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Narratives of recursion Narratives of recursion Dalit Levy Dalit Levy Technion – Israel Institute of Technion – Israel Institute of Technology Technology EARLI 2003, August 27 Padova, Italy
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Narratives of recursion Dalit Levy Technion – Israel Institute of Technology

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Narratives of recursion Dalit Levy Technion – Israel Institute of Technology. EARLI 2003 , August 27 Padova, Italy. Clarifications About Narratives About Recursion. Human beings have a universal tendency to tell stories about their experiences. - PowerPoint PPT Presentation
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Page 1: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Narratives of recursionNarratives of recursionDalit LevyDalit Levy

Technion – Israel Institute of TechnologyTechnion – Israel Institute of Technology

Narratives of recursionNarratives of recursionDalit LevyDalit Levy

Technion – Israel Institute of TechnologyTechnion – Israel Institute of Technology

EARLI 2003, August 27 Padova, Italy

Page 2: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

ClarificationsClarifications

About About NarrativesNarratives

About About RecursionRecursion

A detailed understanding of recursion is essential for CS students. That includes the ability to look at computational problems in a recursive manner.

Recursion is a core concept in any CS curriculum.

Human beings have a universal tendency to tell stories about their experiences.

“Narrative mode of thinking” (Jerome Bruner).

“Recursively thinking” (Roberts).

Page 3: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Recursively ThinkingRecursively Thinking

• Interpret computational as well as everyday phenomena as recursive

• Describe phenomena in a recursive manner

Few Recursive PhenomenaFew Recursive Phenomena

Page 4: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

An argument for narrative constructionAn argument for narrative constructionin (computer) science educationin (computer) science education

In the case of recursive phenomena:

The experience of describing such phenomena in a recursive manner, might help in later construction of formal recursive descriptions (recursive programmingrecursive programming).

Let the learners discuss and search for their their ways to describe various recursive phenomena (using verbal, written, natural language).Let them tell their stories. Let them produce narratives.

Page 5: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

The researchThe research

The fieldThe field

The goalThe goal

The data The data 1 - Ethnographic observations in classes2 - Written recursive descriptions (in Hebrew)

To document and analyze class Discourse and students’ narratives, focusing on constructing the ability of recursively recursively thinkingthinking

Israeli CS class (11 grade)DUET – Discourse-oriented learning environment DD oo uu ee tt

Page 6: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Food for thought…Food for thought…

AA carpet carpet of level N is constructed of of level N is constructed of a squarea square such that there is a smaller such that there is a smaller carpetcarpet of level N-1 at each corner. of level N-1 at each corner.

The basic carpetThe basic carpet is of level 1, and it is of level 1, and it has a square shape.has a square shape.

Draw a carpet of level 3.Draw a carpet of level 3.Draw a carpet of level 3.Draw a carpet of level 3.

Page 7: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Results – I Results – I Describing a given recursive object verballyDescribing a given recursive object verbally

Following the discourse analysis it became evident that a class genre was created and used to refer to recursive phenomena and to describe them verbally.

Shared terminology:Shared terminology:Levels, Basis, N minus oneLevels, Basis, N minus one

Page 8: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Shared Shared (pink)(pink) terminology: terminology:Levels, Basis, N minus oneLevels, Basis, N minus one

Results – IIResults – IIWritten recursive descriptions of a ladder figureWritten recursive descriptions of a ladder figure

“A ladder of level N is constructed from a ladder of level N-1. The basic ladder is defined as a horizontal line, which is continued both sides until the Nth level”

Page 9: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

The students make use of the same basic The students make use of the same basic building blocks. But at the same time, each building blocks. But at the same time, each

student built an individual, private construction student built an individual, private construction from those basic building blocks.from those basic building blocks.

Results – IIIResults – IIIWritten recursive descriptions – surprise?Written recursive descriptions – surprise?

Three salient constructs of the Three salient constructs of the “recursive language” – the agreed-upon “recursive language” – the agreed-upon

constructs of the class genre constructs of the class genre

N minus 1N minus 1BasisBasisLevelsLevels

Page 10: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Some examples of written Some examples of written narrativesnarratives

“A ladder of level N is constructed from the basic shape |----| - above it and below it there is the same basic shape”

Inductive analysis: What can we learn Inductive analysis: What can we learn from these written narratives about from these written narratives about constructing the ability of recursively constructing the ability of recursively thinking?thinking?

Inductive analysis: What can we learn Inductive analysis: What can we learn from these written narratives about from these written narratives about constructing the ability of recursively constructing the ability of recursively thinking?thinking?

Page 11: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Results - IVResults - IV

Eight categories of private syntaxEight categories of private syntax1 - Non-recursive syntax

2 - Seemingly recursive syntax

3 - Syntax circumventing the recursive call

4 - Non-stop recursive syntax

5 - Non-general recursive syntax

6 - Recursive syntax with internal contradictions

7 - Recursive syntax with name swapping

8 - Two-dimensional recursive syntax

Page 12: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Results - IVResults - IV

Eight categories of private syntaxEight categories of private syntax1 - Non-recursive syntax

2 - Seemingly recursive syntax

3 - Syntax circumventing the recursive call

4 - Non-stop recursive syntax

5 - Non-general recursive syntax

6 - Recursive syntax with internal contradictions

7 - Recursive syntax with name swapping

8 - Two-dimensional recursive syntax

Page 13: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

SummarySummary

Result I+IIResult I+II Narratives using shared terminology Narratives using shared terminology Three categories (levels, basis, N-1)

Result III+IVResult III+IV Narratives using private syntax Narratives using private syntax Eight categoriesEight categories

While participating in a DUET, computer science While participating in a DUET, computer science students tend to individually construct unique students tend to individually construct unique narratives of recursionnarratives of recursion. TheirTheir private syntaxprivate syntax might might hint at their different sorts of conceptions when hint at their different sorts of conceptions when dealing with recursion, at diverse stages of dealing with recursion, at diverse stages of conceptual development, and at conceptual development, and at the processes by the processes by which learners construct the ability of recursively which learners construct the ability of recursively thinking. thinking. … No recursive programming yet! … No recursive programming yet! Narrative matters even in CS...Narrative matters even in CS...

Is it only the case Is it only the case of recursion and of recursion and

computer science?computer science?

Page 14: Narratives of recursion Dalit Levy Technion  –  Israel Institute of Technology

Food for thought… - The EndFood for thought… - The End

AA carpet carpet of level N is constructed of a squareof level N is constructed of a square such that such that there is a smaller there is a smaller carpetcarpet of level N-1 at each corner. of level N-1 at each corner.

The basic carpetThe basic carpet is of level 1, and it has a square shape.is of level 1, and it has a square shape.

Thanks for listeningThanks for listening!!