Friday, March 24th, 2017

Common Core Leads to Greater Scientific and Math Illiteracy

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January 2015, The new Common Core guidelines for math and science seem to be flawed. At the middle school levels, the guidelines call for students to show mastery of the content by being able to prove that a digital representation is the best one. This contention might be true if you are talking bit-level accuracy in copies, but fail in many other respects.


One of the core tenets for the overall curriculum for middle school students is to be able to prove that a digital representation is always the best. Check these links for more information:
Science Framework: http://www.nap.edu/openbook.php?record_id=13165

Here’s a link to the new science standards: http://standards.nsta.org/AccessStandardsByDCI.aspx

MS Engineering Overview:
http://ngss.nsta.org/middle-school-engineering-design/

MS Engineering Standards:
http://standards.nsta.org/DisplayStandard.aspx?view=dci&id=66

MS Waves Standards:
http://standards.nsta.org/DisplayStandard.aspx?view=dci&id=59

Ignoring, for right now, the details of digitization, most digital formats and equipment are not able to handle the full range of content available in an analog realm. For example, audio in a live performance or on a good vinyl record might have a dynamic range of over 90 dB. This range is the equivalent to over 30 bits (90 db = 10^9, 30 bits = 1,073,741,824). Some sound sources can generate waveforms with rise times much under a microsecond or slew rates well over 10 V/us. Does anyone make an A-D converter that can do 30 bits at a 10 MHz rate?

Visual stimuli have similar requirements. The eye can detect a range of over 22 f-stops, the difference between the light of a sunny afternoon and the reflected light from Saturn, another ratio of a billion to one. Silver-based film can handle about two thirds of this range and get most of the colors. High-dynamic range pictures, made by combining multiple shots of the same scene are now able to almost match the s-curve of film, but still not as good as the film.

For color, the wide color gamut formats in development might increase the total color space to something above 85 percent of the total possible. Even here, the use of 8- or 10-bits may help the color palette, but don’t address the dynamic range issue.

The whole issue of digitization raises other issues. In figure 1, the classical representation in blue of the sampling pattern at 10 times the input frequency has the first sample on the rising edge near the zero crossing. This sample will give an approximation of a sine.

Figure 1: A sine wave sampled at 10 times the fundamental frequency can reproduce an adequate representation of the input under close to ideal conditions. Less optimal sampling conditions can lead to gross errors. The blue boxes show the ideal sampling, and the green lines show some other start time.

It is just a likely that the sample doesn't start at a good place and the reconstructed waveform might look like figure 2. Definitely not a sine with many very high frequency components. The potential is even worse if the sampling rate is lower, and sampling at the Nyquist rate at the zero crossings would result in a zero output.

Figure 2: A representation of a sampled sine with sampling errors. The green curve is a possible reconstruction of the input signal, clearly not a sine.

Not only is the digitizing process flawed, but the actual converters have many other error producing attributes, including timing jitter, sampling errors, non-linearity, noise, and comparator hysteresis. While a direct digital capture is the ideal, at some point a transducer has to convert the analog world inputs into a digital format.

If the digital representation is the best, why does Hollywood archive movies in 3-color separations on film? A digital representation may be infinitely copied with very high bit accuracy, but how long will these data be viable? Long-term digital storage is a big challenge. Hard disks have a useable lifetime of about 5 years. The same for writable CDs and slightly more for Blu-Ray disks. LTO-6 seems to be the current long-term storage champ at over 40 years. In comparison, negatives and prints from the Civil War are still viable, and with proper care, might last another century.

Digital content suffers from the constantly evolving format and media standards. Who can even read from a 8- or 5.25-inch floppy to say nothing about the lack of any machine and software that can convert those data to a current output device? The Library of Congress is looking at a archive flow that calls for reading back all content and translating it to the latest format(s) before resaving it to tape.

Consider asking your local board of education to seriously consider and under stand the errors in implementation before adopting anything associated with Common Core.
 

 

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