Juggling Reference Frames in the Microworld Mak-Trace: The Case of a Student with MLD

Juggling Reference Frames in the Microworld Mak-‐Trace:

The Case of a Student with MLD Anna Baccaglini-Frank

Dip. di Educazione e Scienze Umane, Università di Modena e Reggio Emilia, Italy

Elisabetta Robotti

Dip. di Scienze Umane e Sociali, Università della Valle d’Aosta-Université de la Vallée d’Aoste, Italy

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Samuele Antonini Università di Pavia, Italy

George Santi

I.I.S. “E. Majorana”, Bologna, Italy

Aim: to study aspects of the educaConal potenCal of Mak-‐Trace (free app for iPad and iPhone) for visuo-‐spaCal empowerment in cases of MLD. In parCcular: •  To analyze processes in managing different systems of reference in the

student-‐arCfact interacCons. •  To study aspects of the semioCc potenCal of Mak-‐Trace, in parCcular

with respect to developing awareness and becoming able to manage different systems of reference.

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The Study

The study is part of the line of research on the use of arCfacts in processes of teaching and learning MathemaCcs in cases of

Learning DisabiliCes

Aim: to study aspects of the educaConal potenCal of Mak-‐Trace (free app for iPad and iPhone) for visuo-‐spaCal empowerment in cases of MLD. In parCcular: •  To analyze processes in managing different systems of reference in the

student-‐arCfact interacCons. •  To study aspects of the semioCc potenCal of Mak-‐Trace, in parCcular

to develop an awareness and ability to manage systems of reference different from one’s own.

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The Study

The study is part of the line of research on the use of arCfacts in processes of teaching and learning MathemaCcs in cases of

Learning DisabiliCes

“...on the one hand, personal meanings are related to the use of the arCfact, in parCcular in relaCon to the aim of

accomplishing the task; on the other hand, mathemaCcal meanings may be related to the arCfact and its use. This double semioCc relaConship will be named the semio)c

poten)al of an ar)fact.” (Bartolini Bussi & MarioV, 2008, p.754)

Methodology: exploraCve case-‐study in mathemaCcs educaCon. CollaboraCon between teachers and university researchers: the teacher and researchers met weekly to adjust (and possibly design new) acCviCes. The acCviCes were conducted with a student diagnosed with severe LD in his regular school seVng, and they were video-‐recorded and analyzed weekly.

The Study

Case analysis Context : Filippo, 15 years old, is in the second year of high school (technical insCtute), he has been diagnosed with severe specific LDs.

The Study

According to recent studies, students with MLD may present different

mathemaCcal profiles, characterized by the presence of mulCple deficits including those of a visuo-‐spaCal

nature (Andersson & Östergren, 2012; Karagiannakis et al., 2014)

Case analysis Context : Filippo, 15 years old, was in the second year of high school (technical insCtute), he has been diagnosed with severe specific LDs. Filippo was helped 4 hours a week by a special educaCon teacher, whom he would work with individually, outside the classroom. The teacher had noCced that Filippo was not able to give or interpret direcCons (giving instrucCons to go from home to school).

The Study

his diagnosis: a comorbidity of severe dyslexia

and severe dyscalculia


The Study

A working definiCon of visuo-‐spaCal abiliCes can be to perceive and operate in

physical space or on mental representaCons, based on

spaCal coordinates (Grossi & Trojano, 2002)


The Study

Filippo seemed to have a Visual-‐SpaCal Disability.

This implies the neuro-‐cogniCve funcCons: •  orientaCon of spaCal acenCon

•  integraCon of visual-‐construcCve and visual-‐motor abiliCes

•  visual-‐spaCal working memory; although a definiCon has not yet been agreed upon

(Rourke, 2002; Forrest, 2004)


The Study

From the “Indicazioni Nazionali per il I ciclo” (MIUR, 2012, p. 50) Learning Goals for the end of grade III of primary school

Space and figures -‐  Communicate the posiCon of objects in physical space, both with respect to the subject, and with respect to other people or objects […]

-‐  Execute a simple path starCng from its verbal descripCon or from a drawing, describe a path that you are execuCng and give direcCons to some one for them to execute the same path.

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Mak-‐Trace

!

immediate feedback of a programmed sequence is not

given

A first analysis: Filippo’s difficulCes became apparent in: -‐  considering systems of reference for spaCal relaCons independent of the self (allocentric)

-‐  transiConing between representaCon with reference to the self (egocentric) to reference external of the body (allocentric)

But …

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We needed a more refined framework to elaborate a fine grained analysis of the difficulCes observed

Looking for a tool of analysis

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Tool of analysis

Grush (2000) (cogniCve psychology) divided “allocentric” into: (A) egocentric space with a non-‐ego object reference point (decentred egocentric); (B) object-‐centred reference frames; (C) virtual points of view (i.e., maps); (D) “nemocentric” maps.

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Points of view

Lucia Giovanni

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Points of view

EGOCENTRIC: Lucia is in front

of me

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Points of view

EGOCENTRIC DECENTERED (type A):

Lucia is to the right of Giovanni

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Points of view

ALLOCENTRIC (type B): Lucia is to

Giovanni’s len

Three of the tasks

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1) program the snail to draw a given path;

2) program the snail to draw a

square; 3) complete the mazes.

ExploraCon of the meaning of the command-‐icons

Task 1 Program the snail to draw a given path Filippo: it is a bit hard. It’s never what it… […] I am not

understanding anything […] wait…I didn’t tell him to go right and he went right. […] These two [R and L] are inverted […] I am not understanding anything […] if this arrow [L] makes it turn right, this one [R] makes it turn len.

Filippo: Every three squares, every three..., every three squares, every three down arrows, the fourth makes it go up...I don’t know. […] if we look only at these arrows here, you can’t really understand much.

Teacher: why does an arrow poinCng to the len make it go to the right?

Filippo: Ask the person who designed the game!

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(B) object-‐centred reference frames It is necessary to consider a snail-‐fixed frame of reference BOTH at the origin AND in terms of orientaCon

(A) decentred egocentric frame

Teacher: ... This is the key-‐word [...] so what do the arrows refer to?

Filippo: it went backwards, not

upwards […]

Filippo: ... it depends on how the snail is oriented.

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(B) object-‐centred reference frames


Filippo constantly bounces

back and forth

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Filippo correctly writes a sequence of commands to

make the snail follow a predefined track. We observe that the track is made up of horizontal

lines and verCcal lines “upward”

(the snail is never oppositely oriented)

Three of the tasks

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(the snail is pointing upwards) Filippo constructs the sequence of command icons FFFFLFFFFL [short pause, he says “yes”]

Task 2 Program the snail to draw a square:

Acempt 1

L R F

B

He seems to be able to pass to an ALLOCENTRIC

perspecCve (type B)

(the snail is pointing upwards) Filippo constructs the sequence of command icons FFFFLFFFFL [short pause, he says “yes”] B [short pause] BBBR [long pause] FFFF.


Acempt 1

L R F

B

He seems to be able to pass to an ALLOCENTRIC

perspecCve (type B)

He gets lost and goes back to the

egocentric decentered perspecCve

Filippo: he inserts the commands FFFFLFFFFL

[short pause, he inserts S, he deletes it, says “eh, alright, it’s enough to make it turn like this”, with his right index he draws a len turn in the air] FFFF [he says “I have to always keep” he gestures an anCclockwise rotaCon with his right hand] RFFFF.

Task 2: Acempt 2 Filippo corrects the third side but he makes a mistake on the turn when the snail-‐fixed system is oppositely oriented with respect to his own:

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Acempt 3

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Filippo starts programming again from the beginning FFFFLFFFFL [he gestures an anCclockwise rotaCon with his right hand corresponding to the len turn that he inserts] LFFFF [he rotates the iPad to see the snail’s perspecCve] “There, I found it”… “I got…I get lost” “When it’s turned around…it goes backwards [clockwise rotaCon gesture with his right hand] so…if I want it to go here [gesture from len to right with len hand]” “uh, I don’t know, let’s try like this” RFFFF (he looks at the sequence) “No wait because otherwise it’s like before” he changes the R with a L [second correcCon without tesCng]

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Filippo starts programming again from the beginning FFFFLFFFFL [he gestures an anCclockwise rotaCon with his right hand corresponding to the len turn that he inserts] LFFFF [he rotates the iPad to see the snail’s perspecCve] “There, I found it”… “I got…I get lost” “When it’s turned around…it goes backwards [clockwise rotaCon gesture with his right hand] so…if I want it to go here [gesture from len to right with len hand]” “uh, I don’t know, let’s try like this” RFFFF (he looks at the sequence) “No wait because otherwise it’s like before” he changes the R with a L [second correcCon without tesCng]

Awareness of the necessity to embrace the snail-‐fixed system (ALLOCENTRIC, type B)

compensatory strategy

compensatory strategy

•  Program the snail to re-‐trace going backwards the sequence it traced going forwards.

•  Dictate sequences to the teacher with a more rapid notaCon (for ex. 3f r 2f r 3f l ...) and use of this notaCon to compare sequences;

•  Formulate a general rule such that, given any path, it allows to find the inverse path.

•  AcCviCes with mazes and con macros. 32

Later acCviCes

Three of the tasks

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Task 3 compensatory

strategy

Conclusion

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to recognizing this perspecCve and trying to embrace it

from not being able to perceive the snail’s perspecCve, and trying to find a way of making sense of the command icons

The student’s confusion seemed to depend on his simultaneous use of the two incompaCble frames.


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to recognizing this perspecCve and trying to embrace it

from not being able to perceive the snail’s perspecCve, and trying to find a way of making sense of the command icons

The student’s confusion seemed to depend on his simultaneous use of the two incompaCble frames.


In the end the student is aware that he can change frames of reference by mentally trying to “be the snail”

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This occurred thanks to: •  the specific tasks proposed, •  the intervenCons of the teacher •  the funcConaliCes of Mak-‐Trace, which required conCnuous juggling between two reference frames.

right for whom? ...the snail turns

refer to...

!

the commands are icons that can be spontaneously

interpreted in the egocentric frame

but that refer to the snail-‐fixed frame

immediate feedback of a programmed sequence is not

given

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•  resorCng to gestures that bridge one reference frame to the other.

compensatory strategies

•  trial and error (since there are two

choices for the turns)

•  trying to define a rule without embracing the snail’s perspecCve (when the snail is upside down everything is opposite)

•  rotaCng the iPad or swivelling a pencil pretending it was the snail (changing his own perspecCve )

Mak-‐Trace appeared to help the student to “remain absorbed in a task for a period of Cme; … tolerate a period of confusion (with appropriate support);… use errors as a source of informaCon about what to try next”

(Russell, 1986, p. 103)

Documents

Juggling Reference Frames in the Microworld Mak-Trace: The Case of a Student with MLD