I took my first investing class as a teenager, and one moment stands out in my memory. A fellow student asked the instructor, a stockbroker, about dividends.

"Dividends?" he asked. "I'm trying to make my clients wealthy. You don't do that waiting for tiny checks in the mailbox every quarter."

Even then, I had enough horse sense to know he was wrong. Paying attention to dividends is exactly how you become wealthy over time.

Wharton professor Jeremy Siegel made a wonderful discovery in his book The Future for Investors. The greatest long-term returns typically don't come from the most innovative companies, or even companies with the highest earnings growth. They come from companies that happen to crank out dividends year after year. Simply put, since the 1950s, "the portfolios with higher dividend yields offered investors higher returns."

Market commentary regularly centers around price gyrations, yet dividends have historically accounted for more than half of total returns.

Reinvest those dividends, and the results are substantially greater. Take, for example, AT&T (NYSE: T). Since the early 1980s, AT&T's shares have increased roughly 500%, but the total return is nearly five times that amount once reinvested dividends are factored in:

Source: Capital IQ, a division of Standard & Poor's.

There's no ambiguity here: Over time, AT&T's share appreciation alone has paled in importance to the power of its reinvested dividends. The results are similar for competitor Verizon (NYSE: VZ) and fellow industrial stalwart Consolidated Edison (NYSE: ED), both of whose total long-term returns are overwhelmingly skewed higher by reinvested dividends. If you're a shareholder, your attention should be devoted to those dividend payouts and your commitment to reinvest them, not daily -- or even yearly -- share wobbles.

And how do those dividends look? AT&T has paid a dividend every year since at least 1984. Its current yield -- 5.6% -- is one of the highest you can find among non-cyclical companies. Over the past five years, AT&T's dividend has averaged 60% of its free cash flow, so the payout is fairly well covered and shouldn't face a cut anytime soon.

To earn the greatest returns, get your priorities straight. What the market does is less important than what your company earns. What your company earns is less important than how much it pays out in dividends. And what it pays out in dividends is less important than whether you reinvest those dividends.

Add AT&T to My Watchlist.  

Fool contributor Morgan Housel owns shares of AT&T, Verizon, and Edison. Follow him on Twitter @TMFHousel. Motley Fool newsletter services have recommended buying shares of AT&T. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.