I need help; Some of my students struggle so with division. They get that division means to divide into equal parts, they get the concept, and we practice, practice, and practice long division until our eyes are weary. And yet,I can see their despair, they do not understand why we are doing the steps we do. So I need a different approach before we move on and put them further behind.
What can I do to make them see the light? I have them explain it to each other but even doing that doesn’t seem to change their understanding. We practice but that is not enough either. There are many smarter people out there, please lend me your ideas.
Pernille Ripp 
Can you use the distributive property (without calling it that) to split it into smaller chunks?
I think the partial quotient method helps students develop number sense and gives them practice doing mental math. It also avoids the need to do several multiplication problems to find the largest number possible for each place in the quotient. http://www.youtube.com/watch?v=M_Ti_7p_O9U&feature=related
I ditto Sue. The partial quotients method works well for some of my students who don't know their facts well.
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I also agree that using partial quotient would be a good strategy for many students. But I think if you are looking for a way for them to understand the "standard algorithm" you need to think about their depth of understanding with place value. Do they get that when they are dividing 584 by 24 they are really dividing 580 by 24 first? There for, it goes in 20 times, rather than 2 (which is why some don't understand where to line up that first number) Then when multiplying 480 should be recorded, not just 48. And using estimation helps with the whole process too, but only if a deep understanding of place value truly exists. And if all else fails a catchy cheer for the "steps" with great body movements- Divide! Multiply! Subract! Loop up! Again!- is sure to grab their attention 🙂
… and if you know PV isnt the issue, I would suggest thinking about learning styles of the kiddos who continue to struggle. I know my visually spatial kids need bright colorful arrows, and maybe numbers color coded too. My logical/mathematical and naturalist kids need the steps labeled (like a sample diagram to refer to). Where my kids who are verbal, intrapersonal or interpersonal need to reflect (orally and/or in writing) about the areas they are understanding and the questions they still have… and again those musical kids sure would LOVE a cheer!!
The issue with place value is one of the reasons I like partial quotient. In the example 584 divided by 24, the 20 – not just the 2 – gets recorded and 480 is subtracted. If they finish by recording their answer in the standard format, they might start making the connections and understand the placement of the quotient above.
These two blog posts/videos might help you understand some of your students' confusion. I recently spent several frustrating days working on long division with 5th graders who were trying to complete the steps without understanding the math. Sometimes I feel that, rather than learning math, they are learning to dislike math.http://crewtonramoneshouseofmath.blogspot.com/2011/02/division-how-not-to-do-it.htmlhttp://crewtonramoneshouseofmath.blogspot.com/2011/02/more-on-division.html
Thank you, thank you, thank you. I have so much to learn. Today was a better day for these kids because I slowed down. Some just needed the practice but others have a fundamental lack of understanding of place value that I know need to work on with them. All of your comments helped me be a better teacher today and I am grateful for that.
Let them come up with their own strategy for how to do a problem like this;I love peanuts I have 625 peanuts in a bag under my desk. If I eat 20 peanuts a day, how many days will the peanuts last?Just give them the problem and see what they can do! They may jump right to the traditional algorithm, and in that case, ask them to do it again, a different way. And when they finish it a different, ask them to try another different way. Have the groups share their strategies and talk about what is going on in each. Start to deconstruct the mathematical thinking. If you are looking for a reference book to help, this is best Math resource for teachers I have ever read;http://www.amazon.com/Teaching-Student-Centered-Mathematics-Grades-3-5/dp/0205408443/ref=pd_bxgy_b_img_b
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