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• ### Anna Clark

Member
July 10, 2022 at 8:32 pm

I’m actually having a harder time thinking through this one! Here’s what I’ve got. I think my biggest question is are we only “graphing” students into the 5 stages on the curve if they are able to thoughtfully produce a correct answer? Is a student in stage 1 if they can’t reason through at all, or are they in the II, III, or IV quadrants?

Solving linear equations (example: 3x+2=8)

Stage 1: “I don’t know how to do this at all. Is the answer 5 because 3+2 is 5?”

Stage 2: “I know 3 times something plus two is 8, but I just have to find that something.” Student may use guessing and checking at this stage.

<font face=”inherit”>Stage 3: Similar to stage 2, students treat x like a blank but use inverse operations (though maybe not in a linear form showing the balancing of the equation.) They may know they need to subtract 2 then see what time 3 gives 8. </font>

<font face=”inherit”>Stage 4: Students use a more algorithmic approach by writing out the problem and showing their work through inverse operations and “zeroing out” the two on the left, then “dividing off” the 3 on the left, but may not know why it works.</font>

<font face=”inherit”>Stage 5: Student knows they need to keep the equation balanced in order for the equivalence statement to remain true, so they use this language when explaining their process. </font>