Blog #5 Response: Teaching Without Algorithms

There are a number of advantages that teaching math without teaching algorithms can bring. One that is outlined in Warrington's essay is that students learn to construct knowledge and find meaning in sophisticated areas that are difficult to truly understand. This is brought about through the careful creation of an environment where students are not afraid to discuss with each other and think for themselves. Students are allowed to be creative and are not "shackled by rules and conventions" that limit creativity. This was illustrated in the experience of Warrington giving the class the word problem about chocolate-covered peanuts.

Disadvantages of teaching math without teaching the algorithms are abundant. As Warrington presented each new question to the class, she would allow for as much discussion as was necessary for the students to get the right answers. If this was done in all classrooms, much material would have to be cut due to lack of time. I do not think cutting necessary topics from the curriculum is an ideal choice of action. A second disadvantage of teaching math without teaching the algorithms is that only the truly interested student will learn and participate. I do not feel every single student in this sort of classroom setting would be fully engaged or comfortable in thinking completely independently, and this could become frustrating and trivial for a number of students. Algorithms and easier to hold on to, and the less-creative mind may have an easier time getting through the course materials with them.

Blog #4 Response: Constructivism

I think what Glasersfeld meant by constructing knowledge is to take in what you hear and see through your own lens of experience and calling that knowledge. A teacher may try to teach a certain subject, but the student may not interpret what is being taught the way the teacher meant it to be. The student constructs their own knowledge based on their own experiences. It is not acquiring knowledge since it is not the information being presented is never quite the same as what is actually being stored in the brain.

If I believed in constructivism, I would teach in a way to rigorously interpret the understanding of my students. If they are all taking in information in different ways, I want to know how much of that is correct or incorrect. I will do this though frequent quizzes, homework assignments, and class activities to see what is really being understood correctly by my students. Possibly it would be wise to have a couple of student-teacher interviews each year so that I might talk with my students one-on-one to see how they are interpreting what is being taught.