Why does breaking the chalk fix the squeaking? It is a well-known phenomenon that writing on a blackboard with chalk sometimes produces a squeaking noise. The explanation is also well-known: the chalk alternates between sticking to the board and sliding over it. This is called the stick-slip phenomenon and underlies many other noises like those of grasshoppers and bowed instruments. 
Breaking the chalk into shorter pieces fixes the problem. My assumption had been that the shorter piece still produces noise, but that the frequency is too high for a human to hear it. However, I recently realized that I wasn't sure about this, and a web search quickly brings up answers like the following: 
Yahoo Answers, What is the solution for squeaking chalk?
In that answer, we read 

Simple: break the chalk in half and use the 'broken' ends. Squeaks disappear! 

This suggests that the rugged surface of the resulting pieces plays a crucial role. I don't recall that it ever made a difference which end of the piece I used, so I have my doubts about this explanation. 
Question: why does the broken piece of chalk not produce an audible sound?
It would be especially nice to know if someone had tried writing with an unbroken chalk cylinder which was short to begin with, because it was produced that way.
Edit: slip-stick -> stick-slip
 A: breaking the chalk squares off the end that you write with so that when it is pressed into the blackboard it makes contact over a small area. dragging the chalk piece across the board with a small contact area creates large pressures at the contact point which tend to shear off chalk particles at an applied stress insufficient to cause the chalk to stick. once the chalk piece's writing end is rounded off with use, then the contact area becomes large again and the chalk can stick before it shears, and it begins to squeak once more. 
A: What happens when you break the chalk off is create a square edge, this sharp edge decreases the surface area applied to the board. When writing for a long time on the same piece, the pressure from writing causes the chalk to become very compact and smooth at the point of contact, therefore you will note that at different angles and point of contact, it will differ between squeaking and transfering chalk to the board. bare in mind that a chalk board has a degree of roughness to it in order to aid in the friction/grip.
The result from breaking the chalk is that with the same amount of writing pressure, the pressure between the chalk and the board increase due to the lower surface area. Another thing to note is that chalk is weaker at the breaking point, enabling a better transfer via friction that decreases over the duration of writing. 
As for the resonating frequency, I don't believe one has been done to prove the squeaking frequencies. 
My best guess is that chalk is made under high pressure and as a result, the squeak is able to resonate, once broken, it loses that residule stress and is not able to resonate properly. However that leads the question if things like Prince Ruperts drops would resonate? I must add that I have noticed that already broken chalk is less likely to break when dropped, but this may be length dependant, and also an already broken piece of chalk can squeak again after repeated use. I personally think it's the conditions at the contact point that causes the squeek. 
