So, Sarah Carter and I chatted on twitter some about practice structures, and she totally beat me to blogging about it. Read her post
here. She also calls for you to submit the practice structures you use.
My goal is to generate a reasonable list of practice structures that will be efficient for me to use and also beneficial for my students. Ones that make them think, move around, and engage in their learning. Efficiency is an issue because I don't want to always spend 15 minutes explaining a new structure. There are lots of options out there and if I'm always doing new things then the focus comes away from the learning. Here is my list so far, and I'm going to explain how I have/plan to use them and what the benefits I see are. I'm also interested in how these can be incorporated into student notebooks.
Card Sort: I most often do this individually where each student gets the whole set and sorts and glues into his/her notebook. I like that it is a sorting activity, so good for organizing the learning in the brain. I like that it goes well into the notebook. I don't like that students don't have to explain. One idea on making this better is to have them do the sort as a group and pick a few each to put into their notebooks with an explanation. Which gives fewer, but more meaningful, examples in their notebooks.
A few times this past year I made a whole class card sort where students each got one card and had to find their match. If the class had an uneven number then I would leave one out on a table and one person would match the table. As they match up they come check with me. Sometimes I time them and they compete class period to class period. Fun, but each student does not see all matches.
QuizQuizTrade: I'm not really sure I do this correctly for it's given name...but I give each student a problem, have them work it out. Then after a set time I make everyone partner up, work their partner's problem (which becomes their problem), and talk through it together. (Maybe I could call it "DoTradeDoTalk"; DTDT for short.) Then after a set time, new partners, repeat. There might be some benefit to having a student keep the same problem as "theirs" the whole time, but I'm not sure yet. Good practice. We often do 48 problems when we use this structure.
I have a handout (pictured below) that they use and keep in their notebook pocket for the unit. This means that the students probably don't look at it ever again, but I feel like this past year my students were better at that, so perhaps I can help my students develop that better. I would suspect it would be easy to get students to put this in their notebooks as well.
Stations: I have 6 table groups set up in my classroom, so I usually do 6 stations. Students rotate based on my timer from group to group. I usually post answers on the back of the next station so students can check their work themselves. I don't always have great participation in stations, but it might be because I haven't found a good way for students to record their work. Sometimes it's just on whiteboards, so maybe they think it's less important?
I have had some thoughts of making stations a more challenging structure  more than just rinserepeat practice problems. This would make it more important for students to work together as a group, hopefully getting better involvement.
Jigsaw: I have only done this a few times, and I think it was all last year. But I use this as a way to jumpstart a class discussion where I want students to "notice" and "wonder" about a new idea. Each table group would be given a problem or group of problems to complete and present to the class, afterwards as a class we discuss patterns and try to draw a conclusion. It would be possible to have discussion questions for groups of students as well, but I generally facilitate the discussion as a class. Perhaps a wellwritten "talking points" could follow the sharing part and precede the group discussion. I want to use this more in the future as it seems to be a good use of class time.
Posted Problems: I tape problems up to my walls and students do whichever they want in whatever order. I usually post answers for them to check as they are working. This gives them movement and the option of working alone or with a partner. Also works pretty easily in their notebooks.
Scavenger Hunt: This is where problems AND answers are posted throughout the room. Students work a problem, then find the answer (to the one they just did) attached to the next problem they are to work. It is self checking (AWESOME), students can start anywhere because it just does a big loop, and makes kids move. A lot like "posted problems", but a little more work to set up and get students to understand the structure. Since I usually post answers so matter, I'm not sure the benefit of one over the other.
Coloring Page Worksheet: Like a worksheet, but includes a picture to be colored as the problems are worked. Answers are placed in spaces in the picture and when students get an answer to one of the problems they find that space in the picture and color it. It is very calming for students to color, however I often have some students who just color and some students who just do the math. The students in the former group are the ones I'm concerned about. However, I feel it beats just a regular worksheet, which I use sometimes, too.
Add Em Up: I'm sure I learned about this from Elizabeth at TMC14 during our morning session, but she has blogged about a complex number placemat activity
here. I've done this once or twice and I need to do more of it. I just don't have a good answer to "What if I have a group of three?" Also it's a lot of paper to give each group all the placemats to do their work. Often I use whiteboards, so I could probably make that work better.
If you haven't done it before, students work problems in their group in "rounds" and they are told what the sum of each of their results will be. In that way it is self checking. Each student does their individual work in the corner of a "placemat" which gets them focused together as a group. If their sum doesn't work out from the beginning then they have to check each others' work.
The Mistake Game: I found this from Kelly. She actually has several posts on this structure, but here is
The Guide. Simplified, groups of students present solutions to problems that include at least one mistake. If they accidentally include more mistakes it is better. The audience has to find the mistakes. This is more engaging for the students. Read her post for more details.
I have done this with my freshmen and my upper classmen. It works really well with my older students, however I don't think it's ever worked well with my freshmen. I'm not sure why. Maybe I need to persist and do it more often? I try to get all students to ask questions and present, but some are really hesitant and expect the other students to find all the mistakes for them :( What usually happens is it ends up taking FOREVER to find the mistake and then a student blurts it out instead of asking a question. Or the same student finds mistakes in 12 out of 15 problems.
I really, really, really like this, but I need to find a way to make it work better in my Algebra classes.
Open Middle Style:
This is where #mtbos is compiling problems of this nature. These problems require a lot more thinking and tinkering with the mathematics than regular practice problems. I would like to provide students with at least one problem like this for each learning target we have. (Maybe these types of problems would work well as stations...hmm...) Sarah has posted some she has created
here and
here, and I have a few I might share as I work through my functions unit. However, there are a lot on the open middle site I linked above, so check them out!
So those are the practice structures I use/have used/want to use. Some of them I want to use every unit (card sort, quizquiztrade, stations, jigsaw, add em up, open middle) and some of them I'm not sure I want to use at all (scavenger hunt, coloring page, mistake game), but now I have a starting point as I work through my units.
Please let me know your thoughts on any of these practice structures! Ones that are great, ones you don't like because..., ones I'm missing here that I should definitely include, etc. I would like to know so that I can use the best ones for my students.

Kathryn