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 your results become even greater. Take JPMorgan Chase (NYSE: JPM) for example. Since the late 1960s, JPMorgan's share price has increased just 318%. Yet add in reinvested dividends, and total returns jump by an order of magnitude:

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

There's no ambiguity here: Over time, JPMorgan's share appreciation alone has paled in importance to the power of its reinvested dividends. The results are similar for competitors Wells Fargo (NYSE: WFC) and US Bancorp (NYSE: USB). Reinvested dividends skew both companies' total long-term returns higher. If you're a long-term shareholder, don't worry about daily share wobbles. Devote your attention those dividend payouts, and your commitment to reinvest them.

And how do JPMorgan's dividends look? Like all big banks, JPMorgan had to slash its dividend in recent years to cope with the financial crisis -- in its case, to a nickel a share per quarter. That payout has since been raised to $0.25 per share, but that figure remains one-third below pre-crisis levels.

In a conference call last week, CEO Jamie Dimon said the bank would "generate significant excess capital" in both the near and long term. "It's quite obvious to us," he said, "we have a lot of extra capital and cash, not just in the next short run, but over next several years, and we will apply [for regulatory approval] for more [dividend increases] as appropriate." If you're a long-term shareholder, expect higher dividends to come.

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.

Fool contributor Morgan Housel doesn't own shares in any of the companies mentioned in this article. Follow him on Twitter @TMFHousel. The Motley Fool owns shares of JPMorgan Chase. The Fool owns shares of and has created a ratio put spread position on Wells Fargo. 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.