In article <firstname.lastname@example.org>, email@example.com (Problem of the Week) wrote:
> In article <firstname.lastname@example.org>, email@example.com > (K.Ann Renninger) wrote: > > > RESEARCH SUMMARY: REPOST > > > > LEARNING AND MATHEMATICS > > > > PAPERT (1993) > > > > Quotes and Comments: > > > > Discussion can be used to bring an issue to > > mind and can then be followed by direct instruction; It can also > > be used following instruction to enable students to consolidate > > their "real" understanding of what has been presented. Discussion > > can also be used in evaluating how students have synthesized their > > understanding of a new skill in combination with prior skills. > > I have found it to be the case that the best way to test my understanding > of something is to discuss it, or even better try teaching it to somebody > else. It is this _discussion_ of mathematics that makes me want to be a > teacher as opposed to a mathematician who only gets to "do" math. What > are other ways in which we can test whether or not a student has learned > something? > > It seems to me that the method used most often now is to give written > examinations. Exams however tend to test a student's ability to DO > similar (if not essentially identical) problems. It was rare in my > education that I was forced to discuss concepts in math class. > In my school I have been working with teachers to implement a component of math journal writing within their math instruction in hopes that students will take time to reflect on their learning and teachers will get a glimpse into their students' understanding of math concepts. A whole class discussion in a class of 20-25 children typically means that only a handful of students really get to talk. Even in smaller groups there are students who do not take the risk of revealing their thoughts to their peers. I am hoping that the math journals will give a voice to those students who are not ready/comfortable discussing their thoughts in a larger group.