Groupthink about group work?

My students always work together, in the sense that they discuss solutions whenever they get stuck, collaborate on investigations, and argue over concepts, methods, and proofs. They are (almost) always on task - and in the classroom buzz you can pick out exactly the kinds of things the above texts recommend: students comparing solutions, explaining to each other, arguing math...

In theory, this is great, and previously I've actively encouraged such cooperation. After all, what better way to learn to communicate math, sharpen argumentative skills, look at concepts and methods from different perspectives - well, y'all know the drill.  Every modern text on teaching and learning mathematics seems to wet itself with excitement over group work. A classroom full of quiet students working alone with their (gasp!) textbook is, or should be, a remnant of older and more ignorant days.
But now I'm starting to change my mind.  I see how students use each other as crutches, easy support instead of the harder work of figuring something out by oneself. Two main negative effects from this: students believe that they have mastered and understood something which they really haven't, and also that they are deprived of the chance to build thinking, memory and confidence by single-handedly struggling with math problems and concepts. 

In an ideal world students would be doing this kind of individual work as homework. This is not an ideal world.

So I'd like to incorporate more of that quiet individual work in class, but at this point I'm not sure how to fit that in with the explorations we frequently have going on. It's a matter of priorities, I'm sure, but even without individual work we're struggling against the clock every lesson. Right now I'd just really like a structure that I can use for each (or at least most) lessons and which includes a brief warm-up review of the previous lesson, an exploration, discussion/summary, group practice, and individual practice. But unless these components on average take less than 10 minutes each (they don't), something's gotta give. It's a pretty nasty dilemma and I welcome any and all suggestions.

First attempts

It's Friday night, and what better way to spend it than read through nrich and ncetm resources? (I don't know whether to take a lengthy think about my life or just be happy that I love my work).
Anyways, I found a few ideas that I've been meaning to try out in my teaching but haven't gotten around to just yet. With a trig unit coming up, and the ncetm resources being so very well-written and inspiring, I decided to jump in and design my own resource based on two (for me) novel ideas.

1. Always, never, sometimes true classifications: Supposedly great for promoting conceptual understanding and constructive discussion.

2. Matching activity: I like this one because it can so easily be differentiated by creating more options and/or leaving blanks.

Here is the actual file, which will probably be changed a bit before use in class on Monday.
Matching Basic Trig

(I do not know why Scribd likes to minimize letters and rotate pictures. The original document looks neater.)

Something I'm not very happy about is the increase in paper copies these kinds of activities seem to require. I'll probably project the classification task on the board instead, and am grateful for any other suggestions.

Testing, testing...

This New York Times article can't be news to anyone by now, and I look forward to reading the details of the original study as soon as Science makes it online accessible to my university library. Of course this is nothing new. Francis Bacon, in the 1620s, said what dozens of research studies in the 1900s have confirmed:

"If you read a piece of text through 20 times, you will not learn it by heart so easily as if you read it 10 times, while attempting to recite it from time to time and consulting the text when your memory fails."

So I've happily been putting testing to more use with my students. Mostly, I'm using the opening and closing activities from Every Minute Counts, and the good news is that it's been very easy to do this in every class (both math and psych).

This is what it looks like right now:

Start of class: "put away notes and books and try your best to solve the problem on the board". Typically I'll have a basic problem that tests recall of previous lesson or homework. Sometimes I'll include another problem which opens up to whatever material we're doing the current lesson. As an example, last time with my Seniors, I started with the question "P(getting 2 sixes by tossing two dice once) = ?" and on the other half of the board had the question "P(getting two pink socks out of a drawer with 3 pink, 2 orange and 2 red) = ?" This led us straight into the distinction between dependent and independent events, and thus served two aims at once.

End of class: "list the main ideas from this lesson". After a few minutes they are allowed to compare their list with a classmate, and a minute or so later check their notes.

This has been incredibly easy. The main difficulty has been that students seem unused to, or unwilling, to let go of notes and book and classmate-support. I've spent a significant amount of minutes convincing them that this is a good idea, even if it feels frustrating to not remember everything you think you should.  I'm usually strong at starting, weak at following up - so the fact that this is working and growing is a sign to me that this is worth pursuing and I hope that students will learn to test themselves while doing homework or revising as well.