Perhaps your students’ mathematical thinking rivals the discussion in this Abbott and Costello skit. I always enjoy that one, and it’s funny in part because it speaks to our befuddlement with math algorithms. I don’t remember learning long division so I can’t comment on how well I understood it at the time. However, if I did understand the meaning behind the mechanics, it was lost over the years such that this Montessori lesson seemed exciting and new. I’m guessing that textbooks include some good graphics and descriptions to conceptually illustrate the algorithm (since I’ve not taught such young grades in a traditional setting I’m not sure what form these take), but I also wanted to share this series of pictures from my training.
A note that in Montessori lessons units, tens, and hundreds are represented using green, blue, and red respectively. Before this lesson children learn place value (including the colors) and work with division more concretely (think Cuisenaire rods — I still remember that day-glo orange). They also do a “first passage” with the board and beads in which they do all the mechanical distributing and exchanging but record only the quotient. I’ve included the complete recording so you can see how the materials lead into each step of the algorithm. Let me know what you think!
One day all children in this nation will have the opportunity to attain an excellent education.
Have a great week!