2x = 4x + 10

I would like to drag the 2x over to subtract from the 4x (or vice versa), but I can only drag the 2 individually or the x individually. (I don’t think 2=4 + 10/x is the most helpful? Oh, I can move the 4 in front of the x so it says x*4 now instead of 4x. Still not helpful.) How do you keep going?

]]>I am so happy to see these public discussions and get this great feedback. I think Dan has a great comment about the TIME required for teachers to learn how to use these tools. As I expect that these tools will become more commonplace, it makes me think that one way our industry can be of service to teachers would be to adopt some “standards” for gestures across the tools, so teachers would not need to learn different gestures for different tools. Do you think this is too ambitious? It might require third-party interface design experts, and instructional designers to drive to a standard.

And David is mostly correct when he wrote that I helped create Algebra By Hand™. Actually, it’s more accurate to say that I created Algebra By Hand. Every line of code. I did it as a labor of love for the minority students that I was volunteer tutoring. I wanted to give them the gift of advanced procedural fluency to improve their accuracy, increase their speed, and boost their confidence when doing simple algebra. I realized that other teachers might want to do the same, so I’ve published the work to make it available to others. So I think GM and ABH have very compatible objectives.

]]>“could we be doing harm by reinforcing the idea (which they may already hold) that math is about arbitrary symbolic manipulations? ”

My seniors who are a year behind have already have this idea that mathematics is just arbitrary symbol manipulation. I think GM could be used in an action/consequence manner to (perhaps) helps these kids make sense of something that has not made sense to them before.

“I’m also concerned that giving this perpetuates a pattern where certain groups of students are regularly exposed to ways of doing math that fail to engage them in deep mathematical exploration. ”

I think GM could be used to engage all students in deep mathematical explorations, not just kids who are behind or kids in IEPs, but especially those kids who are behind or are on IEPs

]]>Algebra By Hand is a great project, and I agree that it could potentially help build procedural fluency! We hope Graspable Math can do the same. One difference, that is both a strength and a caution, is that GM is a more open space, which means that students can also explore properties of equations and derivations, modify them, combine them with other representations (like graphs or geometric structures), and so on. That means that there are lots of interesting ways to use GM to do things that go beyond procedural fluency. http://www.kurtsoeser.at/2018/06/14/graspable-math/ has a great example of this kind of thinking (in German).

]]>I can solve problems undoing the operations, but taking care of the order. ]]>