* 82,000 construction jobs created November to January * Biggest three-month gain since April 2006 * Construction sector added jobs every month since June By Jason Lange WASHINGTON, Feb 1 (Reuters) - The outlook for U.S. construction workers brightened on Friday with a report that showed growing momentum in hiring at building sites. The U.S. Labor Department said 82,000 construction jobs were created between November and January, the biggest three-month gain since the three months ended April 2006. That suggests the recovery underway in the U.S. housing market, seen in appreciating home prices and more housing starts, may be leading to a stronger pace of hiring. "We're seeing more demand for construction workers," said Jed Kolko, an economist at real estate website Trulia. The housing rebound still has a long way to go before a full recovery, but growth in the sector will likely boost economic growth in 2013 for the second straight year. Friday's data was contained in the government's monthly employment report, which showed modest employment growth in January and a small increase in the jobless rate to 7.9 percent. The details of the report showed the labor market in 2012 was healthier than initially estimated, with construction playing a bigger role in job creation. The Labor Department said 335,000 more jobs were created in 2012 than the government had first estimated. Of those, 73,000 were in construction. CONVINCING TREND The report showed the construction sector has added jobs every month since June, and that the pace of growth picked up substantially in October. "Now the upward trend looks more convincing," said Ryan Wang, an economist at HSBC in New York. If the pace of hiring since October continues, the economy could add about 300,000 construction jobs this year, he said. That would be the fastest pace since 2005, though it would only be one facet of the boost a housing recovery would give to economic growth. Economists say that for every new single family home constructed, at least three permanent jobs are created as buyers shell out money to equip their homes. Housing now is a smaller part of the economy than it was even before the housing bubble of the early 2000s, so the current recovery is providing less of an economic boost than it usually would following a recession. Indeed, even if the October-January pace of construction hiring continued throughout 2013, the sector would only regain a sliver of the 1.5 million jobs that it lost in the recession.