Sen. Scott Brown (R-Mass.) and Democrat Elizabeth Warren squared off in their second debate Monday night at the University of Massachusetts at Lowell. The 60-minute debate  hosted by NBC's David Gregory wasn't short on heated exchanges on many of the issues the candidates have been sparring over for months. Here are six takeaways from debate number 2:

* "I am not a student in your classroom": This quip from Brown will likely be the most talked about one-liner from the Monday debate.  After Warren listed the instances in which Brown voted against Democratic-backed bills, a back-and-forth ensued, as the senator tried to respond with a defense of his record. His line brought him some boos. For Brown, who is pitching himself as the likable candidate in this race, lines like this one could cut against the image he has carefully crafted.

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* Native American story kicks off debate (again): Just like in the first debate, Brown and Warren began with a back and forth over the Democrat's claim to Native American heritage. Since the last debate, Brown has aired two ads on the matter, and Warren has responded with one of her own.

Polls show the issue isn't hurting Warren on its own. Brown, perhaps recognizing the danger of overplaying his hand, made sure to mention the importance of jobs and the economy in the campaign before calling on Warren to release her personnel records to substantiate her claim that she has never benefited professionally from her heritage.

* Brown mentions Scalia: When asked who his model Supreme Court justice is, Brown paused before naming Antonin Scalia, who hails from the conservative wing of the high court. As the audience reacted with gasps and some boos, he quickly named others, including Chief Justice John G. Roberts Jr. and Justice Sonia Sotomayor (whom President Obama nominated). But the first name that came to Brown's mind will likely be fodder for charges by Warren's camp that Brown is too far to the right, especially given the state's Democratic tilt.

When Warren was asked the same question, she named Justice Elena Kagan, whom Brown voted against confirming.

* Character, character, character: Brown's assault against Warren's claim to Native American heritage is part of a broader effort to raise questions about her integrity and character. So are the instances in which he points out the legal defense she provided to large corporations. "I think the fact that she has not released those [personnel] records speaks volumes," Brown said during a discussion about Warren's heritage.

But Warren came ready to take on the question of character head on Monday night. "I think character is how you live your life," she said, after reiterating that she never used her heritage for professional gain. Her campaign should be satisfied with the way Warren took on the issue Monday night.

* Both candidates hold their own during McConnell/Romney discussion: Given the Democratic tilt of the state, it's never great for Brown when the discussion turns to Mitt Romney and Senate Minority Leader Mitch McConnell (Ky.). Gregory pressed Brown on whether he'd vote for McConnell as leader, and Brown punted, saying, "He has a lot of work to do to earn my vote."

Brown acknowledged supporting Romney on economic issues, and that allowed Warren to argue that Brown stands against Obama on the signature issue of the election cycle. Overall, Brown navigated the national Republican issue fairly well, but Warren deserves credit for going on offense where it hurts for the Republican.

* Warren takes harder position on Red Sox manager: Warren said embattled Red Sox manager Bobby Valentine, who is on the hot seat after a tough season, should get another chance. Brown, meanwhile, wouldn't say whether Valentine should get the axe or not. Given how poorly Democratic nominee Martha Coakley navigated discussions about local sports in 2010, Warren has been under a microscope on the topic this cycle. To her credit, she's done much better.

WATCH: Full video of the debate between Scott Brown and Elizabeth Warren

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