Well after several occurences where people for various reasons people think tables don't work with screen readers, I would like to officially say...
I love tables!!!
I really do. I can only speak for Jaws in terms of how it operates, but here is how it works for me:
Control plus alt plus arrow keys moves between cells
This method moves you up, down, left or right one cell. It also attempts to read the "title", this being the first cell in the appropriate direction. If you move sideways it tries to read the first cell at the top of that column to try and help you work out which column you're in, moving down it reads the first cell on the left of that row for a similar reason.
Windows key plus arrow keys
Works almost exactly the same, except it doesn't read the title and cell. Instead it reads the entire row or column. Can be handy in some cases.
For example if a shop uses a table for their products, and the first column is the item name you can do the following:
Position yourself in the column for price, availability or whatever you find particularly relevant at the time
Hold control and alt, then keep pressing down.
The cell data is read in a slightly different intonation, so if it was price you were looking at the price would sound slightly different. In this case you might have:
Blank DVD X 20, £5
DVD case X 5, £3
Microsoft wheelmouse, £7
Only with the price in the different tone.
I am sure Hal and Window Eyes will both support tables, and I know NVDA does too. Thunder really isn't worth caring about frankly, it doesn't even support HTML on its own so it has no chance. NVDA is better, free for commercial use, and just as free for individuals.
I can't stop everyone thinking tables are a problem, but if I can show a few people then this is good. After all how hard are tables to work with when you break them down? And considering spreadsheet support such as Excel is common in screen readers, how much different is it?
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To live by honour and to honour life, these are our greatest strengths and our best hopes.