[phoskins11]

For my chemistry class, I recently attempted an experiment from the October 2007 copy of Popular Science, where silicon is purified from silica sand and (SiO2) and magnesium. I did not have silica sand, but instead ground silicate (SiO2) crystals into a powder. I mixed the powder and magnesium powder in a test tube and heated them until they were red hot. At this point, the magnesium ignited. However, my reading online suggests that the reaction should still proceed even though this has happened. I then poured the mixture into a dilute solution of hydrochloric acid (HCl). At this point, the mixture should have ignited, leaving elemental silicon. But nothing happened. We tried again with a more concentrated HCl solution, but instead of purified silicon, the solution turned into a bubbling black goo which overflowed from the beaker. My chemistry teacher doesn't know what went wrong, but suspects the silicate powder. Does anyone know what went wrong?

[Arkcon]

Silicate sand, and ground silicate powder are essentially the same things, if you're sure you used silicate powder, then it should have been the same. 

Now, your references and Google led me to abundant sources for your procedure, with color photos and good explanations and all.  But I wouldn't have done something so exothermic in a glass test tube.  Maybe if you tried it in a porcelain crucible, you might get better yield, having shielded the mass from air, a little better.

As for you black goo in acid, I don't know what that is.  But having done it once, you at least know by how much not to overfill the beaker, so you don't get a spill.

[DrCMS]

How much of each powder did you use?
Was the silicate powder a metal silicate powder?

[phoskins11]

I used about 32 g of silcate powder and 25 g of magnesium powder. We used silicate crystals, which should have been SiO2.

[DrCMS]

Try using more magnesium, 32g of SiO₂ would need 26g of Mg to react and form Si and MgO. 

Use an excess of Mg say 50%.
Do it on a smaller scale say 10-20g total.
Make sure the powders are really well mixed.