Entry #5

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.

Entry #4

I think what Von Glasersfeld meant by constructing knowledge is that our knowledge is built upon things that happen in each of our lives and through prior experiences that we have encountered. One thing that Von Glasersfeld strongly believes is that all of the information we are given is filtered through our own personal experiences, so it is impossible for everyone to have the same knowledge and information. All knowledge is subjective, and there is no way to know if what we see is automatically correct. We draw conclusions from our previous experiences. We can only know if things are incorrect, and we come to know that things are incorrect when something from our prior experience contradicts what we think is true. All of our knowledge is constructed and filtered through our prior experiences.

Knowing that personal experiences help construct our knowledge tells me that I can never assume that the students have the same picture or concept in their head as I do in my head. As a teacher, I think it will be important to ask the students questions so they can describe to me what they are understanding so I can get a better idea of what they know. It is the student who takes in the information I give them and filters and conceptualizes it in their head. I need to make sure to take responsibility to work with the students and have them tell me what they are learning so I can try to make sure that we are all on the same page.