Beginner rbind function - rbind

Question

I cannot for the life of me understand the rbind function. I've tried using the examples on here, but I can't figure out what I am doing incorrectly. All I would like to do is add the data from my second data frame under the first.
Does rbind require the columns be the same name or...?
ParticipantA=c("A","B","C","D")
Score1A=c("21","20","21","21")
Score2A=c("32","40","32","31")
Score3A=c("47","50","43","46")
BlockA=data.frame(ParticipantA,Score1A,Score2A,Score3A)
BlockA$Major=c("Computer_Science","Computer_Science","Computer_Science","Computer_Science")
BlockA$Gender=c("Female","Female","Male","Male")
ParticipantB=c("E","F","G","H")
Score1B=c("28","28","21","22")
Score2B=c("30","36","37","32")
Score3B=c("41","49","49","46")
BlockB=data.frame(ParticipantB,Score1B,Score2B,Score3B)
BlockB$Major=c("Medical","Medical","Medical","Medical")
BlockB$Gender=c("Female","Female","Male","Male")

Answer 1

rbind requires that all columns be of the same name and class.

Answer 2

The problem is in the column titles. rbind uses column titles to orient how it will bind the rows. The columns can be in different orders, R will just use the first element to determine column order.
Alternatively, adding another column to your data frames, with the value "A" or "B" in it could preserve your information without putting "A"s and "B"s in your column names <-- the reason you can't use rbind. The additional column would also allow you to do more analyses in R, e.g. regression and other linear models.
Here is one way to handle your data:
Create a uniform set of column names that can be used for the data frames "BlockA" and "BlockB"
final_colnames <- c("Block", "Participant", "Score1", "Score2", "Score3")
Create a new list to identify which block the participants belong to.
BlockA = c("A", "A", "A", "A")
Your previous data
ParticipantA = c("A", "B", "C", "D")
Score1A = c("21", "20", "21", "21")
Score2A = c("32", "40", "32", "31")
Score3A = c("47", "50", "43", "46")
The label "BlockA" is recycled here to name the new data frame, but not before adding the "BlockA" column list of "A" "A" "A" "A".
BlockA = data.frame(BlockA, ParticipantA, Score1A, Score2A, Score3A)
The new column names have to be added at this point, so that the number of names and the number of columns are equal.
colnames(BlockA) <- final_colnames
Now you can add the remaining columns
BlockA$Major = c("Computer_Science", "Computer_Science", "Computer_Science", "Computer_Science")
BlockA$Gender = c("Female", "Female", "Male", "Male")
BlockB is the same process
BlockB = c("B", "B", "B", "B") # the extra column
ParticipantB = c("E", "F", "G", "H")
Score1B = c("28", "28", "21", "22")
Score2B = c("30", "36", "37", "32")
Score3B = c("41", "49", "49", "46")
BlockB = data.frame(BlockB, ParticipantB, Score1B, Score2B, Score3B)
colnames(BlockB) <- final_colnames # renaming the columns
BlockB$Major = c("Medical", "Medical", "Medical", "Medical")
BlockB$Gender = c("Female", "Female", "Male", "Male")
Uniform column names mean that rbind will now work.
rbind(BlockA,BlockB)