Sunday, August 3, 2008

Algebra 2 is amorphous and has multiple heads

and defies reduction into compact and self-contained little parts. I am still trying to do just that, however. This continues the discussion about applying Dan Meyer's assessment system for Algebra 2, and anyone not deeply interested in this narrow topic may as well go on to the next item in their Reader.

Some time in June, Glenn Waddel wrote:
I have a rough draft of my skills checklist done right now. I am not sure I am going to post it yet. I am not happy with it. I think I am stuck in the “do I have to assess everything?” mode.
More than a month later, that's where I am still... and since time is running out I'm going to post the incomplete work in case that helps accelerate the process.

Glenn has meanwhile posted a carefully worked out list, and written about the tension between assessing specifically enough without introducing an intimidating number of concepts. Reading his list reminded me that the differences between the various versions of Algebra 2 around are significant, and that our final lists will have to be different to accommodate our respective course specifications and student groups.

In particular, my Intermediate Algebra course leaves conics and discrete math for the Trig/Precal course, which uses the same textbook and picks up where my course leaves off. I do not need to include assessments on these topics, then. On the other hand I must make sure that graphical features of quadratics, polynomials and exponentials are covered carefully, as this will not be repeated in Precal, and this increases the number of skills for these topics beyond what may be needed in Glenn's course. Also, Intermediate Algebra is for the students who do not make it to Honors Algebra 2, and so I need to include a lot of Algebra review. Dan Greene's version of Algebra 2 is similar to mine in the topics it covers, but students arrive directly from Algebra 1 without Geometry between, and so may need somewhat less review. I'm guessing that Sam Shah's course is for relatively advanced students. However, while our lists will need to be different in order to take these things into account, comparing notes could still be very useful.

Dan Greene and I met a few weeks ago, and made some progress on breaking down the chapter on Exponential and Logarithmic Functions, a unit where I am replacing all of my concept test items from last year. So far, the unit on Numbers and Functions has been the most demanding unit, I think. There are so many big, abstract and quite unfamiliar ideas there. On the one hand, the process of breaking down this chapter into parts that can be practiced separately may therefore be all the more necessary in order to make it accessible to students. On the other hand, much of the point is for students to recognize an abstract idea, such as the transformation of a function, across pretty different contexts, and this is just hard to assess in a piecemeal way. Or so it seems to me.

Finding a convenient format or platform for technical discussion of how to slice a topic into discrete skills and concepts is a challenge of its own, though. A series of blog posts, one for each chapter, seems both clunky and overly time-consuming (and school starts in just over a week over here). Instead, I've stored my work-in-progress on this Google Site, and if you have time and inclination to think some about what are the essential things to test for each topic or anything else, suggestions would be much appreciated.

9 comments:

Kate said...

You are way ahead of me, I haven't looked at Algebra 2 since June. I became disgusted when I had reached 100 concepts before the end of the first marking period.

Sarah said...

And scaring me. I've made it through Algebra 1 and half-way through Geometry. Haven't tackled the Algebra 2 Beast yet this summer.

3 weeks left. Motivation indeed. And once I catch up, I'll try to contribute something useful.

Sarah said...

Different question for everyone. What textbook are you using? (Or are you not using one?) How much do your "topic areas" flow from chapters? How much do you pick and choose?

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H, after poking around the site some more, I'm all the more impressed.

Still in early browsing stages. Minor suggestion for the Functions and Relations quiz. On the table question, have only one number repeat in the f(x) column. (Or change the direction to change at most one entry.)

Kate said...

I feel maybe we should start a new post somewhere instead of hijacking, but, we are using AMSCO Course III for one more year, then changing to Prentice Hall. It's my first year with this course, so I'm not planning on reinventing the wheel for one year, I'm going to rely heavily on colleagues notes, assignments, and other assorted materials.

H. said...

Oops - thanks for the correction, Sarah! I've fixed it now. My school starts next week, so I'm afraid I'm rather more behind than you are. I'm leaving this for a day or two now to do other planning, though - have somehow had enough of this for a bit.

As for hijacking the thread - I'm still at the stage where comments of any kind, on topic or off, are exciting:) On the textbook question: we use Holt, Rinehart & Winston. I've mostly followed the same progression as the book, while using a good deal of external materials. I did switch the order in a few cases, for example in order to do a little on quadratic graphs before the functions chapter, since the textbook's going on and on about transformations of quadratics (chapter 2) before the chapter on quadratics (chapter 5) would make little sense otherwise. The chapter on functions (chapter 2) was pretty much inaccessible as it was, while Dan Greene's handouts were very effective. I don't think this textbook is written for my kind of students, and Dan Greene's placement of the functions unit rather later in the course would, for example, be better for students who need to learn graphing by hand from scratch ("how do we get the points?"). Jumping straight into transformations is just too fast.

On the other hand, I've gotten suggestions from both a few students and a colleague that it would be better to stick more closely to the book, because it's easier for parents and tutors to follow along then, and besides all the handouts raise issues of their own in terms of organization and paper consumption. I'm trying to provide a specific textbook reference for each target skill this time, and otherwise organizing more of the handouts online.

While the HRW textbook for Algebra 2 works okay with some supplementary materials, we're switching to McDougal Littell for Algebra 1. It's MUCH better. For example McD&L covers how to place numbers on the number line and omits closure of sets, while HRW does the reverse. For Algebra 1.

If anyone feels like being added as contributors to the site, and uploading their own sample assessments (within the same units or on separate pages) we could end up with quite a number of different ways of going about this. Mutual commenting on assessments would be much easier that way. On the other hand this could suck up far too much time...

Another thing is aesthetics of these assessments. Some of mine feel sort of cluttered/cramped, but I don't necessarily see how to fix it. But - that will need to wait too. Away from this!

Kate said...

I would be happy to post what I have so far...basically just our first unit (maybe 2, I don't remember). You might have to poke me to get later units, but I'm a big fan of sharing materials far and wide.

H. said...

Cool! My gmail user name is hrc.math - could you send me your google user name to that address?

Kate said...

I looked through your site, and I'm having trouble matching up what you do with what we do. Looking back at what I did in June, I've only written questions for our first unit which is mostly multiplying, dividing, and factoring various polynomials. I couldn't find a category in the ones you have posted so far that seemed to correlate. But, I posted the questions I wrote so far and my concept list for the first quarter as an attachment on the front page. Maybe in later units you will find it useful - I'll keep looking at it periodically.

H. said...

Thanks for the files, Kate! And wow - your course really is structured very differently from ours. I rather like the thing of starting with multiplying and factoring polynomials - not too demanding conceptually while providing lots of practice and review on combining like terms, signed numbers, and prime factorization at the beginning of the year.

It seems even more clear now, though, that the very idea of coming up with some shared list of concepts through online collaboration wasn't realistic. It's educational to see others' lists - but the benefits are hardly in the areas of saving time or effort!