So what is my goal with my math students? That is the question I am addressing, it is my "over-arching" question as I review the first half of the year and think about the remaining year & more importantly future years. Am I trying to create little mathematicians/engineers (no), am I trying to create drones (no), I am trying to give them the problem solving skills they need to succeed in the world. I ask this "goal" question as I pull together ACT data from the last 2 tests and measure my students (thus myself). The real challenge is tying the ACT to the CCSS to the skills really needed by my students.
The ACT is just a measurement made popular by colleges, but it does provide insight. Making my students unafraid of problems with numbers that require thought and processing is my goal, the ACT does not measure that well at all. But it does check the basic skills, it does indicate whether they are ready for college and/or career. The skills/material we learn is just the tools we need for problem solving (now and later). So as I enjoy my time off and lie around getting healthy (I was sick nearly all of December - 18 straight days of misery) I think about the CCSS (Common Core Standards), how it ties to the ACT and I wonder why there are so many standards in the CCSS. An example may help....
I was talking with another local math teacher at a basketball game and she asked if I was still not teaching matrices in Algebra 2, and I am not. The reason is if I put in big mathematical problems with processes there simply in not enough time to do it all. I have no problem pushing matrices out of Algebra 2 into Pre-Calculus (I teach matrices in Pre-Calc in May - thus you see how little value I believe they have), Some students need them for college but it is something that can easily be picked up at college and I use that Algebra 2 time for problem solving and being really good at the Algebra/Geometry. Maybe in the future more Algebra will go from grade 8/9 to 7/8 then 6/7/8 & allow time for more topics, but right now there is no time for matrices.
I judge myself (and my students) if they are ready for college level math (not remedial) and/or career. I judge myself (and my students) on whether they know the basics conceptually and understand that effort/studying is the key to math success (not math IQ). But I learned one thing in my previous career you need measurements.
Data is the key to knowing where you are and where you are going, running by gut feel is the worst thing - so I track a few stats. I track scores on the recursive quizzes I give, I track the ACT scores (it is what students need to do well on), and I track, what I believe may be most important, post HS data to really judge my students. My post HS data is math placement and first math course success in college (that is the best part of a small school - tracking 20 out of 30 students is easy). Funny thing is most schools that I have spoken with don't track post HS success -- but heck I view that as my true end-product. I am unsure how the CCSS should be tracked, I am waiting (with baited breath) for the Smarter-Balanced exam and see the data it provides.
All the success, failure, tears, etc don't matter if I create a student who cannot handle the next challenge. I continually chant that the students want me to be hard, so they struggle & learn with me, versus struggling later in college or career. But how does this all this tie to the CCSS and its practices? That is the question I cannot quite answer yet.
So as I pull together my ACT numbers I see many successes. Our trend is great, our scores are good, but there are still students on the fringe and those are the ones that I will try and set up systems to help. My favorite discovery is my D students can do math -- and that is important key -- if they can pass they have the basic skills and thus can succeed - otherwise they should stay for more instruction (so my line in the sand seems correct for passing/repeating students). The data lends to the idea that grades are timed-based thus not a great indication of ability. A student who does poorly in my Algebra class does not escape it in Geometry, they continue to practice and do quizzes through-out Geometry on Algebra topics. That allows the student who need more time to get it, it also makes sure the rest remember it. And it seems to work, my Juniors/Seniors do well compared to the rest of the country (where 5 years ago they were slightly below the rest of the country).
So I have found some success with recursive quizzes bi-weekly on previous topics that were taught conceptually. I have found a gap in my measurements and the CCSS, which I am unsure on how to bridge. I have found that while the CCSS spells out lots of good things, but it fails to point out the great, which as a small school teacher makes deconstructing them a priority with all my free time with 7 preps! Yet I know this is a slow progression, just like in business, the CCSS cannot be achieved over-night, and I will continue to track data, ask the big questions, and push for 3-5% improvement per year -- which is results oriented!