At the end of the project, all 24 students provided feedback on the experience by completing an anonymous online survey. There were eight questions in total. Questions 1, 3, 5, and 7 asked students to choose from five options (strongly agree, somewhat agree, neither agree nor disagree, somewhat disagree, strongly disagree) to voice their feelings about specific statements related to the project. The four statements were:
The first statement was intended to elicit student commentary on the computational skills and concepts they had used over the fifteen sessions. The other three are connected to the three UDL principles and were included to gain insight into the extent to which students felt that CT and coding made mathematics more accessible. After each of these four questions, students were asked to provide reasons for their choices (questions 2, 4, 6, and 8).
- Coding has changed the way I think about and approach problems.
- Coding has helped me feel more engaged in my learning.
- Seeing math concepts demonstrated in Scratch has helped me understand them better.
- Coding is a good option for expressing my understanding of math ideas.
The first statement was intended to elicit student commentary on the computational skills and concepts they had used over the fifteen sessions. The other three are connected to the three UDL principles and were included to gain insight into the extent to which students felt that CT and coding made mathematics more accessible. After each of these four questions, students were asked to provide reasons for their choices (questions 2, 4, 6, and 8).
1. Choose the option that best reflects your feelings about the statement below.
Coding has changed the way I think about and approach problems.
2. Please support your choice for the question above by providing a reason for your answer.
All 24 students answered question 1. The class results are shown in the table to the right. The majority of the class indicated that the use of coding with Scratch had an impact on the way they viewed and solved problems. 14 out of 24 students, or 58% of the class, agreed to some extent with this statement. One student explained his/her choice by writing, “because there is always another way in code or another block.” It is difficult to know exactly what a student’s comment means on an anonymous survey. It is possible that this student refers to the flexibility of Scratch, and that this flexibility has enabled him/her to envision multiple approaches to problems, or that learning about CT has given him/her another mode of thinking with which problems can be addressed. Another student wrote, “I agree because when your code does not work you have to debug [it] and this requires you to look over your code and work through [it].” This student is clearly referring to the importance of testing and debugging as components of CT. One student commented directly on his/her thinking: “Sometimes I overthink a lot of stuff and coding the computer does exactly what I tell it to and that kind of [makes] me not overthink the problem.” Again, it is difficult to determine the student’s exact meaning without an interview, but he/she appears to mean that the use of computational skills and concepts within a coding environment allows him/her to approach and solve problems with greater clarity (i.e., without overthinking them). Perhaps he/she is alluding to the logical, algorithmic thinking that is required to communicate instructions to a computer. If so, it would be interesting to see this student transfer this type of thinking outside of the coding environment.
Coding has changed the way I think about and approach problems.
2. Please support your choice for the question above by providing a reason for your answer.
All 24 students answered question 1. The class results are shown in the table to the right. The majority of the class indicated that the use of coding with Scratch had an impact on the way they viewed and solved problems. 14 out of 24 students, or 58% of the class, agreed to some extent with this statement. One student explained his/her choice by writing, “because there is always another way in code or another block.” It is difficult to know exactly what a student’s comment means on an anonymous survey. It is possible that this student refers to the flexibility of Scratch, and that this flexibility has enabled him/her to envision multiple approaches to problems, or that learning about CT has given him/her another mode of thinking with which problems can be addressed. Another student wrote, “I agree because when your code does not work you have to debug [it] and this requires you to look over your code and work through [it].” This student is clearly referring to the importance of testing and debugging as components of CT. One student commented directly on his/her thinking: “Sometimes I overthink a lot of stuff and coding the computer does exactly what I tell it to and that kind of [makes] me not overthink the problem.” Again, it is difficult to determine the student’s exact meaning without an interview, but he/she appears to mean that the use of computational skills and concepts within a coding environment allows him/her to approach and solve problems with greater clarity (i.e., without overthinking them). Perhaps he/she is alluding to the logical, algorithmic thinking that is required to communicate instructions to a computer. If so, it would be interesting to see this student transfer this type of thinking outside of the coding environment.
Ten students did not agree with the statement. Of these, only 3 out of 24 students, or 13%, disagreed with it. They all tended to concur with one student who wrote, “I have not used what I have learned in coding to approach problems in a different way.” This is an interesting statement. He/She does not say that it is not possible to approach problems in a way more akin to how one might program computers, only that he/she has not done so. As our project did not include the explicit transfer of CT skills and concepts to non-programming problem solving situations, it may not have occurred to the student that these ideas could be applied elsewhere. This raises the question of how such students might have responded if the study had included a final module wherein CT was applied in various settings. However, this is a question for a future study.
3. Choose the option that best reflects your feelings about the statement below.
Coding has helped me feel more engaged in my learning.
4. Please support your choice for the question above by providing a reason for your answer.
All 24 students answered question 3. The class results are shown in the table to the right. The purpose of these questions was to determine the extent to which the students felt that CT and coding offered them multiple means of engagement. The numbers are quite compelling. 20 out of 24 students, or 83%, agreed that they felt engaged in their learning during the project. Only 2 students, or 8% of the class disagreed. It must be noted that one of the respondents supported his/her choice by writing, “because I don’t like work.”
Several students supported their agreement with the statement on the grounds that coding was interactive. One such student wrote, “I enjoy coding because it is different than textbook work and it is more hands on than just regular worksheets.” The fact that using CT skills and concepts in a programming setting requires the user to be more active-minded than “textbook work” does appealed to several students. One student pushed this idea further by writing, “I believe that it does because coding added an ability to control what your math does rather than your hard work not leading to an accomplishment.” There are two important ideas in this explanation. First, the student recognizes that his/her own agency (“ability to control what your math does”) is important. The ability to make choices that direct his/her use of the math provides engagement. Second, he/she indicates the importance of a purpose behind the application of mathematics. His/Her use of CT skills and concepts led to feelings of accomplishment because they were directed to a specific purpose. We are left to infer that he/she does not feel the same way about other math work done in class.
Coding has helped me feel more engaged in my learning.
4. Please support your choice for the question above by providing a reason for your answer.
All 24 students answered question 3. The class results are shown in the table to the right. The purpose of these questions was to determine the extent to which the students felt that CT and coding offered them multiple means of engagement. The numbers are quite compelling. 20 out of 24 students, or 83%, agreed that they felt engaged in their learning during the project. Only 2 students, or 8% of the class disagreed. It must be noted that one of the respondents supported his/her choice by writing, “because I don’t like work.”
Several students supported their agreement with the statement on the grounds that coding was interactive. One such student wrote, “I enjoy coding because it is different than textbook work and it is more hands on than just regular worksheets.” The fact that using CT skills and concepts in a programming setting requires the user to be more active-minded than “textbook work” does appealed to several students. One student pushed this idea further by writing, “I believe that it does because coding added an ability to control what your math does rather than your hard work not leading to an accomplishment.” There are two important ideas in this explanation. First, the student recognizes that his/her own agency (“ability to control what your math does”) is important. The ability to make choices that direct his/her use of the math provides engagement. Second, he/she indicates the importance of a purpose behind the application of mathematics. His/Her use of CT skills and concepts led to feelings of accomplishment because they were directed to a specific purpose. We are left to infer that he/she does not feel the same way about other math work done in class.
Other students brought up the idea of choice as being important to their engagement. One student wrote, “We also have a little bit of freedom too,” while another wrote, “Coding makes me feel engaged because you get to make your own code and discover what happens when you add or take away commands.” These statements reference the idea of student-centred learning. In a true UDL classroom, the teacher sets broad parameters and allows the students to make choices that will enable them to achieve the learning goal(s). The very nature of computational thinking mimics this process. Goals are set, and the students, in the programming environment and with the use of computational thinking skills and concepts, choose what they need to “discover” the math and achieve the goals.
Several student comments provide evidence of elevated mindset concerning mathematics. One child wrote, “I don’t like math a lot and I love using Scratch. It is the fun way of doing math. I learned more geometry and angles.” This statement may indicate the beginning of a change this student’s mindset. Perhaps he/she is in the process of discovering that it is the way math has been taught, and not the subject itself, that he/she dislikes. And perhaps this growing understanding will make math less threatening in his/her eyes. If so, further use of CT and coding to learn math may help increase his/her engagement with the subject. Another student wrote, “I feel smarter every time I do coding.” This individual certainly developed positive feelings for the subject throughout this project. Finally, one student indicated a desire to transfer new knowledge from one context to another by writing, “Now that I learned new math from coding I look forward to trying to find out questions with the same math as coding.”
Several student comments provide evidence of elevated mindset concerning mathematics. One child wrote, “I don’t like math a lot and I love using Scratch. It is the fun way of doing math. I learned more geometry and angles.” This statement may indicate the beginning of a change this student’s mindset. Perhaps he/she is in the process of discovering that it is the way math has been taught, and not the subject itself, that he/she dislikes. And perhaps this growing understanding will make math less threatening in his/her eyes. If so, further use of CT and coding to learn math may help increase his/her engagement with the subject. Another student wrote, “I feel smarter every time I do coding.” This individual certainly developed positive feelings for the subject throughout this project. Finally, one student indicated a desire to transfer new knowledge from one context to another by writing, “Now that I learned new math from coding I look forward to trying to find out questions with the same math as coding.”
5. Choose the option that best reflects your feelings about the statement below.
Seeing math concepts demonstrated in Scratch has helped me understand them better.
6. Please support your choice for the question above by providing a reason for your answer.
All 24 students answered question 5. The class results are shown in the table to the right. These questions were intended to elicit the students’ thoughts about how the use of CT and coding enabled them to perceive and comprehend mathematical concepts. 16 out of 24 students, or 67% of the class, felt positive about the representation of math in this manner. Although one-third of the class did not share this opinion, only one student disagreed with the statement. His/Her explanation (“Scratch doesn’t help me with math”) does not provide any insight to his/her reasoning.
Of the seven students who chose “Neither Agree nor Disagree,” two indicated that they understand math concepts well enough outside of the CT/coding environment. Another stated that the work done in the project did not increase his/her understanding and that Scratch is “just a different way of presenting math concepts.” These comments speak to the key UDL idea of learner variation. Although learning mathematics through a CT/coding approach may work for many students, neuroscientists know that there is not a single approach that will work for everyone. It makes sense that some students would profess a preference for a different mode of representation. Another student from this group wrote, “I believe that it has and hasn’t helped me with math concepts because Scratch to me was more a tool to unleash what I had learned previously.” Once again, it is difficult to extract exact meanings from short responses, but it appears that this student feels that he/she already knew much of the content that we worked with throughout the project. The phrase “unleash what I had learned previously” is a curious one. Perhaps this student sees the value of CT in a coding environment as being more about how he/she might express his/her understanding than it is about perceiving and comprehending content.
Seeing math concepts demonstrated in Scratch has helped me understand them better.
6. Please support your choice for the question above by providing a reason for your answer.
All 24 students answered question 5. The class results are shown in the table to the right. These questions were intended to elicit the students’ thoughts about how the use of CT and coding enabled them to perceive and comprehend mathematical concepts. 16 out of 24 students, or 67% of the class, felt positive about the representation of math in this manner. Although one-third of the class did not share this opinion, only one student disagreed with the statement. His/Her explanation (“Scratch doesn’t help me with math”) does not provide any insight to his/her reasoning.
Of the seven students who chose “Neither Agree nor Disagree,” two indicated that they understand math concepts well enough outside of the CT/coding environment. Another stated that the work done in the project did not increase his/her understanding and that Scratch is “just a different way of presenting math concepts.” These comments speak to the key UDL idea of learner variation. Although learning mathematics through a CT/coding approach may work for many students, neuroscientists know that there is not a single approach that will work for everyone. It makes sense that some students would profess a preference for a different mode of representation. Another student from this group wrote, “I believe that it has and hasn’t helped me with math concepts because Scratch to me was more a tool to unleash what I had learned previously.” Once again, it is difficult to extract exact meanings from short responses, but it appears that this student feels that he/she already knew much of the content that we worked with throughout the project. The phrase “unleash what I had learned previously” is a curious one. Perhaps this student sees the value of CT in a coding environment as being more about how he/she might express his/her understanding than it is about perceiving and comprehending content.
Several students who agreed with the statement highlighted the fact that the visual nature of the coding environment made the math easier to see, and therefore, to learn. One student provided greater detail by writing, “I strongly agree with this statement because it shows your learning and it’s way easier to see your mistake.” This student appears to appreciate the fact that he/she gets instant feedback when he/she makes an error. This means he/she uses the CT skill of testing and debugging often in the coding environment. In this statement, he/she links these CT skills to the UDL principle of multiple means of representation.
7. Choose the option that best reflects your feelings about the statement below.
Coding is a good option for expressing my understanding of math ideas.
8. Please support your choice for the question above by providing a reason for your answer.
All 24 students answered question 7. The class results are shown in the table to the right. These questions assess the students' feelings about the extent to which computational thinking in a programming environment provides them with multiple means of action and expression. Once again, 16 students, or 67% of the class agreed to some extent with the statement whereas 8 students, or 33% of the class, did not feel the same way.
The explanations that accompanied some of the “Neither Agree nor Disagree” votes are interesting. One child wrote, “it depends on what you are doing in math.” He/She seems to see the value of using a programming platform to express his/her understanding of some mathematical topics, but not others. Perhaps if he/she were given coding as one of several means of action and expression, he/she would select it for some topics, but would select other modes of action and expression for others. Two other members of this group wrote that coding “sometimes” helps them express their mathematical understanding, but that the real value comes from making original codes “to help others understand.” Perhaps they misunderstood the original question; if writing a code is a good way to help others understand a mathematical concept, and the writer of the code understands that concept, then would it not follow that the student views coding as an effective means to express that understanding so that others can perceive it?
Coding is a good option for expressing my understanding of math ideas.
8. Please support your choice for the question above by providing a reason for your answer.
All 24 students answered question 7. The class results are shown in the table to the right. These questions assess the students' feelings about the extent to which computational thinking in a programming environment provides them with multiple means of action and expression. Once again, 16 students, or 67% of the class agreed to some extent with the statement whereas 8 students, or 33% of the class, did not feel the same way.
The explanations that accompanied some of the “Neither Agree nor Disagree” votes are interesting. One child wrote, “it depends on what you are doing in math.” He/She seems to see the value of using a programming platform to express his/her understanding of some mathematical topics, but not others. Perhaps if he/she were given coding as one of several means of action and expression, he/she would select it for some topics, but would select other modes of action and expression for others. Two other members of this group wrote that coding “sometimes” helps them express their mathematical understanding, but that the real value comes from making original codes “to help others understand.” Perhaps they misunderstood the original question; if writing a code is a good way to help others understand a mathematical concept, and the writer of the code understands that concept, then would it not follow that the student views coding as an effective means to express that understanding so that others can perceive it?
Two students disagreed with the idea that coding is a good option for expressing mathematical understanding. One of these wrote, “it doesn’t express my understanding of math ideas,” without explaining why. The other student wrote “because it does not feel like math.” This is an interesting statement to justify one’s disagreement with the statement in question 7. It seems that this student has a deep-seated preconceived idea of what math should “feel” like. One wonders if he/she could not reconcile the work done during our 15 sessions with his/her vision of mathematics in school, and lessened the value of the former, in his/her mind, as a consequence.
Students agreed with the statement for a wide variety of reasons. Some students highlighted the interactive and visual nature of Scratch. Others made general statements about coding being able to express math more effectively, but did not provide specific reasons or examples. One student wrote, “I can show what I know a lot more now.” Another wrote, “I can show how I feel and make things with my understanding.” This is particularly interesting statement as it mirrors Papert’s constructionism, a learning theory that states that learning happens most effectively when people create actual models in the real world. This student identifies a learning preference that involves the building of models exterior to himself/herself. Yet another child who strongly agreed with the statement described how CT and coding allow for multiple strategies and solutions for a single question.
Students agreed with the statement for a wide variety of reasons. Some students highlighted the interactive and visual nature of Scratch. Others made general statements about coding being able to express math more effectively, but did not provide specific reasons or examples. One student wrote, “I can show what I know a lot more now.” Another wrote, “I can show how I feel and make things with my understanding.” This is particularly interesting statement as it mirrors Papert’s constructionism, a learning theory that states that learning happens most effectively when people create actual models in the real world. This student identifies a learning preference that involves the building of models exterior to himself/herself. Yet another child who strongly agreed with the statement described how CT and coding allow for multiple strategies and solutions for a single question.