Use rectangles formed by identical small square (rows and columns).

Then there are N objects (ex: number of N = 24), the quotient is the number of columns in your rectangle (ex: Q = 3). We cut the rectangle into three columns or small identical rectangles and watch how many objects exist in each of these separated new parts (R = 8).

If you use pieces of beans, you are able to demonstrate remainder, too.

Example: 25/4

You can give 25 pieces of beans in a cup to a group of students. Ask them take 4 pieces of beans from the cup as long as there are less than 4 pieces of beans in the cup. Thereafter, ask two following questions to the group.

- How many times have you taken pieces of beans from the cup?

- How many pieces of beans left in the cup?

salaam

using a compass and a straight edge to divide a circle evenly from the foci is fun.

Thank you for all the responses and it is so helpful. The challenge is that.... we have pupils of various abilities. One technique works for a group of pupils but it might not for others. I would really appreciate is everyone could share their experiences teaching pupils this concept .   

Explain to pupil that division is dividing a whole into desired equal parts with or without reminder.

For performing division, multiplication is mandatory.    It is easy to understand multiplication. Division is reverse of multiplication with or without reminder.

algorithms or program written for software, is good for understanding division step by step.   

In our book on research-based guidance for teaching mathematics to students aged 9-19, we have a section reviewing recent research on "early understanding of multiplication and division"; see:

https://global.oup.com/academic/product/key-ideas-in-teaching-mathematics-9780199665518

Marzita's question was about understanding, not using techniques for division. In a world where increasing is the norm, it is not surprising that adding and multiplying (perhaps through repeated addition) is easier than subtraction and division. Although division is the inverse of multiplication, using an opposite of repeated addition is not easy to understand. Using tangible objects, geometric shapes, is one way. We can be sure that understanding in this area will be easier if many many instances are used, with different shapes such as circles and rectangles, for example. The process of induction from instances to the general case is hard. It also needs teachers to be explicit about every instance, and link with the specialised language used (halves, thirds, quarters, in English).

I agree with John. There might be also ideology at subconscious level. I think that in egoistic society it may be more difficult for pupils to accept division. "Why to divide if this all belongs to me?"

In the societies where collectivism and altruism was the desired norm (I am talking about the USSR and other socialist countries) understanding of division was never a problem at school. Teacher could say: "Maria, suppose you and 3 friends found  8 apples. How should you divide them honestly between you all?" - Answer: 2 apples for everybody.

Maybe to try the game of social planner. Like "We collected $1000 to help poor. If we have 100 poor in our community, how much should we give to everybody?" - Answer: $10.

Some pupils want visual support. Then you can draw squares on a board and divide them in parts. Or distribute playing cards one by one, so that everybody has 6, for example.

Going to fractions may be more difficult. But then teacher can use some infinitely divisible object like 1 kg of bread. If there are weights, it is possible to divide it in any N fractions.

For older children or in universities division can be clearly explained as an inverse operation to multiplication. And the object can be more complex, like inverse matrix. But students should be able to think abstractly at this stage.

This may not be proven by research, but pupils tend to get certain concepts better when their own mates explain it to them, maybe because they relate to them more than their teachers. I, for instance, was taught long division by a friend - and got better at it than him. I think pupils who understand the concept of long division should teach their mates who do not understand, more of the time. It works.

  Division is confusing because it works two separate ways .  I use my hands to illustrate these .

  I hold out all my fingers to my students and say "How many fingers do you see ?" , so the answer is 10 .  Then I wave each hand but on each side of me , and ask "If I was to split 10 into 2 equal groups , how many would be in each group ?" , so the students all say 5 .  That was easy .   I write on the sum onto the board 10/2=5 (please imagine the proper division sign , not the fractional representation).

  I then ask again "How many fingers do you see ?" - so 10 again .  Then I ask "If I put them together in groups of 2 , how many 2s will I have ?" .  I then put my fingers against each other in turn and hold my hands up sideways to the students , again they answer 5 . And again I write the same sum .

  So I say to the students that the division sign is used two ways .  One way is for splitting things up big things , the other is for grouping small things . Although the sum is written one way , it can be representing either of these processes .

 I believe this is where the confusion comes from .  As teachers we generally only explain it one way , but then we also use the same sign for another process  .  Students look for simplicity , so they do not like something that works more than one way .

Dear Marzita,

You are right. And, this is an essential topic. I'll be happy if I got a time to devote for this topic in a series of publications or a chapter f a book. When you want to teach it will, you have to go not only to the concept of division, but before that the concept of multiplication. I hope that this would be of help.

Best wishes,

George

Dear George,

Thank you for your reply. Yes, I totally agree with you as I find it helpful and meaningful to relate division with multiplication. They seem to understand the idea of division  easily through the concept of multiplication as it is the reverse order. Thank you

Dear Marzita,

What you mention is correct in means of performance. In means of understanding, the whole idea is reveal the difference between the concept of multiplyer and the concept of multiplicand. Thus, the two meanings of division can be deeply understood. 

Wishing you all success.

George