"Teachers often talk about administrative matters and don't plumb the depths of the matter."
"Teachers mostly talk about administrative things and don't probe deep into the heart of the matter."
"plumb" を使う場合はこう言えます。
"Teachers often talk about administrative matters and don't plumb the depths of the matter."
"teachers" 「先生は」
"often ~" 「〜が多い」
"talk about ~" 「〜な話をする」
"administrative matters" 「事務的」
"don't plumb the depths of the matter" 「心の奥底を探らない」
この場合は "plumb" より"probe"の方が適切と思いますのでこう言えます。
"Teachers mostly talk about administrative things and don't probe deep into the heart of the matter."
"mostly ~" 「だいたい〜」
"administrative things" 「事務的」"matters" と "things" は同じ意味、"things"はの方がカジュアルな言い方になります。
"don't probe deep into the hart of the matter." 「心の奥底を探らない」
"probe" 「探る」
"deep into the heart" 「心の奥底」
オーストラリア 
