Serious research has been conducted over the last fifty years into the benefits of teaching children about mathematics through non-traditional means like playing chess. Playing chess involves using logic, strategy and many other skills that are transferable to mathematics. The large amount of available research but narrow topic makes teaching children mathematical skills through chess playing an ideal topic for a meta-analysis.
Debates have raged over the centuries about the true discoverer or inventor of many topics in mathematics. For example, there's some debate over whether Sir Isaac Newton, Gottfried Leibniz or even the ancient Greeks invented calculus. Pick a mathematical topic like calculus, trigonometry or even "zero" and trace it back through time. Present both sides of the debate, analyze the evidence, then make some guesses of your own as to the "true" inventor or discoverer of that particular topic.
History is rife with people who have lied using statistics. Statistics is a complex subject that can easily be manipulated to meet an agenda. For example, Merck, the makers of Vioxx, has been accused of standing behind a curtain of lies regarding heart attack risks for Vioxx. Merck has responded to claims by stating it fully disclosed the risks of the drug (in a heavy statistical analysis report). Choose an event like the Vioxx recall, the spread of AIDS, dog bites or the health care debate and investigate to what extent statistics (or misuse of statistics) played a part in the debate.
There's a debate in teaching mathematics about the use of technology. Proponents cite better test scores, higher engagement and lower attrition rates for students who regularly use technology in math classrooms. Opponents state using technology erodes the foundations of mathematics. Write a thesis on the technology debate, making sure you present both sides of the debate before drawing your own conclusions.