All+purpose+Algebra+2

=On this page, you'll find a variety of things...please peruse:)= First, I have now taught every level of math from 6th grade general math to AP Calculus. I feel very comfortable saying that I know what tools students should have and what tools they'll need as they progress through different years of math.  One of several "ah-ha" moments occurred over ten years ago when I was teaching dividing fractions to a great class of 6th graders. I demonstrated how to do the math, asked for questions, then turned them loose on a worksheet of 30 similar problems. As I watched the students work, I thought 'what good was this?' If I weren't a math teacher, I wouldn't be dividing fractions...and my life would still be ok. I started focusing on more than just the content and resolved to never be satisfied with just telling students what to do day in day out.

I started trying to stretch myself and the minds of my students. I published one of my units in a national math magazine // (http://www.eric.ed.gov:80/ERICWebPortal/search/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=EJ668813&ERICExtSearch_SearchType_0=no&accno=EJ668813 // then several years later, volunteered for an action research project sponsored by National Science Foundation which resulted in a five year commitment, four or five presentations (with the other eight teachers who also volunteered) at national and regional math conferences, and the publication of a book that tells of the action research projects undertaken by our group. We all authored one chapter. Not exactly a national best seller, but still pretty cool! (//http://www.nctm.org/catalog/product.aspx?ID=13484)//

So this leads me to ponder what should a high school mathematics classroom look like? In my vision (which is supported by NCTM, work I did with the discourse action research group, and other articles), the math classroom should We teachers also have process standards to try to implement. My best way of summing it up in a neat and tidy fashion is to say that essentially, don't do the same thing over and over and over again. By the way, here's a link to the Common Core math standards. You'll want to look at the high school section. In particular, look at the 'construct arguments' and 'critique the reasoning of others'. The expectations go way beyond what 'we' grew up with. [|Common core standards] Thankfully, these beliefs fit in with the DSM schools math vision. The DSM district adopted a new textbook series called CME that is to be used in Algebra 1, Geometry, and Algebra 2 classes (here's a couple of links for you to go to and read an overview of the series: http://www.mypearsontraining.com/pdfs/TG_CME_ResearchPhilosophy.pdf http://www.edc.org/newsroom/articles/high_school_mathematics http://www2.edc.org/cme/showcase/HabitsOfMind.pdf It is NOT a "teach yourself" philosophy necessarily but it DOES require that students take a more ACTIVE role in their learning--this is uncomfortable for students at first who are used to being told EXACTLY how to do something. And, quite honestly, it's just as difficult for us teachers (me included) to relinquish the control that comes from being 'the sage on the stage'. Teaching is both an art and a science: the science comes from knowing the pedagogy (what should the students learn and when should they learn it) and the art comes from me, the teacher, knowing what method (direct teaching, small group, individual exploration) to employ. The CME series serves as a great framework for me to make more explicit not only the CONTENT of Algebra 2, but the THINKING that drives the material. In this type of classroom, expect students to say 'he doesn't answer my question' or 'he makes me ask my neighbor' or 'he asked what do I think instead of telling me how to do it'. I may be more direct with answers to some students than to others--I'm just using my best professional judgement to figure out how to make the kids exercise their minds.
 * Encourage students to conduct thought experiments ('what ifs' as I say)
 * Have students writing to help process their thinking (in the district it's called Writing to Learn)
 * Get students to argue and conjecture (I routinely try to get students to propose their own conjectures about stuff like 'rules of exponents' or 'does the commutative property hold true for operations in matrices?')
 * Give students adequate practice in the computational aspects of mathematics (in my mind, this is the aspect that is overemphasized in many classrooms because of national focus on test scores)
 * Support the different needs to students (easier said than done...I try different teaching styles depending on the thinking needed and the content to be digested...I also attempt to differentiate the assignment sheet and expectations of what students should complete)