Varying nature of M and invariance ofangle measure Exteriorizing of the variable nature of
M and the set on which it varies


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Plan Some remarks from the 1rst seminar Introduction DGS
 An institutional analyse: actual situation in Vietnam
 Teacher professional development

 Conclusion

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Conclusion
 Related to research about the integration in ICT in mathematicaleducation, there is a almost no significant result in Vietnam
 Teacher professional development in the domain: a huge demand
and a lot of effort to do Some research show:- The integration of ICT is a long and complex process- Political will and the hardware are necessary but not sufficient- Professional development is critical for contributing to increase theconfidence of teachers- The role of research is crucial+ Time for investigating different kinds of tasks+ A better knowledge of students faced with different kinds oftasks
Informing professional development

Conclusion New devices (tools) are coming in Vietnam classroom:- Forum- Tablet- Smart interactive board….

New researchquestions

New challenges forteacher professional
developpmentReference ARTIGUE M., (2005), The instrumental approach: the institutional

dimension, Seminar at the Unversity of Leed, England
 CHAACHOUA H., (2013), Formation des enseignants et nouvelles
technologies, France – Vietnam Conference in Didactic of mathematics,
HCM city, Vietnam
 KEITH J., (2002), ‘’Implication for the classroom: research on the use ofDGS’’, Micromath, England LABORDE C. (2002), The design of tasks taking full advantageof dynamic geometry: what kinds of knowledge does it require fromteachers?, Conference CERME LABORDE J. (2010), ‘’Does DGS matters ?’’, the 14th ATCM, Malaysia
 NGUYEN C.T. (2006), « Integrate the dynamic geometry software Cabri
in to the pratices of Teachers: a didactical perspective », Workshop at the17th ICMI Study Digital technologies and mathematics teaching and learning:
Rethinking the terrain, Vietnam

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