One of the big things that jumped out at me from the Math Minds article was the sentence “when tasks are organized such that each piece builds on understanding of the previous, assessing understanding at the end of a lesson or even at several intervals during a lesson is not enough.” This is something that we have discussed at Galileo a lot. William and Leahy (2015) talk about the need to formatively assess students up to even every 10 seconds. This is something that sounds extremely overwhelming to a teacher, how are we to assess our students understanding every 10 seconds?! I actually thought that when I first heard it in Galileo, not thinking back to what we’d learned this summer. Now reflecting, we can do this with ribboning. Adding on an additional layer from this course, ribboning is not enough, we do this through intentional variation paired with ribboning.
I’m reflecting on my percent unit right now. I would argue that I effectively ribboned and varied my examples when working with benchmarks. Student’s definitely have an understanding of this, so much so that even when I give them the option to use another method (convert to a decimal, multiply the decimal and the number) they still are choosing to use benchmarks. I find this super empowering actually as my students are choosing to perform their math calculations mentally instead of using a calculator.
We’ve now started to look at GST and sales in stores, etc. Through an activity today I’ve realized that I did not ribbon or vary that idea very effectively at all. When I reflect back to the lesson, I realize that I showed examples over a few days, but the ribboning wasn’t present to allow students that ability to practice immediately and get feedback. This will definitely inform where I am taking my lesson on Monday. We will start with calculating 5% of various numbers and then to become familiar with our idea of GST, we will add these amounts to our original number. From here, we will look at calculating 10% of the same numbers, but this time to familiarize ourselves with sale prices, we will subtract the amount. I will then ask, can I use the 5% we’ve already calculated and add this onto our discounted prices as tax? (No – we will talk about how tax is not added to the original price, but the sale price). Using this understanding I will look to bridge this understanding by asking:
“The cost of an item is $20. At one store there is a 20% off sale. At another, the item is already on sale for 10% off, with an additional 10% off the sale price.
Will the item cost the same amount at the till? Prove your reasoning”
I will have students explore this idea, using calculations to prove their solutions and/or a combination of the numbers on the board to support their work. Following this discussion I will have tasks that allow students to continue to practice this skill and for those that have mastered it, the opportunity to extend their understanding through various challenges/problems.
I feel like I’ve moved through the process, but am worried that I’ve made too big a jump at the end. Thoughts?
Until next time,
Metz, M., Preciado-Babb, P., Sabbaghan, S., Davis, B., & Ashebir, A. (2017). Using variation to critique and adapt mathematical tasks. In P. Preciado Babb, L. Yeworiew, & S. Sabbaghan (Eds.), Selected Proceedings of the IDEAS Conference: Leading Educational Change, pp. 169-178. Calgary, Canada: Werklund School of Education, University of Calgary.
William, D., & Leahy, S. (2015). Embedding formative assessment. West Palm Beach, FL: Learning Sciences International.