Hello, Math and Numeracy Colleagues,
November 18 - 22, 2019 has been designated by the Department of Education and Department of State as International Education Week. In the spirit of learning and valuing different cultures and people from around the world, I am going to post resources that explain different mathematics concepts done in unique ways. This is a great time to expand your own thinking and try out some of these methods for understanding the process and procedures to arrive at the same solution.
When you try the new method, please post a picture of it so we can join in on the fun! Remember, to post a picture to links follow these directions, For those who want to use the web site https://postimages.org/ for uploading a screenshot, be sure you copy the Direct Link option and then paste it into the URL field found in the Image box found in the toolbar of your LINCS post.
Here is a short video on European Long Division: https://youtu.be/lnUJ_ugt6U
If you have your own fun resources - please post them, too. Let's celebrate our world together!
Looking forward to seeing your work!
Here is a resource: https://www.csus.edu/indiv/o/oreyd/ACP.htm_files/TODOS.operation.description.pdf
The comparisons are interesting - did you know the difference between 12.000 and 12,000?
What did you notice?
Here is an interesting approach: https://youtu.be/GQynm_2pAJI
Could you incorporate this method into your classes?
Have you seen this method?
What I find fascinating about this is that it's full of explicit visual-kinesthetic elements, especially the ones he says "you don't need to do this" (but ... do it anyway while you're learning, to keep track of the complex procedure).
I always marveled at the number of students who could very competently change a mixed number to an improper fraction, with a confident smile.... I realized it was because it was a motor memory. I know many math teachers want to "nix the tricks" that can mean understanding doesn't happen (I can tell you that lots of my improper fraction folks really had no idea what those digits meant), but for fractions and long division, the process just *is* so complicated that I think it's a great idea when we tie the marks to the meaning. We're putting that grouping curve over the 25 because we're working with the big amounts first... the 2 is really 200 but we can't five hundreds, so we go with our 25 tens...
I appreciate that it is so much like how I learned it here, but making more visual sense and ... a whole lot easier to keep track of with the little notations. I wonder if switching would help students (perhaps the ones who just went to calculator, period) ... or if including some of the notations in our approach would. While long division is definitely a Thing You Really Never Ever Do, No REALLY?!?!? ....I've read research supporting the idea that mastering it is what hammers down basic numerical understanding and fluency in those tricky inverse operations. It's nonsense, though, if it's just a horrible procedure we suffer through 'til it's over and we never master it anyway. (Happily our pre-Algerba course has enough not-too-hard long division practice sprinkled through the semester that ... I've seen it happen w/ a few students...)