Re: Taxonomy development: graphics in science and mathematics disciplines


> On May 15, 2015, at 12:16, chaals@yandex-team.ru wrote:
>
> 23.03.2015, 20:10, "White, Jason J" <jjwhite@ets.org>:
>
>
>> Graphs in a rectangular coordinate plane are likewise important and ubiquitous, as may be recalled from secondary school analytic geometry and calculus.
>
> Also in very basic science, learning to record things in bar charts is essentially done on a rectangular grid.
>
>> I suspect these graphs could be described by concepts in the taxonomy that should be included in any case to capture data visualization. Whether a graph represents data or a mathematical function doesn’t make any difference, in principle, to its content.
>
> I don't think that is true, and I think the key differentiator is that mathematical functions, especially as presented in school, tend to be continuous, while data graphs are often not. The difference between a sine wave and a scatter plot seems important to me, albeit at a very initial stage of thinking about the problem.
>
I suspect we’re closer to agreement than may initially appear. As you note, functions don’t have to be continuous and may not form a line or curve, even though that’s the norm in secondary school mathematics courses.

Informally, a function f is a relation where, if (a,b) and (a,c) are in f, then b = c.

So, returning to SVG and the taxonomy, at a high level it’s important to capture the fact that a set of points in the plane is being represented. At a more detailed level, knowing that it’s a line or curve, whether it’s continuous or not, etc., are all important facts that the user should be able to ascertain easily. I suppose the line or curve is part of what Doug rightly calls the implicit semantics of SVG that a user agent or assistive technology should be able to classify for itself. Even if we don’t want to add roles for linear, quadratic, cubic, hyperbolic, exponential, logarithmic, trigonometric, etc., cases, not to mention all of the other possibilities (e.g., relations such as circles, ellipses, etc.), we should at least indicate which geometric construct in the SVG is the object that appears in the coordinate plane so that the UA or AT can synthesize a classification or description. At a minimum, role=none should not apply.

>> Thus I think this important class of graphics can be easily addressed within the scope of work already proposed. There are however special cases, for example, a graph in which a certain area under the curve is shaded to indicate the integral that a student is expected to calculate (perhaps analyzable as the combination of an interval and a graph/path in the plane).
>>
>> Many closed figures, configurations of lines, etc., occur in geometry. Perhaps it would be best to rely on a combination of the implicit semantics of SVG (to the extent that these can be queried by assistive technologies) and author-supplied labels and descriptions to handle these cases. Some common shapes could be incorporated into the taxonomy if necessary, but a more general approach would clearly have advantages.
>
> Actually, taking these two things together, I think there are interesting things SVG can do with bounding boxes and shapes, to describe areas and help people understand things like calculus - or the magic of π and how it lets us work out the area of a circle.
>
> And I agree that where we already have taxonomies, such as rectangles, or text, or arcs, within SVG source, it is useful to leverage them as far as possible.

We’re thinking in accord, then.


________________________________

This e-mail and any files transmitted with it may contain privileged or confidential information. It is solely for use by the individual for whom it is intended, even if addressed incorrectly. If you received this e-mail in error, please notify the sender; do not disclose, copy, distribute, or take any action in reliance on the contents of this information; and delete it from your system. Any other use of this e-mail is prohibited.


Thank you for your compliance.

________________________________

Received on Saturday, 16 May 2015 01:13:33 UTC