Introduction
Theory of Learning
Literature Review
Data and Methods
Research Questions
Conceptual Framework and Methodological Approach
Research Participants and Context
Interview Protocol and Data Coding
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Q1: Can you tell me a few ways that you might use what you learned last week to complement conventional physics instruction?
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Q2: Can you think of any kind of an activity developed by you or someone else that you think is a good example of integrating programming with physics learning?
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Q3: Is there any physics content that you see differently after this workshop — enhancements, contradictions, limitations in understanding?
Results
Example Data
...there’s a really good link between calculus [and CM] oddly enough, and, you know...and calculus-based physics. What I consistently find is my kids could take a derivative or take an integral, but they don’t understand what a derivative or an integral is. The way that computer science is presenting it is in this discrete way, which is the definition [of integrating or differentiating]. … [Students] don’t realize they’re thinking in terms of calculus…
...[students] look at episodic reads, instant one to instant two. Kids naturally do that. And, up until this point, we’ve ignored the fact that that’s the natural path for the kids, and we’re like, let’s do this cumulative[ly], because that’s how physics does it. We’ve covered up their impulse to do it episodically. ...it would require very careful thinking about how to honor students’ thinking and allows them to understand continuous functions the way physics does it. So [teaching with CM] was slightly less intuitive for me, but with some thought could be very well constructed.
“...I think there’s backlash against [computational modeling] because as teachers and as people trained in physics, we are very married to the idea of time-based equations, but I don’t think that’s actually the easiest way for a person new to the subject. The idea that these equations aren’t the only way, or even the best way. For example, trying to write an equation for a ball bouncing back and forth, using a time-based equation, is a nightmare situation, whereas if you have it position-based, it’s very simple. Even just giving students that example of the way that we have to look at most things works really well for some situations, but not as well for others, is something that I try to reinforce in my teaching.”
I would have pre-made simulations that students could manipulate certain variables of. They would have access to the code and explicit instructions to change certain parameters to see how the simulations would respond. After looking at the code, they might be asked to create their own code. I didn’t see creating their own code as something I would do in class, just because of time constraints. … There’s definitely some really good simulations made, but at the same time, there’s already existing simulations like through PhET and other resources.
It’s a jumping off point (for integration). That alone isn’t much of an integration. I feel like if you’re going to teach coding, that’s a good place to start. … Throwing an example beyond constant velocity at a student who doesn’t know physics and doesn’t understand computer science I think would be really challenging.
Indicators of Horizontal and Vertical Boundary Stretching and Boundedness
Code | Type of integration | Conceptual examples | Excerpts from teachers |
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V-X | Using CM to make more meaningful connections between physics concepts that are typically taught to algebra-based students. | Supporting students’ conceptual jumps from: ● Constant velocity → constant acceleration ● Rectilinear motion → parabolic motion → circular motion | “I think with the constant acceleration stuff that we were showing…about the differential form and the table and laying out a set of states and from those states finding a pattern and working backwards, without having to use a time parameter.” (Latresia) |
V-F | Using CM to go conceptually further with physics concepts that are not typically taught to algebra-based students due to time or math limitations. | Solving series of complex equations Solving non-analytical problems: ● Measuring air friction as a function of speed ● Measuring rocket height as a function of mass and propulsive force ● Determining the location of a particle in a gaseous mixture after a period of time | “For example, the trying to write an equation for a ball bouncing back and forth, using a time-based equation, is a nightmare situation, whereas if you have it position-based, it’s very simple.” (Marcos) |
V-C | Using CM to conceptualize physics concepts and practices in a new way. | Coordinating representations Determining how to solve a problem | “The Pyret and Bootstrap lends itself very nicely to motion maps. So, one of the things I plan on doing is have students generate motion maps using the Pyret coding, and then having students trying to figure out what the students did to get that map.” (Marcos) |
V-R | Using CM to model real practices of professional physics. | Explaining that physics with CM is how modern physics research is done. | “we have this way of showing kids how modern science functions” (Allison) |
Code | Type of integration | Conceptual examples | Excerpts from teachers |
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H-XC | Using CM to make explicit, specific connections between concepts in physics, computing, and/or math. | Supporting understandings about the following: ● States and systems ● Relationships among variables | “I would really like to see them strengthen their own math confidence and have a better understanding of functions. They focus too much on x as always x, and they don’t understand what that x represents. I’m thinking that computer science might help with that.” (Evan) |
H-XP | Using CM to make explicit, specific connections between practices in physics, computing, and/or math. | Support the following practices: ● Problem-solving ● Representing data ● Representing relationships. | “I’m attracted to the idea of having students take data from their own experiments and put it into tables and then use a function writing process to fit a curve to it rather than have it, Excel or Plotly or some other black box, fit a curve to it and the equation is what it is. So, I’m thinking that process, of writing their own equation, will help them understand what equations do and what they are for and how they get there.” (Jake) |
Code | Type of integration | Conceptual examples | Excerpts from teachers |
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B-AS | Using CM exclusively as an application or a supplement to normal teaching. | Intentionally teaching computing at the conclusion of normal instruction, such as at the end of a unit or at the end of the year if time remains, to reinforce concepts or skills already taught through traditional instruction. | “Right now, I could only see it is as supplemented. I couldn’t see how they could take that and build like a physics curriculum with Pyret…” (Andrew) |
B-CT | Using CM to serve a purpose other than to teach physics. | Helping students prepare for careers “other” than physics or to be technologically literate in general. | “For me it wasn’t so much how am I going to use these tools pedagogically but more where it was a chance for me to improve my own computer science ability and my own coding and this particular coding language.” (Henry) |
B-F | Teaching CM as fragmented concepts with little attention to helping students general computing ideas or skills. | Splitting the computing domain into what is necessary and what is not necessary for physics, or what is understood or not understood by the teacher. Emphasizing simulations as the end-goal of programming, rather than focusing on modeling itself. Emphasizing coding or context over programming. | “But I can imagine introducing the language briefly without writing the functions, just here’s a tool we can use to solve some basic math problems, like as an alternative to a graphing calculator.” (Rogers) |
Participant | Boundary-stretching score (average) | Implementation outcome during following academic year |
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Gina | 4 | Limited persistence Implemented materials at the start of the year only, owing to pressure from colleagues to remain coherent with curriculum and instruction of other physics teachers in the building. |
Connor | 1 | No persistence (?) Did not maintain communication with the program. |
Allison | 5 | Persistence Implemented materials as a supplement to existing content. Returned in 2017 as curriculum developer. |
Andrew | 1.5 | Limited persistence Adopted some materials, and returned in 2017 as curriculum developer, but did not demonstrate evidence of having implemented in own classroom. |
Evan | 1 | Limited persistence Adopted some materials. Expressed that had technology issues, but still implemented as much as possible, including many of the “unplugged” programming planning activities. Returned in 2017 as curriculum developer. |
Latresia | 3.5 | Persistence Adopted materials to the best of ability, and created a number of new resources. Returned in 2017 as curriculum developer |
Marcos | 5 | Persistence (super user) Returned in 2017 as curriculum developer, then in 2018 as workshop leader, supported national workshop presentation, got offered to author a book on differential elementary physics, and created additional units beyond the materials created by the cohort. |
Anisa | 4 | Persistence (super user) Returned in 2017 as curriculum developer, supported national workshop presentation. However, because not assigned a physics class, elected to teach drop-in units in colleague’s computer science and engineering classes. Maintained participation in community gatherings for three years. |
Sylvia | 3 | Persistence (super user) Returned in 2017 as curriculum developer, continually active in community (3 years in), regularly provides feedback on continuous development, expressed interest in being a workshop leader |
Jake | 3 | No persistence Did not complete the program. Left after the first week of the workshop. |
Henry | 4 | Persistence Returned in 2017 as curriculum developer |
Rogers | 4.5 | No persistence Became an administrator during the following academic year. |