k i understand this, but...
... what does this mean? Does this mean:
first, sing a quarter note C
then, play an eighth note C
then, rest for an eighth rest
then, sing a quarter note F
then, play an eighth note F
then rest for an eighth rest
... and repeat?
What does "forced choice with immediate check" mean? Does it mean like I am forced to try to choose the right note to sing when I sing the C, and then I immediately check it by playing an 8th note C, then I rest an eighth rest and am forced to try to choose the right note to sing for a quarter note F, and then i immediately check it by playing an eighth note F?
K your advice sounds good but I just want to make sure I understand what you're saying. And unfortunately I only kind of have the C major scale down but I'm not so good with the other major scales and definitely not the minor scales. 
I really appreciate the advice timothy42b!
@ zoecalgary: I have been dabbling around at the piano off and on for over a year but in terms of skill I am a complete beginner. Do you recommend the alfred or faber book or what in addition to the paul harris and four star books i'm already using?
Sorry, my explanation could be misinterpreted.
No need to take it beyond C major for now. Once you get the intervals in your head they generalize to some extent.
You have succeeded in memorizing two intervals, the major second and the minor second, by playing the scale.
Now I'm suggesting adding a couple more intervals, the fourth and fifth. You don't have them memorized now, you are finding them by adding up the scalewise intervals that you do have memorized. Well, you can memorize the fourth EXACTLY the same as you did the scale, and then you can sing them directly without having to work your way up. Lots faster.
Does this mean:
first, sing a quarter note C
then, play an eighth note C
then, rest for an eighth rest
then, sing a quarter note F
then, play an eighth note F
then rest for an eighth rest
No. Just goes to show, I knew what i meant, but that didn't mean I said it!
I want you to sing a quarter note C, and while holding it, play an eighth note C. I want you to do this in strict rhythm, with the metronome. If 80 is too fast try 60 or 40, doesn't matter, as long as you are staying "in time." So it would be as if you had two staffs, the top one for your vocals where you sing quarter notes, the bottom one for the piano where you play one eighth rest AND one eighth note for every quarter note you sing. The top staff would have quarter quarter quarter quarter forever, and the bottom staff would have eighth rest eighth note eighth rest eighth note forever.
Forced choice means you have to guess, and have to guess on time. That speeds learning. Immediate check means you hear the correct note an eighth note space later, so you know if you did it correctly.