Bad lighting and/or bad camera placement are the cause. If you can't move the lights or the chalkboard, such as in many typical classrooms, the first thing you should try is moving the camera.
You can think of the chalkboard surface like a mirror. In fact, if you hung a mirror flat against the chalkboard, you'd see that the position of the chalkboard "hot spots" corresponds exactly to the position of the reflection of light sources in a mirror. The difference is that microscopic abnormalities in the surface of the chalkboard scatter the light more randomly, which effectively "blurs" the reflection.
If you can't avoid the glare by moving the camera, or by moving/dimming the lights, then there is one other way to fight glare: Use a polarized lens filter. These work the same way that polarized sunglasses work to cut glare. There are screw-on variants made for photography cameras called CPL's or "Circular Polarizing Lenses," which let you adjust the polarization angle for best effect. Polarized filters don't work for all reflections though, and their efficacy depends on the polarization of both the light source and the reflective material.
CPL's are fairly cheap. You can probably pick up a used one for $15-ish, and new ones are usually below $100. Just make sure you buy the right size to fit your lens. Either inside the camera's lens cap, or written on the lens, you'll see a number next to the symbol "ø". This is the filter size, and should match whatever you buy.
If you wanted to go totally shittyrigs cheap, you could tape one of the lenses of a pair of disposable movie theater 3D glasses in front of your camera lens. The 3D variant filter polarized light like any other camera filter or sunglasses on the market. The difference is that the polarization of the left and right eye is offset by 90º.