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

2. Clarifications Clarifications About Narratives  About Narratives About Recursion  About Recursion 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).

3. Recursively Thinking Interpret computational as well as everyday phenomena as recursive Describe phenomena in a recursive manner Few Recursive Phenomena

4. An argument for narrative construction in (computer) science education In the case of recursive phenomena: recursive programming The experience of describing such phenomena in a recursive manner, might help in later construction of formal recursive descriptions (recursive programming). their Let the learners discuss and search for their ways to describe various recursive phenomena (using verbal, written, natural language). Let them tell their stories. Let them produce narratives.

5. The research  The field  The goal  The data 1 - Ethnographic observations in classes 2 - Written recursive descriptions (in Hebrew) recursively thinking To document and analyze class Discourse and students ’ narratives, focusing on constructing the ability of recursively thinking Israeli CS class (11 grade) DUET – Discourse-oriented learning environment D o uet

6. Food for thought … A carpet of level N is constructed of a square such that there is a smaller carpet of level N-1 at each corner. The basic carpet is of level 1, and it has a square shape. Draw a carpet of level 3.

7. Results – I Describing 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: Levels, Basis, N minus one

8. Shared (pink) terminology: Levels, Basis, N minus one Results – II Written 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”

9. The students make use of the same basic building blocks. But at the same time, each student built an individual, private construction from those basic building blocks. Results – III Written recursive descriptions – surprise? Three salient constructs of the “ recursive language ” – the agreed-upon constructs of the class genre N minus 1 BasisLevels

10. Some examples of written narratives “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 from these written narratives about constructing the ability of recursively thinking?

11. Results - IV Eight categories of private syntax 1 - 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

12. Example: Example: Syntax circumventing the recursive call “ The ladder of level N is composed of a basic ladder … and a ladder of level N-1 composed of a basic ladder with another basic ladder above it and below it ” Is he trying to “ escape ” ?

13. Example: Example: Recursive syntax with internal contradictions “ A ladder of level N is constructed of a longer ladder of level N-1 …. How does she “ tie ” the levels together?

14. Example: Example: Recursive syntax with name swapping “ A figure of level N … A basic level ladder look like |------| ” What is the importance of “ naming ” and how can it help in “ recursively thinking ” ?

15. Results - IV Eight categories of private syntax 1 - 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

16. Summary Result I+II Narratives using shared terminology Three categories (levels, basis, N-1) Result III+IV Narratives using private syntax Eight categories While participating in a DUET, computer science students tend to individually construct unique narratives of recursionTheirprivate syntax might hint at their different sorts of conceptions when dealing with recursion, at diverse stages of conceptual development, and at the processes by which learners construct the ability of recursively thinking. … No recursive programming yet! Narrative matters even in CS... While participating in a DUET, computer science students tend to individually construct unique narratives of recursion. Their private syntax might hint at their different sorts of conceptions when dealing with recursion, at diverse stages of conceptual development, and at the processes by which learners construct the ability of recursively thinking. … No recursive programming yet! Narrative matters even in CS... Is it only the case of recursion and computer science?

17. Food for thought … - The End A carpet of level N is constructed of a square such that there is a smaller carpet of level N-1 at each corner. The basic carpet is of level 1, and it has a square shape. Thanks for listening!