This is the second in a series of posts concerning questions, concerns, issues related to the 1989 NCTM publication "Curriculum and Evaluation Standards for School Mathematics." All questions are numbered consecutively for later reference purposes. If you have missed any and want them, just e-mail me direct and I'll send them your way.
Ron Ward/Western Washington U/Bellingham, WA 98225
4. It is clear from the Introduction that creating a vision of what it means to be "mathematically literate" is CENTRAL to this document. Literacy items permeate the "new societal goals" on pages 3 & 4, and, in the discussion of "new goals for students," the writers declare: "Educational goals for students must reflect the importance of mathematical literacy." It is interesting to COMPARE what this document says about literacy with the message of Everybody Counts [I've included an excerpt later on in this post *]. It is also interesting to note that relatively little is said about literacy in the Professional Standards ["Being mathematically literate includes having an appreciation of the value and beauty of mathematics as well as being able and inclined to appraise and use quantitative information.], and literacy is not really discussed per se in the Assessment Standards.
A related concept is "mathematical power," defined in the C&E document on page 5. It is worth comparing that definition with a brief one from Everybody Counts ["A capacity of mind of increasing value in a technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives"]. Later in this post I also include some statements about mathematical power from both the Professional Standards and the Assessment Standards.**
I am interested in the CONNECTION between math literacy and mathematical power. The C&E Standards gives a very brief comment about this on page 6. How do YOU see them as related? Does your awareness of the meaning of either one affect the way you prepare your students? Can you think of any way in which the discussions about literacy need to be updated? [both the C&E Standards and Everybody Counts came out about seven years ago.]
----------------------------------------------------------------- *Here is the LITERACY discussion from Everybody Counts that I referred to earlier. The writer is Lynn Arthur Steen, the sponsor is the National Research Council, and the publisher is National Academy Press.
"To function in today's society, mathematical literacy--what the British call 'numeracy'--is as essential as verbal literacy. These two kinds of literacy, although different, are not unrelated. Without the ability to read and understand, no one can become mathematically literate. Increasingly, the reverse is also true: without the ability to understand basic mathematical ideas, one cannot fully comprehend modern writing such as that which appears in the daily newspapers. Numeracy requires more than just familiarity with numbers. To cope confidently with the demands of today's society, one must be able to grasp the implications of many mathematical concepts--for example, chance, logic, and graphs--that permeate daily news and routine decisions. Literacy is a moving target, increasing in level with the rising technological demands of society. Indeed, there is some evidence that the decline in reading comprehension scores over the last several decades is due in part to the growing mathematical content of what one is required to read. It is not just computer manuals or financial reports that require an understanding of mathematical ideas; so do reports of political polls, debates about AIDS testing, and arguments over the federal deficit. Even Supreme Court decisions resemble mathematical arguments whose subject matter is law rather than numbers; often, legal cases rest as much on probabilistic inferences (for example, DNA fingerprinting, fiber analysis) as on direct evidence. Functional literacy in all its manifestations--verbal, mathematical, scientific, and cultural--provides a common fabric of communication indispensable for modern civilized society. Mathematical literacy is especially crucial because mathematics is the language of science and technology. Discussion of important health and environmental issues (acid rain, waste management, greenhouse effect) is impossible without using the language of mathematics; solutions to these problems will require a public consensus built on the social fabric of literacy. The study of mathematics can help develop critical habits of mind--to distinguish evidence from anecdote, to recognize nonsense, to understand chance, and to value proof. Citizens in a democracy must recognize that change is a process with expected regularities; that order can beget disorder (as in turbulence) and vice versa (as in statistical experiments); that similar mathematical models can represent different phenomena (for example, patterns of growth in biology, economics, and chemistry); and that simple models can clarify complex systems (as in linear models of economnic systems), even though simplistic analysis can result in misleading interpretations. Citizens who are bombarded daily with conflicting quantitative information need to be aware of both the power and limitations of mathematics. The great majority of American children spend most of their school mathematics time learning only practical arithmetic. Few retain much of what they learn about geometry; fewer still learn anything about chance. Secondary education is particularly devoid of exposure to modes of mathematical thought required for intelligent citizenship. Even colleges and universities seem unable to infuse appropriate mathematical ideas into liberal education. There is no consensus whatsoever on a collegiate mathematics curriculum for students outside the preprofessional programs where mathematics serves a well-defined yet strictly utilitarian purpose. Rarely does mathematics contribute as it should to liberal education, to the honing of values, and to effective citizenship." [pages 7-9]
----------------------------------------------------------------- ** Some additional comments about MATHEMATICAL POWER from the Professional Standards:
"Mathematical power includes the abilit y to explore, conjecture, reason logically; to solve nonroutine problems; to communicate about and thru mathematics; and to connect ideas within mathematics and between mathematics and other intellectual activity. Mathematical power also involves the development of personal self-confidence and a disposition to seek, evaluate, and use quantitative and spatial information in solving problems and in making decisions. Students' flexibility, perseverance, interest, curiosity, and inventiveness also affect the realization of mathematical power."
and from the Assessment Standards:
"... the phrase "mathematical power" has been used to capture the shift in expectations for all students. The shift is toward understanding concepts and skills;drawing on mathematical concepts and skills when confronted with both routine and nonroutine problems;communicating effectively about the strategies, reasoning, and results of mathematical investigations; and becoming confident in using mathematics to make sense of real-life situations. It is away from mastering a large collection of concepts and skills in a particular order. In this document, the terms 'know,' 'know how,' 'be able to do,' and 'disposition toward' are used as indicators for the complexity of 'mathematical power.'"
Thus, in a sense, the Assessment Standards make assessment the process of gathering evidence about a student's mathematical power. Therefore, it seems to me that there has been a major shift in emphasis from MATHEMATICAL LITERACY in 1989 to a focus on MATHEMATICAL POWER in 1995. Comments?