How, do i convince my my mom to get me a DSLR camera for my birthday.?

Im 13, and my 14th birthday is coming up soon. For the past 3-4 years i have asked for a camera, asking for a more expensive one each Christmas. Next year as a freshman im taking photography class and i need a dslr. My mom always gets made when i take her camera and gets mad at me for using it. she did get me a camera the past 2 Christmas. both have been awful pixelted quality(she over paid for both and one of them i saw at Walgreen's. Now currently my plan is to see all the cost for my little sisters birthday and party and show her how much she spent on her. and say its not fair. I,ve been looking at prices since January and know what i wanna buy ( Nikon d3100 with starter lens and body along with diana lens and adaptor) Now keep in mind that this is the only thing i want for my birthday (no party either) and im gonna try and pay some of the price too but her only argument is "I'm not gonna buy a 14 year old a $600 camera.".