There are many advantages to the style of teaching used by Warrington in this paper. Students were given the opportunity to explore the material with fellow students. This led to a lot of student interaction and the exchange of ideas in order to help them come up with the best solution. This helps the students to learn how to converse in mathematical discussions. Secondly, since they were not taught any new type of arithmetic they had to build off of the knowledge that they already had. By this time the students had a firm understanding of division and created understanding built on that solid foundation is good. Students also were able to adapted their ideas during the class discussion. Another advantage that I think is really good is that for me personally when I have struggled through the learning process and figured something out on my own then I have been able to remember and recall that knowledge much more easily than when I have simply had things explained to me. Lastly the students were able to strengthen their ability to solve problems. They started by estimating, and then they used this knowledge along with their knowledge of division of whole numbers to solve problems.
Along with these advantages comes many disadvantages that need to be considered. The first of which and probably the greatest disadvantage is that it took more time. If the students spend a week on this subject alone then it will cut into the amount of time that can be spent on other topics. The invert and multiply idea is very easy to teach very quickly. If every topic were taught with as much depth as the division of fractions was in Warringtons paper then you would not be able to cover nearly so much material in one year. Another possible disadvantage is that if this was not done correctly then students may never come to an understanding of how to come up with the proper solution. I know that there have been a few times in Math Ed 117 where I thought I had the right thought process and later found out that I didn't even have the right answer. So teachers teaching using the method discribed in Warringtons paper would need to know how to guide the students to coming up with the right answers and/or have a way of ensuring that the students were reaching the correct conclusion.
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You did a great job responding to the prompt and using clear writing.
ReplyDeleteIt does take longer to learn this way. But it does save time in other ways. Not as much time would have to spent reviewing and students can apply what they have learned to new situations. In this classroom, the teacher would have to carefully consider how much time should be spent on each given topic.
It's also important for the teacher to have a good sense of their students understanding. They would need a way to assess their reasoning.
I like what you said about students working together and how it could be an advantage to the way warringtone teaches. I myself have almost always been a lone when it comes to math work, but I think that their are strengths in numbers.
ReplyDeleteI am not entirerly sure if the longer time it takes for the students to learn math would nessessarily be a dissadvantage. Yeah they may not cover as much, but what if they convered a lot of material in a shorter amount of time and did not really understand it because the amount of material in a short time would just be an overload and they might only have a shallow understanding.
Overall good thought process!
I agree with what you said about how this kind of teaching is very time intensive. I feel like as teachers, this will be one of our hardest challenges-trying to decided what topics warrant more time in the classroom when we have so much to teach already. One thing that you didn't mention that concerns me is that when learning in a group setting, some students will let their peers take the lead and not participate and not gain a relational understanding. We would have to come up with a technique to combat this if we were using this teaching method in our classrooms.
ReplyDeleteI agree with one of the main disadvantages you stated - I think this type of teaching is harder to get right, and could be disasterous if done incorrectly. Having a wrong understanding is harder to correct than having no understanding at all!
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