Chapter Three of Minds on Mathematics by Wendy Ward Hoffer is called Tasks.
The PoD presented is: How can we design math learning activities that generate student understanding?
I liked Hoffer's idea of changing from Shallow Math (rote learning- no critical thinking) to Deeper Math (understanding and building connections), but was becoming impatient. I already limit rote learning in my classroom. Yes, I still use it. Let's be realistic.. there are some areas of mathematics where practicing the same type of skill over and over builds memory muscle. Many students can't transition to higher level critical thinking without the rote foundation to lean back on. They have to trust the base of the tree before they climb out on the branches.
One thing that I do like that Hoffer stresses is using what you already have, and not stressing that the materials or text book that you are currently working with are inadequate. She suggests Re-sequencing or Modifying Existing Tasks. Often some of the higher level pieces within the text are at the back of the chapter. Hoffer suggests those should come toward the beginning. We currently use an online math program called DIGITS. One thing that happens in each DIGITS lesson is the use of a launch. It is a word style problem that is designed to get students thinking and talking about mathematics. Some of them are really goo.. other eh.. I could live without them. And here is my YEAH BUT....
It's that dreaded work again... TIME.. IF I try to complete the launch for each lesson with my students, I won't get through the lesson! My lessons do not include a ton of practice problems, so I'm not making students sit and do rote practice. Usually the lesson is divided into 3 parts. Part 1 contains the basics. It has an example and usually one or two "GOT it" style problems. Parts 2 and 3 follow the same pattern with increasing complexity of both text and critical thinking. Even if I skip the launch.. I have trouble getting through all of the material.
I know what Hoffer would say... 1) understanding, not coverage is the goal. 2) Challenging tasks generate and demonstrate understanding. 3) Devote your class time to making meaning.
So I'm hoping that others who have read or are reading this book have any insight into this matter?
Leave me a comment or two if you are thinking the same, or better yet, have found a solution to my Yeah But.
Also, link through to visit Sherrie at Middle School Math Rules and see what other's have posted about Chapter 3.
Enjoy your weekend!
Hi Michelle,
ReplyDeleteHow do you like digits? It was one of the math series we looked at it when we were in a math review, but chose Carnegie Learning.
I would say that when planning the work time you would carefully choose the problem(s) each group is working on. Each group may be working on a different problem, then they can share results, instead of having every student do every problem. This way you can differentiate the problems based on ability (well that's one example). We really need to carefully choose the best problems for students to sink their teeth into.