Warrington Paper

One advantage of teaching mathematics without telling the students the procedure/answers is that it promotes discourse among the classroom. For example when the students were stuck on 4 2/3 ÷ 1/3 if the teacher had told them straight away that the lone girl was correct, there would be no point in the other students arguing their ideas any longer. Also because she had to explain it against the whole classroom they all listened to her reasoning. They didn't simply wait for the teacher to back one answer. Another advantage I saw was that the teacher used the previous topic in order to introduce the new topic. She started with whole number division and worked her way to compound fraction division. It seemed like the students followed her transitions pretty well.

Some disadvantages of not telling the students the procedure/answers is that some students get lost with such little direction, and the material may get confusing without concrete terms and procedures. The teacher is obviously running the discussion in this classroom, but the students seem to dominate the discourse. Its hard to learn from peers because they aren't trained to teach, thus some students have an easier time listening to the teacher who can explain it with a confident voice. I know that when I'm in classes sometimes I disregard students telling me what they do because it just confuses me more. Oftentimes I need to have direction straight from the teacher and these students don't seem to get that firm direction. The other disadvantage I mentioned is varying terms. If there are not set names and rules math can get really confusing when moving into a different class. If the students in this class discover things such as slope or trig functions they will have a difficult time taking all their procedures and realizing that maybe what they do is less efficient than the new class, and they may take a while to relearn the real names. I didn't see examples of these disadvantages in the reading, but I'm not convinced that her class is always this perfect.

haley bly

TRYING to make sense of von Glasersfeld and Constructivism

When von Glasersfeld said constructing knowledge, he means the students have to create what they come to know. When a student listens to a lecture they do not take in exactly what the teacher said. The student filters the information and constructs it into knowledge based on how they saw the information through their OWN lens. Von Glasersfeld did not call this aquiring knowledge or gaining knowledge because the student doesn't actually take in what the teacher said. They take in what they thought they heard. It's usually wrong...or as Dr Seibert suggested, viable; however it is not correct knowledge because it is simply how that particular student interpreted what they heard.

If I believed in constructivism I would have a hard time seeing what my students gained from my class/lectures. So in order to work with that problem I would have my students write in math journals. At the end of each class period the students will take about 5 minutes to write what new things they learned and explain to me how they understood it. They can also ask questions etc. As a constructivist I don't believe students actually "aquire" what I have tried to teach. They construct their own knowledge so in order to better teach them I would use journals to properly assess what the students have constructed about the material. This way I can reclarify what was misunderstood and I can keep tabs on my students' knowledge.

Haley