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).

Hi Karl....I think this is where a lot of teachers are at. They see the possibilities but when it comes to actually trying to find a way to put them into action it's hard work.

ReplyDeleteI keep coming back to what Dan Meyer http://blog.mrmeyer.com/ talks about in deconstructing math problems and finding videos that you can hijack, take out the interesting parts and make an interesting question.

I've had good success with teachers and using Dan's approach with video and bleeping out a part of the information and allowing students to struggle to find the answer.

That's all I got for now....racking my brain for ya. :)

Thanks Jeff. Rest assured I have stolen (umm, borrowed) as much of Dan's stuff as I possibly can.

DeleteWhen I was in fifth grade my teacher let us move on to the next section if we "got it". He probably was teaching 5-6 small groups in the class. Can you "gamify" the tasks and maybe some kids can finish Algebra 1 AND Algebra 2? This may keep the kids involved and focussed and out of Wlfram Alpha.

ReplyDeleteMaybe if they finish your class they can start taking one of the online college classes?

As a student I would be highly motivated by a goal different than having to complete 186 days of algebra to move on. Perhaps imagine yourself in the students seat on Day 1. What do they want?

Interesting idea Brandt, but unfortunately I don't have that kind of flexibility.

DeletePretending for a moment that I did have that kind of flexibility, I see both positives and negatives with that approach. If you view Algebra as mainly a collection of skills, I think that would be a great approach and many students would respond to it. My concern is that while I want them to get those skills, I also want the bigger skills of thinking and inquiry and exploring, and I think that would be really difficult to manage with so many groups. (Not that it can't be done, elementary teachers are excellent at it, but I just don't think I can do it very well.)

I really like your idea of imagining myself in the student's seat on Day 1 - gonna have to play around with that a bit.

I am not toally sure about what you're looking for, but if it's an attempt to reconcile assessment, conceptual and procedural understanding (perhaps with the use of ICT) some elements of my thesis could be interesting: http://igitur-archive.library.uu.nl/dissertations/2011-1116-200647/UUindex.html

ReplyDeleteHi Karl, for what it's worth, my work is ALL about engaging students with relevancy, the application of content to context for longer term retention and authentic assessment. Disclaimer: I am not a math teacher nor do I spend time in front of a classroom of any kind with students. However, I spend lots of time with K12 facilitators who teach and assess applied math, science, technology, critical thinking, ELA, collaboration in context every day in their learning environment. No sales pitch, I just love my work! I will email you some examples of our curriculum. Hope you find it useful. Jeanne

ReplyDeleteHi Karl, First, I have enjoyed following your blog and thanks for sharing. I think finding that balance is what we continue to wrestle with in education. As Jeff Utecht said in an earlier comment, Dan Meyer has some great ideas. If you haven't read much by Dr. Keith Devlin, his philosophy on creating innovative mathematical thinkers is quite strong, while also honoring the need for traditional mathematics for those students who aspire to the fields that require it. Here is his blog entry on the Huffington Post: http://www.huffingtonpost.com/dr-keith-devlin/all-the-math-taught-at-un_b_1371977.html

ReplyDeleteI work with younger students, but I'm wondering if you could at get some ideas from the stuff that inspires me. Could you get your students to create, design, and think like programmers by having them learn Scratch or Python? Then you could have them make or remix math-based projects like this fraction vizualizer: http://tinyurl.com/d92vZqu. (To see the actual code rather than just running the program in a browser window you could download Scratch and the vizualizer game from the MIT website.) Students like yours could probably be up and running with Scratch after just one mini lesson!

ReplyDeleteKarl, you may have considered this already, but perhaps asking the students for confidence/reflection/journaling? This won't prevent them from simply getting the answer using Wolfram Alpha, but by sharing their confidence while answering the item, adding justification, and reflecting on their answer and rationale post-assessment - coupled with goal setting - might encourage them to take more ownership over their knowledge. Take a look at Naiku as an example.

ReplyDelete