I am actually giving my Algebra 1 students their assessment over systems of equations tomorrow and found it interesting the author commented on this topic in her article.  I would love to give more open ended questions to my students, but I feel that they have enough trouble trying to answer the questions.  I will start giving a few in my warm-ups to introduce them to the idea of open-ended questions before I start putting them on their assessment.  If I could just get them to AT LEAST check their answers that would be a step in the right direction.  As someone stated in another post; it would be nice if they were seeing more open-ended questions earlier on in their math classes.  I do try to get my students to stop and at least say "Does this answer make sense??" but even that is hard to do.  They are so worried about getting the problems done; they don't seem to care if it is correct.

 

How do we convince our students that they need to just slow down and see if their answers make sense.  I feel this is where I need to start before I can really give them open ended questions.

 

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I think questioning their thinking helps somewhat with this. "Why do you think that answer is correct?" "How did you solve this problem?" "Does this remind you of any other type of problem you have seen before? How did you approach that problem?" I make it happen to question correct thinking as much if not more than erroneous thinking.
I like how you mentioned questioning correct thinking as well as erroneous thinking. When a student gives an answer I try to follow with, "tell me why", without giving any indication as to whether they are right or not. I think this also keeps other students on their toes and teaches them to not take for granted that the teacher is calling on the person who he/she knows has the correct answer which I have been guilty of in the past. It is amazing what we learn from wrong answers.
I wonder also about asking students to use another representation to justify the reasonableness of their solution. So if they used an equation, how might a table or graph confirm their solution, and what would a good explanation look like supporting that justification. (I guess I lumped a few things together here :)

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