In Mary Ann Warrington's paper about teaching division of fractions describes many advantages of teaching constructively. Teaching constructively, requiring the students to figure out mathematical procedures rather than simply teaching them, fosters inventive thinking to find the answer. This was demonstrated by the student who unintentionally used the invert and multiply rule. Another advantage she mentioned was the intellectual autonomy demonstrated by the students. When all of the students had agreed on an answer for a difficult problem, one girl refused to accept that answer because she did not think, or understand how, it could be correct.
Despite the benefits mentioned by Mrs. Warrington, there are also some disadvantages. A class room where everyone understands exactly what is going on is hard to imagine, probably because everyone has been that confused person at some point. For this reason, it seems likely that some of the students in the class room were just listening to other students and going by what they say rather than think about it for themselves. They may not understand and may be given the answers by the other students, which defeats the purpose of teaching constructively.
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I agree with the advantages you have stated, but I don't see that you have reasons as to why they are advantages. For instance, why is inventive thinking an advantage in mathematics? I do not see you have answered that question.
ReplyDeleteI think you give a great disadvantage in you second paragraph. I totally agree.
I really appreciate the topic sentences you have for your paragraphs. They completely match the contents and serve as an advanced organizer. I also agree with your advantages.
ReplyDeleteI think that you've identified a serious disadvantage in the second paragraph. I wonder, however, if this might be a disadvantage of many types of instruction. For example, if Warrington had just taught the procedures and then had students practice them, she would also have ended up with students who perform computations without thinking. Can you think of an instructional approach that would ensure that all of the students are thinking and reasoning?
Your structure was very easy to follow and understand, and you hit many of the main points. I really liked that. Though I did feel like I lacked information. I wanted more details and explanation about the advantages.
ReplyDeleteI think it is a great disadvantage that some students will still have no idea what is going on. A student cannot explain a concept as well as a teacher, in my opinion. However, I believe that in many classrooms students will be left behind. A teacher must try his or her best to teach to all students, but in large classrooms it is difficult to tailor to every students needs.
ReplyDeleteI really agree that it is hard to believe that all the students would have equally understood the problems. I think many would have just fallen in line with the more outspoken students. I disagreed with how teaching constructively was used. I think that could have many different meaning and I was a little confused by what you meant.
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