If I understand what you are after, you should add role="region" to the section elements, like so:
<section role="region">
This will tell the screen reader that the section is indeed a section, and will provide the correct accessibility information to the user. This role is an WAI-ARIA role. Ideally it would not be needed, as the section element has implied semantics, but there is better support for ARIA in screen readers than there is for HTML5 elements, so this plugs the gaps until support is widespread.
You can add the aria-labelledby
attribute to the section
element and associate it with the ID of the h* if you want the heading to be announced by the screen reader when it is announcing the section, such as “Example 1 region” in Jaws.
For each of your headings in the sections, it could be a good idea to include them in a header
element too, like so, although not strictly needed (I often do it just for the main article heading)
<article role="article" aria-labelledby="title">
<header>
<h1 id="title">An article about markup!</h1>
</header>
<section role="region" aria-labelledby="eg1">
<header>
<h1 id="eg1">Example 1</h1>
</header>
</section>
<section role="region" aria-labelledby="eg2">
<header>
<h1 id="eg2">Example 2</h1>
</header>
</section>
<section role="region" aria-labelledby="eg3">
<header>
<h1 id="eg3">Example 3</h1>
</header>
</section>
For more information see http://blog.paciellogroup.com/2011/03/html5-accessibility-chops-section-elements/, http://blog.paciellogroup.com/2010/10/using-wai-aria-landmark-roles/ and http://blog.paciellogroup.com/2013/10/using-html5-section-element/