[verb ます-stem] + つつ [verb ます-stem] + つつも
つつ joins two actions done by the same person at the same time: "while doing". It goes after the ます-stem of a verb, and it is the written counterpart of ながら; the main action comes second.
In conversation, use ながら: てれびテレビをみ見ながらたべる食べる.
With も added, つつも means "even though": you do something while knowing or feeling that you shouldn't. The verb in front is usually one of knowing or feeling – しる知る, おもう思う, わかる分かる, かんじる感じる – or one of saying. Plain つつ can carry this meaning too.