Pensamento Computacional como uma iniciativa heurística: soluções de estudantes sobre problemas de programação

Silva, Ricardo Scucuglia Rodrigues da; Gadanidis, George; Hughes, Janette; Namukasa, Immaculate Kizito

Ricardo Scucuglia Rodrigues da Silva Corresponding author: Ricardo Scucuglia Rodrigues da Silva- Unesp (Education) - Rua Cristóvão Colombo, 2265, São José do Rio Preto, SP, Brazil, 15054-000

Universidade Estadual Paulista Júlio de Mesquita Filho – Unesp, São José do Rio Preto, SP, Brasil. http://orcid.org/0000-0002-5810-2259, ricardo.scucuglia@unesp.br

http://orcid.org/0000-0002-5810-2259

George Gadanidis

Western University – UWO, London, ON, Canada. https://orcid.org/0000-0002-5982-6056, ggadanid@uwo.ca

http://orcid.org/0000-0002-5982-6056

Janette Hughes

University of Ontario Institute of Technology – UOIT, Oshawa, ON, Canada.https://orcid.org/0000-0002-3463-8382, janette.hughes@uoit.ca

http://orcid.org/0000-0002-3463-8382

Immaculate Kizito Namukasa

Western University – UWO, London, ON, Canada. https://orcid.org/0000-0001-7231-0671, inamukas@uwo.ca

http://orcid.org/0000-0001-7231-0671

Corresponding author: Ricardo Scucuglia Rodrigues da Silva- Unesp (Education) - Rua Cristóvão Colombo, 2265, São José do Rio Preto, SP, Brazil, 15054-000

Content	Description
Session 1 – (1 hour)	Students explored an app involving coding and arts (colors and sounds). That was their first experience and familiarization with a “simplified” tool of coding and a visual-artistic-aural way of exploring patterns. Based on the experimental actions with the app, the task was introduced to the students, in which they explored sequences of colors related to multiples of 3 (pages 1-2). They were also encouraged to create their own sequences of colors and variations of their sequences, creating different types of patterns of colors (pages 2-3).
Explored an introductory activity using the app available at http://researchideas.ca/wmt/c2a0.html Explored the “play with patterns” activity of the task (pages 1-3 of researchideas.ca/patterns/repeating-patterns-tutorial.pdf )
Session 2 – (1 hour)	That was students’ first experience with the Repeating Patterns computational-mathematical environment. They developed an initial familiarization with commands and functions of the parameters of the application. They were engaged in conjecturing connections between the computer code and the respective execution of the computer, that is, connections between representations (Borba & Villarreal, 2005Borba, M. C., & Villarreal, M. E. (2005). Humans-with-media and the reorganization of mathematical thinking: information and communication technologies, modeling, visualization and experimentation. New York: Springer.). For example, they discovered that commands such as <set x to #> and <set y to #> refer to the initial position of the sequence of shapes, that is, the visual computational display regarded a Cartesian plane. Other commands explored by the students were <set angle to #>, <set step size to #>, <set stamp rate to #>, <add color shape to pattern> and <repeat # times <do #>>. In this activity, students created and saved their first repeating pattern algorithm/image and solved three problems in puzzle #1.
Explored “play with code”, “predict, edit, and test” and “solve puzzles #1” activities of the task (pages 4-6 of researchideas.ca/patterns/repeating-patterns-tutorial.pdf )
Session 3 – (1 hour)	The main objective of this activity of the task was to engage students in the exploration of nested loops. Through this ability/resource, students were able to construct grid patterns, displaying a repeating pattern sequence of shapes 2-dimentionally (in a grid arrangement). Puzzle #2 is formed by 6 problems. Both groups of students had difficulty in solving problems #1 and #2. Actually, Grade-6 students were unable to present a satisfactory final solution. Undergraduate students presented solutions with some incoherence, mistakes and/or imperfections.
Explored the “create a grid pattern” and “solve puzzles #2” activities of the task (pages 7-9 of researchideas.ca/patterns/repeating-patterns-tutorial.pdf )
Session 4 – (1 hour)	In the last part of the task, the episode we selected as the one we discuss in this paper (Marshall, 1996Marshall, M. N. (1996). Sampling for qualitative research. Family Practice, 13(6), 522-526.). Students explored combined patterns using nested loops. That is, they elaborated and ran two algorithms simultaneously. A first algorithm (pattern 1) was given to them and they elaborated pattern 2 based on the first. One of the reasons we selected this episode was because it is a natural extension of using nested loops to create more elaborate repeating patterns. Another reason was because the nature of the final solutions between the two groups was qualitatively different and allowed us to connect to the goal of this paper—to understand how students at different levels engage with the same task. Within the last 1-hour session, the selected episode lasted about 20-30 minutes.
Explored the “combine patterns” and “solve puzzles #3” activities of the task (pages 10-13 of researchideas.ca/patterns/repeating-patterns-tutorial.pdf )

School Level	Participants in the research	Selected participants for the current report
Grade-6	3 pairs of students (11-12 year old)	1 pair (two 12 year old males)
Undergraduate	2 pairs of students (21-24 year old)	1 pair (21 year old female / 22 year old male)

Reflection and Debugging	Problem solving component	Heuristic endeavour
(actual/chronological transcription)	Problem solving component	(transcription related to analysis and exploration)
Teacher: Something is missing! Student C: The directions of the diagonals are wrong too. Student D: But we did not change anything in relation to the first pattern. Teacher: The position is correct, right? Student C: Only the first line of pattern 2 is right. Teacher: What if you start pattern 2 from another position? Student C: Let us change y to 100, change y by 40 and… Student D: … and put the sequence as blue, blue, yellow, yellow.	Analyzing: students’ explicit descriptions; actual configuration of parameters	Student C: Let us change y to 100, change y by 40 and… Student D: … and put the sequence as blue, blue, yellow, yellow.
	Exploring: students’ debugging actions related to the information (given/requested) and/or computer executed image.	Teacher: Something is missing! Student C: The directions of the diagonals are wrong too. Student D: But we did not change anything in relation to the first pattern. Teacher: The position is correct, right? Student C: Only the first line of pattern 2 is right. Teacher: What if you start pattern 2 from another position?

Solution	Reflection and Debugging	Description	Execution
First attempt of solution	Teacher: How did you solve the puzzle? Student A: First, we were trying to repeat the pattern starting from the left to the right. Then, we decided to start from the right to the left. Teacher: How did that work? Student B: In our first attempt, we figured out we had to change the position, that is, x and y. So, our first try was 500 and 295. Then, we figured out that to start from right to left, we had to change the angle from 0 to 180. Also, we changed the parameters at the repeating command like this [point out the finger to the parameters of the command], because the first patterns had 5 lines and the second had 4 lines. Teacher: Did that work? Student B: Not exactly, you see?
Final solution	Teacher: How did you fix it? Student A: We adjusted the initial x position to 660 and we changed the sequence of blocks from blue/circle, blue/circle, yellow/star, yellow/star to yellow/star, yellow/star, blue/circle, blue/circle. Do you see? We made the sequence of blocks opposite. Teacher: Great! Anything else? Student B: Yes! We also changed the x position within we repeat command to 660. Teacher: And why is the y position -40 within the repeat command? Student A: We did not know at first, but after trying a couple of times we discovered… Student A and Student B: …it is because the step size is 40. Teacher: Great! You guys figured out the puzzle!

Solution	Reflection and Debugging	Description	Execution
First attempt of solution	Teacher: Now you guys must construct this pattern, ok? Student C: Do I have to change this? [point at the change y by -40 command]. Teacher: You already made the pattern above, which goes until the middle. What do you guys have to change over there? Students explore the x and y position commands. Teacher: For each line, how long is it? Student C: What do you mean? Teacher: From the first to the second line, how is it changing? Student C and Student D: 40 [refers to step size]. Student D: We must consider 5 times 40, because we have 5 lines. Teacher: So, what happens with the sequence? Student C: It changes. Teacher: Right. It was blue, blue, yellow, yellow. And now…? Student C: We will try blue, yellow, yellow, blue. But look. It is not supposed to be 40 there [step size]. Each line takes 40. So, I think it is -200, because we want 5 times 40 below. Teacher: Well, are you sure you should change y by -200 within the repeat command? Student D: I see! We must change the original y position from 500 to 300. Student C: Let’s see what we get.
Second attempt of solution	Teacher: Something is missing! Student C: The directions of the diagonals are wrong too. Student D: But we did not change anything in relation to the first pattern. Teacher: The position is correct, right? Student C: Only the first line of pattern 2 is right. Teacher: What if you start pattern 2 from another position? Student C: Let us change y to 100, change y by 40 and… Student D: … and put the sequence as blue, blue, yellow, yellow.
Third attempt of solution	Student C: Oops! There is one 40 over the top. Student D: Let us try 140?
Final solution	Student C: it is still wrong. Look! What if we take off another 40? Teacher: Try it. Student D: Then one line will overlap another. Student C: Change y to 180. Student D and Student C: Beautiful!

First attempt of solving – Grade-6 students (10 min)
Exploring
Verifying
Analysing
Planning
Final solution – Grade-6 students (10 min)
Exploring
Verifying
Analysing
Planning

First attempt of solving – undergraduate students (8 min)
Exploring
Verifying
Analysing
Planning

Second attempt of solving – undergraduate students (6 min)
Exploring
Verifying
Analysing
Planning

Third attempt of solving – undergraduate students (4 min)
Exploring
Verifying
Analysing
Planning

Final solution – undergraduate students (4 min)
Exploring
Verifying
Analysing
Planning

[1] Corresponding author: Ricardo Scucuglia Rodrigues da Silva- Unesp (Education) - Rua Cristóvão Colombo, 2265, São José do Rio Preto, SP, Brazil, 15054-000

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Pensamento Computacional como uma iniciativa heurística: soluções de estudantes sobre problemas de programação

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