Papert and Sherin made clear that there a lot of opportunities to use programming to support math learning, from statistics to geometric constructions. I thought that it was interesting the Sherin was using traditional construction strategies to draw a perpendicular bisector. It seems like you could draw a bisector more purposefully with a program, because you could walk back exactly half the line, turn 90 degrees, and draw that line. I can see how you get a different understanding with traditional construction, but I wonder what that version buys us when we have new tools to think with now.
I also thought it was interesting how much Grover and Pea emphasize learning by doing for CT, but their pre-post assessments don't allow students to "do" in the same way that they would if they were working with the tool of the computer. They remind me a lot of the assessments we see in AP or college classes where students are asked to write out, predict the output of, or debug code without the tool of the computer that they have learned to think with. They artifact-based interviews seem to be more likely to provide a sense of how students see programming and what they can do with programming tools and what kinds of thinking they are engaging in. I wish I could see more of the rubrics they used for grading programming projects.
In terms of math projects, I could see having kids try to develop a tool to help them do a certain mathematical task efficiently and accurately, kind of like Fai's sliding number line for proportions. I think that would be best assessed with interviews based on their artifact where kids could explain why their tool was useful, how they built it, and what they wish it could do (that way you could get a sense of what they think the limitations are).
I could also imagine programming in scratch being really helpful for high school math, like algebra 2 and calculus, because you could write functions that show things like limits or areas under curve to get a sense of how those things can be built up iteratively or estimated and to get a sense of space for them. It could also be useful for projects like Megan's 2nd year talk with 1st graders - kids could use Scratch to define isometry as they rotate or reflect shapes and by moving shapes over each other to see if they are "exact copies" to check for congruence.
In all cases, I think that math knowledge could potentially be assessed with traditional math measures, but CT is harder to get at, because it is a way of thinking and not an output. I really think to assess CT you have to be watching what kids are doing and asking them about the choices they are making.
I also thought it was interesting how much Grover and Pea emphasize learning by doing for CT, but their pre-post assessments don't allow students to "do" in the same way that they would if they were working with the tool of the computer. They remind me a lot of the assessments we see in AP or college classes where students are asked to write out, predict the output of, or debug code without the tool of the computer that they have learned to think with. They artifact-based interviews seem to be more likely to provide a sense of how students see programming and what they can do with programming tools and what kinds of thinking they are engaging in. I wish I could see more of the rubrics they used for grading programming projects.
In terms of math projects, I could see having kids try to develop a tool to help them do a certain mathematical task efficiently and accurately, kind of like Fai's sliding number line for proportions. I think that would be best assessed with interviews based on their artifact where kids could explain why their tool was useful, how they built it, and what they wish it could do (that way you could get a sense of what they think the limitations are).
I could also imagine programming in scratch being really helpful for high school math, like algebra 2 and calculus, because you could write functions that show things like limits or areas under curve to get a sense of how those things can be built up iteratively or estimated and to get a sense of space for them. It could also be useful for projects like Megan's 2nd year talk with 1st graders - kids could use Scratch to define isometry as they rotate or reflect shapes and by moving shapes over each other to see if they are "exact copies" to check for congruence.
In all cases, I think that math knowledge could potentially be assessed with traditional math measures, but CT is harder to get at, because it is a way of thinking and not an output. I really think to assess CT you have to be watching what kids are doing and asking them about the choices they are making.
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