Can't really understand the problem. For some reason - IE10 presents Hebrew in reversed order. If I use compatibility mode(IE Developer Tools, IE 10 compatibility mode) it works fine... http://www.undergraduate.technion.ac.il/rishum/index.html
Tried all sorts of RTL fixes(Css, dir attribute, etc.)
I'm no expert in RTL, but considering it works in compatibility mode, then in short term try adding
<meta http-equiv="X-UA-Compatible" content="IE=5">
In long term (or if that doesn't work) you show consider rewriting the pages to current HTML standards. You should at least
BTW, use http://validator.w3.org/ to check for the worst errors. Since this is a framed site, you'll need to check each frame document separately.