No flames from me, Helen!! I very much appreciated your post. However, I have taught elementary school (primary level mostly) for 25 years and have encountered few students who were turned off to math--even when I taught traditional rote procedures almost exclusively. Since I began teaching math guided by the NCTM standards (about 7 years ago) I have encountered very few who didn't LOVE math. Now, I'll admit, I'm very enthusiastic about math and I know that comes across, but I think there are things that happen to turn off students as they get older--hormones probably first and foremost--but in my limited experience with middle school and high school math it seems to me that at that level there is more tendency on the part of teachers to believe that only a certain number of students will really be able to learn math. What do you think? (I know there are gobs of wonderful teachers like you who certainly don't hold with this belief, but aren't there even more who do?? Forgive my likely prejudice on this!) Cindy Chapman
---------- > From: Helen7502@aol.com > To: email@example.com > Subject: Re:Adding fractions > Date: Saturday, June 21, 1997 1:12 AM > > First, I admit I have read only the last few posts on this topic and do not > know how it got started. > > I have taught - over the last 18 years - students from very low ability > levels to very gifted mathematically. You cannot teach these students as if > they were all alike! I don't think anyone has implied that you can, but the > discussion appears to be over procedure v.s. understanding? > > High ability students tend to understand concepts almost regardless of > teaching method and average ability students seem to need to be taught both > procedure and concept and then shown how the two are related. Those who care > will advance to understanding and those who don't care will at least master > procedure. The low ability students MUST be taught procedure! They are so > used to failure that a conceptual approach is simply dismissed as one more > thing that is too hard to learn. A procedural approach gives them the > oportunity to master the contents and the mastery gives them a little more > confidence in their ability. That confidence opens the door to concepts but > that confidence is new and tender and EASILY destroyed. For the last several > years I have concentrated on the low ability student. Most of them actually > have ability but have no confidence and the confidence level is what > determines effort and success. > > I think we all need to recognize the fact that, unfortunately, most Americans > detest mathematics and are very intimidated by it. Most of our middle > students and high school students are seeking careers where they can - they > think - avoid mathematics. There is little we can say or do to convince them > otherwise. The only thing that works is developing mastery and competence. > The result is confidence and an opening mind. The math-hungry may be more > fun to teach, but those who do not want to be taught must still master some > mathematics. We mustn't be snobs about understanding at the expense of > reaching the math-avoiders. > > And, while I am on my soap box, let me throw this out about calculators. I > use them, my students use them, and I teach their use. However, I believe > that calculators have convinced an even larger proportion of the population > that mathematics - even at the arithmetic level - is a study far too > difficult for the average mind. I know I am dating myself, but I remember > that in pre-calculator days most students DID learn how to work with > fractions and decimals. Now, even my advanced students can't "do" fractions > and really don't have a clue that decimals and fractions are essentially the > same thing. Unfortunately, there is not time in the geometry curriculum to > re-address the arithmetic algorithms. > > Please, if you flame, flame gently!