Can solutions of polar covalent compounds conduct electricity? I learned in class that solutions of polar covalent compounds are weakly conductive, while ionic solutions are strongly conductive.

But I'm getting different answers online. According to this lecture, "They do not conduct electricity in the liquid state, or when soluble in water, do not conduct electricity in aqueous solution."

I saw in lab, however, that a dextrose (D-glucose) solution weakly conducted electricity, and so did that of levulose (D-fructose).

So can solutions of polar covalent compounds conduct electricity? If so, how? Since it's covalent, it's not like anything can dissociate to form ions, right?
Consider for example this lab where polar covalent bonds are said to be strong, weak or non-electrolytes : ELECTROLYTES AND NONELECTROLYTES CHEM 151

The part of the molecule which dissociates has strongly ionic character but the molecule itself is described as being polar covalent. Not not all bonds in the molecular have the same level of covalent character, but most are covalent and it is polar.

There are also other ways for molecules to allow conduction, conjugated systems can do it by a very different process see for example the wiki on Conductive Polymers