> On Sat, 25 Feb 1995, Michael Paul Goldenberg wrote: > > > ...define what YOU mean by "poorly stated." Finally, the burden is on > > you to show examples from the Standards. Like Mr. Saxon, you seem to be > > uncomfortable with the Standards, but you don't articulate very clearly > > what your objections are. For me to cite examples, let's just say that I > > `Poorly stated' means `unclear' or `ununderstandable'. > How can I have objections to something I don't understand ? > You claim that you understand ? But you cannot explain. > And don't mix me with Mr. Saxon. Andrei Toom > > > > Well, let's not jump to any conclusions about what I "cannot explain." I thought you might have the courtesy of citing one particular standard that you find "unclear or ununderstandable." Since you didn't, it seems reasonable to conclude that you feel such terms apply across the board. Hence, you should not object to MY selecting one for discussion. I'll choose #6 from the K-4 standards:
"6. The K-4 curriculum should make appropriate and ongoing use of calculators and computers."
As a stand-alone statement, this doesn't seem particularly opaque. I'd say it suggests that calculators and computers need to be employed in the K-4 mathematics curriculum in a manner which is appropriate to the age-level of students in those grades. By "appropriate" one might suggest that the state of the art in cognitive research should inform how calculators and computers are applied. Alternately, a more pragmatic approach might be employed. The key point, to my thinking, is that students are allowed, taught, and encouraged to use these devices in their exploration of elementary mathematics.
There is no need for my interpretation, however. Here is what follows immediately on p. 19 of the Curriculum and Evaluation Standards:
"Calculators must be accepted at the K-4 level as valuable tools for learning mathematics. Calculators enable children to explore number ideas and patterns, to have valuable concept-development experiences, to focus on problem-solving processes, and to investigate realistic applications. The thoughtful use of calculators can increase the quality of the curriculum as well as the quality of children's learning.
"Calculators do not replace the need to lean basic facts, to compute mentally, or to do reasonable paper-and-pencil computation. Classroom experience indicates that young children take a commonsense view about calculators and recognize the importance of not relying on them when it is more appropriate to compute in other ways. The availability of calculators means, however, that educators must develop a broader view of the various ways computation can be carried out and must place less emphasis on complex paper-and-pencil computation. Calculators also highlight the importance of teaching children to recognize whether computed results are reasonable.
"The power of computers also needs to be used in contemporary mathematics programs. Computer languages that are geometric in nature help young children become familiar with important geometric ideas. Computer simulations of mathematical ideas, such as modeling the renaming of numbers, are an important aid in helping children identify the key features of the mathematics. Many software programs provide interesting problem-solving situations and applications.
"The thoughtful and creative use of technology can greatly improve both the quality of the curriculum and the quality of children's learning. Integrating calculators and computers into school mathematics programs is critical in meeting the goals of a redefined curriculum"
Okay. Now what SPECIFICALLY is unclear here, Andrei? What is ununderstandable?
-michael paul goldenberg/University of Michigan
"Flaubert's vision of stupidity is this: Stupidity does not give way to science, technology, modernity, progress; on the contrary, it progresses right along with progress!" MILAN KUNDERA: 'Art of the Novel'