The practice of teaching mathematics without telling students the procedures or even the right answers has many advantages. First, students’ interaction and exchange of ideas plays an essential role to the their acquirement of knowledge. The students are able to convince each other of their reasoning or why a certain answer is not feasible; additionally, they build off each others’ ideas in order to come up with the best solution. Secondly, the students are able to adapt and apply their knowledge. The students were able to use what they knew about whole number division and apply it to division of fractions. Furthermore, students modified or adapted their ideas during the class discussion. Next, students develop the skill of problem solving. When first figuring out division of fractions, they started by estimating, and then they used that knowledge in conjunction with their division of whole numbers knowledge in order to solve the problem. Lastly, students are taught to think of themselves. They come up with their procedures and methods for division of fractions, rather than relying on their teacher as the source for invert and multiply. Overall, this teaching method appears to have many advantages for the students.
However, there are also disadvantages associated with this teaching style. It takes longer for the class to go over the material than maybe a more traditional teaching style would. The students spent at least a week working with division of fractions; whereas, the invert and multiple rule could be taught easily in a day or two. As a result, it appears the students would not get through as much material in a year. Additionally, there is a lot of responsibility on the students. In Ms. Warrington’s class the students volunteered answers and participated in “intellectual bantering,” but if students did not participate or did not feel comfortable in the classroom, then this teaching style would be impossible. Therefore, you need willing students and a positive classroom in order for this style to be successful. Lastly, there is great responsibility on the teacher too. The teacher needs to know how the children are thinking, which will take a considerable amount of time and effort. Also, the teacher needs to know when to intervene in a discussion or just let the students struggle. If the teacher is not aware, then the students can easily make incorrect assumptions and get off the path of learning accurate mathematics. This teaching style does appear quite advantageous, but the disadvantages need to be considered too.
Subscribe to:
Post Comments (Atom)
I definitely agree with the idea that when students come together when trying to solve a problem they can build off of each other. If one student has some idea of how to do it and another student has a different idea, then when they come together they can learn from each other and build understanding.
ReplyDeleteThough I don't necessarily agree with the idea that students are effective all on their own. In Warrington's paper I got the feel that though her students were smart, only one of them got the answer right when given a particularly hard problem. They need some guidance and a way to check their answers I think.
I actually agree with a lot of what you said, but one of the main things was the disadvantage of how much time it would take to teach this way. You wouldn't be able to fit a years worth of material in if you taught everything this way, so you would have to pick and choose what you decided to teach this way in order to fit all the the material in.
ReplyDeleteI think that this way of teaching is a great way to entice students to participate, so I don't think that lack of participation would be a huge problem though I agree that it is certainly something that the teacher should watch for.
You did a great job following the prompt and using topic sentences.
ReplyDeleteThis method of learning does take more time initially, but it also saves time in some ways. Not as much time has to be spent reviewing and students can apply their knowledge to new situations.
I don't think that more responsibility for the students and teacher is a disadvantage. Students should come to class prepared to think. That's why they're in school.
I agree with you for sure that students are able to think for themselves. This is so true. I was thinking about this method, and putting myself in the place of those students and thought that if I had learned this way, I would be so much more confident thinking about mathematics for myself.
ReplyDeleteOne think that I think a little different on is the fact that spending more time on something is a disadvantage. Yes it is fact that they would have to spend a little longer on it, but they would never forget it, and they would completely understand it. I feel that this would probably be more of an advantage, at least to me.
Great job!