Some advantages of teaching mathematics without giving the students specific algorithms or procedures or even correct answers include the students become more independent and they gain the ability to explain their reasoning to their peers in order to conclude when they believe they have found the correct answer. When the students are not thinking of algorithms to find the solutions, they have more freedom to find their own methods to solve the problem. There are many different strategies to find the solution, and this way the students find the one that makes the most sense to them. Furthermore, when the students find their own method of solving a problem, they also have some sort of justification as to why their method works. In Warrington’s class, the students would find a method to divide the fractions, and then they had to explain how they found their answer and why their answer is correct. The students work together to determine when a certain method works. Overall, the most important advantage of teaching mathematics this way is that the students rely on themselves to find the answer. They are confident in their own skills to find their solution and justify their reasoning.
Some disadvantages of teaching mathematics without specific algorithms or procedures is that this type of teaching requires a large amount of time and without giving the students the answers, they may never know when they have come to a correct solution. Warrington spent lots of time with her students, and they engaged in lengthy discussions in order to solve the problems involving fractions. So these types of classes would be extremely slow paced, and the student would not cover as much material in a class that teaches the algorithms. This could cause a problem if a student moved into a class that taught procedures. Although the student would have a deeper understanding of some of the things covered, the student would not be as far in the curriculum as this new class might be. Also, teaching mathematics without giving the students answers could cause confusion among the children. If one student’s method seems to work and make sense, and so does another student’s, but they have two different answers, this may cause confusion among the other students in the class. It might be better for the teacher to step in and explain which is right and way, so the ideas would be clear to the students, and the class could move past it without any students who would still be confused.
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Good job on your exlpanation of Warrington! I think you have explained correctly what Warrington was researching very well. I have no questions about it. I totally agree.
ReplyDeleteI really liked what you said about the advantage of letting the different strategies of finding a solution. If student are using their previous learning then they will be able to form solutions using which ever way is most comfortable to them, which is a big bonus on helping them enjoy mathematics.
ReplyDeleteYou touched on the fact that students are solving problems and that they are becoming more independent, so this "suggestion" may not be necessary. But I think one advantage I would have added more explicitly would be that through struggling and working through this assignment the students are developing their ability to think critically, and they are becoming better problem solvers. This is a crucial ability that needs to be taught in the classroom
I love how you built on the point that this type of learning leads to understanding by saying that the child is able to explain their knowledge to others, therefore increasing their understanding. I don't know that I would say individual methods are solely an advantage as it is easy for the student to get mislead by an improper method, but their learning is definitely expanded by their own personal thinking.
ReplyDeleteYou had very clear topic sentences and did a good job following the prompt.
ReplyDeleteI'm sure that time is an issue that has been brought to Warrington's attention on numerous occasions. Why do you think she continues to teach in this manner? Do you think her classes are behind other classes at the end of the year?
If two students have different answers, then I think the students would go back through both of their reasoning and find the place where the reasons don't quite sync up.