Question was answered on another site.. thank you!
BTW, the code that accomplished what I needed was:
$categories = get_categories('child_of=31');
foreach ($categories as $category) {
//Display the sub category information using $category values like $category->cat_name
echo '<h2>'.$category->name.'</h2>';
echo '<ul>';
foreach (get_posts('cat=".$category->term_id) as $post) {
setup_postdata( $post );
echo "<li><a href="'.get_permalink($post->ID).'">'.get_the_title().'</a></li>';
}
echo '</ul>';
}