This link has been bookmarked by 5 people . It was first bookmarked on 26 Nov 2007, by wfpiggie.
-
01 Nov 09
-
We live in an age of ambiguity where it is far more profitable to be fluent and verbose than it is to be articulate.
-
carefully
-
worded expositions as well as appreciation of carefully drawn distinctions,
-
If we emphasize the applications of school mathematics in a wide variety of problem solving situations two good things will happen; (1) the student will somehow learn the mathematics needed to solve these problems, and (2) seeing that mathematics is useful, he will be motivated to learn more mathematics.
-
To expect them to learn mathematics in the process of applying it is preposterous.
-
According to my experience, students must know the mathematics before they can apply it.
-
intrinsic values of school mathematics
-
an ideal arena for the application of logic to the thinking process
-
beauty of mathematics
-
natural language, gradually expanded to include symbolism and logic, is the key to both the learning of mathematics and its effective application to problem situations.
-
the use of appropriate language is the key to making mathematics intelligible.
-
hey get by on memory and facility until the cumulative effects of these deficiencies ultimately overwhelm them, and they leave mathematics in frustration and despair.
-
he most important use of problem situations in school mathematics is to ensure that the students can employ the formalized language of mathematics to demonstrate their understanding of the underlying theory
-
When explanations are inadequate or missing entirely, students attribute their resulting lack of understanding to the idea that there is something abstruse and forbidding about mathematics which they will never be able to understand.
-
For too long have we sheltered our students from explanations deemed to be too difficult for them.
-
This "mathematical mind" syndrome has hurt us enormously. It leads to the mistaken notion that mathematics is easy for those with this mysterious native ability and beyond the reach of those who lack it, no matter how hard they work.
-
We must focus on building proficiency in the formalized natural language required to apply the thinking process in mathematics.
-
The able ones are more likely to be repelled by a formless, flaccid curriculum in which no structure is discernible and which, as a consequence, provides no basis for understanding anything.
-
he teaching of mathematics should be regarded initially as an extension of the teaching of language.
-
" How do we know?" in the early grades (12) continue with the introduction of formal proof not later than grade 9 (perhaps with the aid of flow-diagrams) and culminate in the ability to read and write lucid essay proofs by grade 12.
-
Geometry with proof is the keystone of the secondary mathematics sequence. Geometry without a strong emphasis on proof offers little more than an unstructured collection of geomerric facts including many the student has already encountered in junior high school. Such a course is not worth the student's time.
-
In secondary school they need a well-defined program which develops their ability to read, write and think in the formalized, symbolic language of mathematics.
-
-
05 Oct 08
Megan Hayes-GoldingSpeech by former NCTM president Frank B. Allen, given in 1988.
-
07 May 08
-
26 Nov 07
Would you like to comment?
Join Diigo for a free account, or sign in if you are already a member.