Knowing that pedagogy for each age group is different, I will say right off the bat I am talking about working adults.

I am noticing more and more, that despite people's phobias about math, they are often quite good about dealing with those special cases specific to their subject.

Today I will talk about units and measurement. The typical discussion of measurement uses Area and Length and feet and inches. These are considered "universal".

In practice, these units of measurement are not the most useful. Here is an example from a page on website, related to a course on Web design I am reading:

Example: Mozilla CSS docs on length (Relative and Absolute Units)

enter image description here

enter image description here

These are not your typical units of measurement. We have the inch and centimeter but also

  • the pixel which is measure relative to the device you are using and
  • the em which is relative to the font being typed.
  • There are also percentage units which are measured relative to the width and height of your window, or even whether you are holding your phone straight or sideways.

These units of measure are dynamic since these lengths or proportions are based on information that is changing with time.

A web designer's job is to take an aesthetic or conceptual description of a web site and turn it into a precise and more quantitative version for the computer to understand. Moreover, the same set of proportions have to work under a variety of circumstances of which they do not have any control.

How can we discuss the geometry of websites when there is so much variation?

It seems are textbooks are do not reach far enough in addressing real-life practical measurement. Why are web designers able to understand delicate geometric concepts in the context of the theory of Cascading Style Sheets but not within the traditional mathematics framework?

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    $\begingroup$ I have no proof, but I would think that web designers actually use their reasoning skills when confronted with a rich problem in a context which matters to them, but students are given contrived contexts together with "recipes" to solve them, and never engage their reasoning processes at all. $\endgroup$ Nov 20 '15 at 17:52
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    $\begingroup$ People generally don't abstract their problem-solving strategies. We can wish that they did, but they don't. The only solution is exposure to as many contexts as possible. This synchs up with neuroscience on reading (needing as many different contexts as possible). $\endgroup$ Nov 20 '15 at 19:31
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    $\begingroup$ The general idea behind your final question -- that one would be able to understand contextualized, work-related mathematics but not structurally similar problems in (what you call) the traditional mathematics framework -- has been studied in the past. One reference is T Nunes' book Street mathematics and school mathematics, which follows the work of HP Ginsburg (and others) on "informal versus formal mathematics." $\endgroup$ Nov 20 '15 at 23:52
  • $\begingroup$ (Here in Table 2.2 is an interesting excerpt from the aforementioned Nunes work.) $\endgroup$ Nov 21 '15 at 0:02
  • $\begingroup$ Web design is kind of extraneous. But its the first example that comes to mind. You see this in finance or even sports. People who are very uncomfortable in math class just find in practical situations. Can I simplify or rephrase this question im any way? $\endgroup$ Nov 21 '15 at 12:50

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