Flawed and Uneasy Compromise

I'm stuck. I don't particularly like how I'm assessing in Algebra, but I'm not bright (creative?) enough to figure out how to do it better.

I've tried to strike an uneasy balance the last two years between my fairly traditional Algebra curriculum and some of my more "untraditional" views.  The compromise has been to assess over the traditional Algebra skills using a semi-standards-based-grading approach (see this and this and this and this to get an idea), while trying to utilize a more inquiry-based approach to exploring the concepts (followed by traditional, algorithm-based approaches via video in order to reinforce the skills and simultaneously free up the class time to actually do the inquiry first). It's been a flawed, uneasy compromise, but I still think it's been more successful than my more traditional approach in my first incarnation as a math teacher.

What I'd like, however, is to somehow transform my assessments into something a bit more higher order/meaningful, while still retaining the ability to assess whether the students have mastered the discrete skills that are still a big part of my curriculum. My students will have laptops this year (more on that in a future post) and, ideally, I would love my assessments to be open-Internet assessments.

But this is where I keep running into a brick wall - I haven't been able to figure out how to design assessments that not only test the skills that students are required to learn, but with problems that can't be solved effortlessly with Wolfram Alpha (and thereby don't give me enough information to tell what my students have learned about the Algebra). I haven't been able to figure out how to come up with more meaningful assessment activities for my students, but that still fit within the very limited time I get to see them (and also retain the ability to easily re-assess outside of class that I've utilized the last two years). I haven't been able to reconcile my belief that students still do need algebra-sense (akin to number sense), to know how to think about mathematics and perform some of those algorithmic algebra skills, with my just-as-strong belief that learning those skills in isolation and without context is pretty pointless (and not as successful as I'd like, either).

Some of this, undoubtedly, is a result of trying to balance two pretty incompatible things, yet that's still where I find myself. I can certainly stick with the assessments I've used the last couple of years and ignore my views about students being able to use resources on the Internet to help them, and redouble my efforts to come up with better inquiry-based activities to push my students' thinking. But I suspect that, while I might feel a bit more successful if I accomplish that, I'll be sitting here one year from today feeling essentially the same - that the whole is in this case actually somewhat less than the sum of the parts.

Now that I've gotten this far, I really have no idea what the point of this post is, other than a Hail Mary out to the blogosphere for someone to leap very high and pull me in. Any words of wisdom or links to resources would be appreciated (but, truly, I don't need any "I'm sure you're doing great . . ." type of comments, although I appreciate the kindness and intent of such comments).