An accident happened to me while teaching Algebra 2 this year. A very good accident. I was teaching solving equations, and I always tell my learners that solving equations is about looking for 1’s and 0’s. I stress this fact, and point out the 0’s and the 1 every time we solve something.

And of course, before we can do equations, inequalities, or absolute value equations, we do expressions. And EVERY single person in the class can rattle off “Please Excuse My Dear Aunt Sally For Looking Too Rough” (did you forget the “from left to right too?).

I taught the lesson, I had SADMEP written on the board, and as I looked at it, I realized that if I wrote the 0 and the 1 down in the right places, it would help. Then I taught Inverse and Identity, and I realized that I had the Inverse and Identity right there!

But then I had an IEP learner in my room later, and he asked me to explain it again. He was confused on when to use SADMEP and when to use PEMDAS. He has been told since elementary school that PEMDAS was how to do problems, and in high school it was all different. He really struggled in Alg 1(I had him then also), and his struggles have not abated. So, I wrote down something else on his paper. It looked like this:

Link: http://www.box.net/shared/2msix7air5

And the learner looked at this and said “AHA!  I understand now! We are doing different things.”

The whole issue of Expressions and Equations became clear to him, and I realized I had just written down something that made sense. It have him a HOOK to attach his learning.  PEMDAS was a hook as well, but it no longer works for solving, and putting them side by side made sense to him.

When the learner looks at it, she can see that if you have addition, you need a subtraction. If you have division, you need a multiplication. The Identity is written right there, and the inverse is the opposite! They groupings GIVE the learner a HOOK to LADDER what they know to solving equations.

My learners tell me it makes sense to them. I realize it is a ladder that allows them to practice what they know in a new situation and it gives them the same structure that PEMDAS did for expressions. It does not give them answers, it gives them KNOWLEDGE about how to solve equations.

I like it.

Well, I have gotten into the school year, and I am getting comfortable in the routines.  It was more difficult this year with three preps, so I have spent some time getting more prepared and have had to focus constantly on how I am planning.

Some things I have done to make sure I am successful.

1. I have been using PocketMod to keep myself organized.  I have the current week, the next week, a yearly calendar, and then to do lists for Algebra 3-4, AP Stats, Gateway Math, and UNR Class, with one blank page for general stuff.

2. I have flirted with the idea of installing PlansUnfolding.It is a turbocharged version of PocketMod.  Both are free but PocketMod is web based and requires no installation of Latex like PlansUnfolding does.  However, Latex could be very helpful to learn.

3. One thing that killed me this year was that I did every lesson free hand on my SmartPanel last year.  It worked, it was cool, and it left me absolutely nothing to reuse for this year. I am essentially starting over from scratch! Bad Glenn.  Bad Bad Glenn.

4. So, in response I have chosen my Algebra 3-4 class (everyone else’s Alg 2) and am doing every lesson on OpenOffice Impress.  I would rather be chained to opensource than Microsoft, although I have started playing with Presentations ver. 2007, and it is nice.  I don’t know if my current laptop can handle the software though.

5. Finally, I am recording my lectures for Alg 2 (about 15 minutes per day) and posting the MP3 version of it on Edline for my learners to download.  They actually have been downloading the podcasts.  I am using an 80 Gig iPod video with the iTalk.  I purchased the iTalk on ebay for $12, including shipping.

Finally, I have gone over the deep-end on use of technology in the class room.  I will do a separate post on that.

So one of the biggest problems with using skills based assessment, or standards based assessment, or any of the other names that can be given to the process that Dan Meyer has been educating us on is that Alg 2 is just way to darn big.

I mean, really.  Rational functions?  Composition of functions?  If we break these down in to the smaller, little skills that are part of either of these two concepts, then we will never actually assess the larger skill that is essential.

This is a problem. H. already discovered this, and she was very willing to say so.  A couple of other people have said the same thing in the earlier comments on my blog.  Given the previous experiences, should I scrap my idea of using this for Alg 3-4 or should I forge ahead and figure out a way to do it?

I vote for forging ahead.

I already posted a Concept checklist for Alg 3-4.  It is still a rough draft, and I will be editing it and refining it. ESPECIALLY given my most recent idea.

I was introduced to “I Can” statements a couple of times this year, both in different contexts.  What I thought of doing is making the learners do “I Can” statements and then using those “I Can’s” to create assessments based on my Concept Checklists.

Yes, the learners would have to keep track of two different things. They will have to keep up on what they Can and Can’t do AND keep up with how they are doing on their Concept Assessments.  The Concept Assessments need to be linked to the “I Cans” very carefully and justified very well. If they are not justified both directions, then the reason for doing all of this work goes out the window.  The learners will see it as busy work and throw away the paper on their way out the door.

Before I really get into this one, I must first say that I will use the terms Alg 3 to mean the first semester and Alg 4 to mean the second semester of my District’s second year algebra class.  I am specifying this because as I have talked to and grown in my understanding of Math, I realized that every district does this differently.  This is my attempt at mitigating  a little of that confusion.

Right, so before I can post the third (and far from final) draft of my Alg 3-4 Skills checklist, I think it would behoove me to first share what my starting point is.  Here are my district’s expectations for Alg 3 and Alg 4.

First off, ignore the dates at the bottom.  This class has not been updated with either the new standards (adopted a year and a half ago) or been re-formatted to be standards based instead of textbook based.

Does anybody else see a difficulty with what I am trying?  Some of the topics here are HUGE!

So, I needed some ground rules.  First off, I can not assess everything I teach.  This is vital, and essential.  Second, these skill assessments can not be the only assessments I give.  I am going to have to assess in a comprehensive manner. in addition to my skills assessments.  Finally, my skills list must fit on one page, single sided.

Okay, that last one seems kind of arbitrary, but it is not.  Part of my goal with this assessment strategy is to give the learners a recognizable and achievable set of goals, even if, or ESPECIALLY if, they hate math.

Giving them a three page list of skills the first day of class is saying to those learners, “you are going to fail this class because the amount of things to learn is ginormous”.  I can’t do that.

One page, even if I have to leave off some skills, even if I have to double up on some skills, is still better than overloading my learners.  Now the burden is on ME to focus my efforts and make sure I don’t leave off some important aspects of the math.  Their burden is to learn.

So, here it is. 

I tried to match my District’s blueprint, since that is what the CRT is based on.  This is not a final draft, by any means.  I am very open to suggestions and criticisms.

H tried this with Intermediate Algebra (my district’s Alg 3-4) and found it to be lacking.  That makes sense to me, because Alg 3-4 is more complex.  At least Alg 4 is.  The first semester of Alg 3 is really just a review of Alg 1-2. 

Well, not to be discouraged with what H found out, I am going to try it as well in my Alg 3-4 classes as well.  I think, however, that H is right on the money when she says that Alg 3-4 covers HUGE amounts of math more than Alg 1-2 does.  This means that the objectives either need to be very vague and all encompassing (kind of like the standards are) or I need to have 40 or 50 skills to assess.

Obviously there is a problem here.  I have worked over my district’s blueprint once, and then went back and read what H had to say on the matter as well as Dan Greene and looked at the amazing video project that Sam did with his class.  My bottom line is that I think it is possible, but not easy to do.

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 on this later after I yank myself out of that mode into a more productive setting.