Prior to the start of this project, I interviewed the host teacher to learn about the students before I met them. In the past, I had noticed that students who struggle in traditional mathematics lessons often perform at higher levels when the same concepts are offered in a programming context where computational concepts and skills are more naturally applied. I wanted to know who these individuals might be in this grade 6 class. She described five students who, for various reasons, found math difficult. Three of these had learning disabilities in the area of language. They currently had Individual Education Plans (IEPs) with modifications for Language. One of these, in addition to having a modified Language program, worked toward modified expectations in Mathematics. The other two students did not have IEPs, but were flagged as having consistent difficulty in most academics.
All these students experienced success using computational concepts and skills in a programming environment. However, I would like to focus on one. Ryan was one of the five students flagged by the host teacher. She described him as being very disengaged from all things academic. He had a learning disability in the area of language, and it is possible that his consistent disengagement was a response to the difficulties that arose from the disconnect between traditional pedagogy and the ways in which he learns most effectively. She commented that he simply did not begin assigned tasks and that it was very difficult to get him to produce any work. She also noted that, on the rare occasion that he did produce evidence of learning, he never asked for assistance and he never shared his work.
All these students experienced success using computational concepts and skills in a programming environment. However, I would like to focus on one. Ryan was one of the five students flagged by the host teacher. She described him as being very disengaged from all things academic. He had a learning disability in the area of language, and it is possible that his consistent disengagement was a response to the difficulties that arose from the disconnect between traditional pedagogy and the ways in which he learns most effectively. She commented that he simply did not begin assigned tasks and that it was very difficult to get him to produce any work. She also noted that, on the rare occasion that he did produce evidence of learning, he never asked for assistance and he never shared his work.
The host teacher noticed a radical change in Ryan during our work with Scratch. He worked diligently on every assigned task, and he was eager to show his work to others. Although I was a relative outsider, he approached me many times for advice and coaching when he encountered problems that he could not solve by himself. His work demonstrated considerable ability to think computationally. He was among the first students to successfully create a code to generate a square spiral. Although it was long and labour intensive (he did not use a loop on this, his first attempt), his work demonstrated that he was able to think algorithmically about the problem and generate a sequence of steps to solve it. The fact that his code was long and labour intensive speaks to a resiliency that the host teacher had not previously seen from Ryan.
Early in the project, the host teacher had the occasion to have a telephone conference with Ryan’s mother. She learned that Ryan had voluntarily and enthusiastically shown his mother the work that he had done in Scratch to that point. This was a significant finding because, according to his mother, Ryan had not demonstrated any excitement for learning in recent years, and he would only share his work at home when prompted. This event speaks to the engagement that Ryan had throughout the project.
Early in the project, the host teacher had the occasion to have a telephone conference with Ryan’s mother. She learned that Ryan had voluntarily and enthusiastically shown his mother the work that he had done in Scratch to that point. This was a significant finding because, according to his mother, Ryan had not demonstrated any excitement for learning in recent years, and he would only share his work at home when prompted. This event speaks to the engagement that Ryan had throughout the project.
There was a great deal of student engagement connected with this project. Part of it had to do with the simple fact that it was different and fun. Every time we gathered to explore mathematical ideas in this environment, students were observed to be enjoying themselves. They were truly excited about what they and their peers created. However, the engagement ran deeper than that. What Papert says about errors in a typical math class versus errors made in a coding environment was witnessed in our project. All students made mistakes in their programming. However, their reaction to their errors was very different to what I have observed in regular math classes. First, the students received immediate feedback about their errors when they tested their programs and saw that they did not function as desired. In this environment, the students knew that a mistake had been made, whereas in a typical math class, errors often go undetected. Second, for most students, it was natural to address the error instead of ignoring it. The logical nature of computational thinking and the impartial nature of the programming platform created an environment in which errors did not threaten the student. They were, therefore, more naturally drawn to the correction of those errors.
For some students, the computational representation of mathematics in Scratch enabled them to perceive concepts in a new way. Ryan’s reaction to this project makes one wonder if his increased engagement is at least in part due to the fact that he was really seeing math, to a certain extent, for the first time when presented computationally. It is impossible to know on an individual level, but we do know that learner variation exists in every classroom and that multiple means of representation are required to ensure that all learners can perceive and comprehend the content. Who is to say that computational thinking is not the means that works best for Ryan? Certainly, the lack of language in Scratch provided greater accessibility for those in the class whose IEPs described difficulties with reading and writing. This characteristic, along with the absence of syntax and the easy-fit nature of the colour coded blocks, allowed many students to focus on what was important at the time: the mathematical concepts at play.
For some students, the computational representation of mathematics in Scratch enabled them to perceive concepts in a new way. Ryan’s reaction to this project makes one wonder if his increased engagement is at least in part due to the fact that he was really seeing math, to a certain extent, for the first time when presented computationally. It is impossible to know on an individual level, but we do know that learner variation exists in every classroom and that multiple means of representation are required to ensure that all learners can perceive and comprehend the content. Who is to say that computational thinking is not the means that works best for Ryan? Certainly, the lack of language in Scratch provided greater accessibility for those in the class whose IEPs described difficulties with reading and writing. This characteristic, along with the absence of syntax and the easy-fit nature of the colour coded blocks, allowed many students to focus on what was important at the time: the mathematical concepts at play.
The students in the grade 6 class had at least one opportunity to debug their intuition. At the beginning of the project, once they had learned how to draw a square and then refined the code with the use of a loop, they were challenged to create a triangle. As they had already learned that an equilateral triangle has three 60° angles, they confidently modified the code for a square by changing the 90 to a 60. There was considerable shock when the sprites on several computers drew half-hexagons. They were so sure that three 60° turns would yield a triangle. The scene unfolded very much as Papert might have predicted it would. The students did not give up, and they did not simply latch on to a procedure that they did not understand. This was probably due in large part to the fact that they had created an external model of their problem. That the model did not act as expected was an obvious problem that needed to be solved, but, because it was external to them, addressing it came at very little personal cost. Every student asked the same question: Why? And that question gave us the opportunity, as a class, to convert our perceptions of what had happened into a deeper understanding of angles in polygons.
In terms of action and expression, something that was evident in every session was the flexibility of the programming environment that is described by Israel et al (2015). Regardless of the assigned task, the class always generated multiple ways to represent it computationally. Multiple means of action and expression are inherent in computational thinking when the teacher provides a prompt of what to do, but does not prescribe the manner in which it is to be done. The prompts that were provided during this project were big enough that students were, once they had had significant exposure to computational concepts and skills, drawn to the use of abstraction, modularization, algorithmic thinking, testing and debugging, and data practices as means of coping with them. However, within the use of these ideas, they had considerable latitude, and they used it to create a wide variety of programs to respond to the same prompts.
Keeping within the principle of multiple means of action and expression, considerable student executive functioning was also observed throughout this project. It was previously noted that, at one point in the project, students were given the opportunity to develop projects based solely on their interests, and that most of these projects were very wide in scope. In order to succeed, students had to set goals (and, in some cases, modify them), develop plans and strategies, and monitor their progress. Their CT abilities assisted them with these executive functioning skills. In many cases, the students’ ability to modularize their projects helped them develop their plans and strategies. Breaking their big ideas down into the “mind-sized bites” that Papert mentions allowed the grade 6 students to see what needed to be done without being overwhelmed by the sheer size of their chosen tasks. As well, the testing and debugging skill was in constant use as a monitoring strategy. Students tended to run their programs directly after making changes. In this way, they were able to provide themselves with a constant stream of feedback that guided their progress.
Keeping within the principle of multiple means of action and expression, considerable student executive functioning was also observed throughout this project. It was previously noted that, at one point in the project, students were given the opportunity to develop projects based solely on their interests, and that most of these projects were very wide in scope. In order to succeed, students had to set goals (and, in some cases, modify them), develop plans and strategies, and monitor their progress. Their CT abilities assisted them with these executive functioning skills. In many cases, the students’ ability to modularize their projects helped them develop their plans and strategies. Breaking their big ideas down into the “mind-sized bites” that Papert mentions allowed the grade 6 students to see what needed to be done without being overwhelmed by the sheer size of their chosen tasks. As well, the testing and debugging skill was in constant use as a monitoring strategy. Students tended to run their programs directly after making changes. In this way, they were able to provide themselves with a constant stream of feedback that guided their progress.
References
Israel, M., Wherfel, Q. M., Pearson, J., Shehab, S., & Tapia, T. (2015). Empowering K-12 Students With Disabilities to Learn Computational Thinking and Computer Programming. TEACHING Exceptional Children, 48(1), 45-53. doi:10.1177/0040059915594790
Papert, S. (1980). Mindstorms: children, computers, and powerful ideas. New York: Basicbooks.
Israel, M., Wherfel, Q. M., Pearson, J., Shehab, S., & Tapia, T. (2015). Empowering K-12 Students With Disabilities to Learn Computational Thinking and Computer Programming. TEACHING Exceptional Children, 48(1), 45-53. doi:10.1177/0040059915594790
Papert, S. (1980). Mindstorms: children, computers, and powerful ideas. New York: Basicbooks.