PreCalculus in 2016-2017

In the earlier parts of the summer vacation there was a bit of discussion on Twitter about the topics typically covered in precalculus. For our course, use the 8th edition PreCalculus textbook by Demana, Waits, Foley, and Kennedy.  You can find a list of the topics by chapter here.  This may seem rambling, stick with me.  

The first semester of our course covers chapters 1 through 3.  This primarily means we discuss the analysis of various types of functions including linear, quadratic, cubic & other polynomials, rationals, logarithms and exponentials.  In our study, we talk about the basic concepts related to these functions: domain, range, continuity, extrema, symmetry, intercepts, etc and then examine how these change (or don't change) when various transformations are applied.  These chapters also include some great opportunities for applications of the functions including vertical free fall problems and finance problems.  

Our study of trigonometry begins upon finishing chapter 3.  This past year that fell about 2 weeks before Christmas break.  Typically we cover the functions, their inverses and the associated identities most of the second semester.  This means our year typically ends at the end of chapter 5.

Goal for this year...

Our algebra 2 teacher did an AMAZING job last year of digging more deeply into functions.  I expect this will speed our study this year.  My goal for the upcoming year is to finish at least chapters 1-4 in first semester and start with trig identities in second semester. 

My questions...

Am I expecting too much to cover that much material in first semester?

Calculus teachers:  Should I follow the order of the book - Vectors (Ch 6), Matrices (Ch 7), Conics (Ch 8), etc - or are there certain chapters that I should DEFINITELY cover to best prepare my students for calculus?

Vertical Articulation inspired by @TracyZager

I'm missing #TMC16 this year as I have the past few years, but I am thoroughly engrossed in keeping up with it from afar.  This morning, I watched the keynote speech by @TracyZager from that conference and was astounded at how well it spoke to me.

Our district admins have scheduled vertical articulation meetings at the end of each of the past few school years.  Generally, these meetings are attended by teachers representing various grade levels. In a meeting at the end of the 2014-2015 school year with teachers from grades K-12, we discussed the strengths and weaknesses we are seeing at each grade level.  It was worth noting that several grade levels voiced concerns over the same topics (multiplication skills, comfort when working with fractions, etc - the typical stuff).  The problem I saw with that meeting was that we never addressed how these problems should be tackled.  There was no game plan established.  At the end of the past school year the meeting took place between the MS and HS teachers.  We discussed where we had left off and noted that nothing had changed since the last meeting.  We all acknowledge that the problems exist, but have no idea how to tackle the problems we are seeing.

Like most districts and schools, we are driven by our standards and standardized tests.  I can't help but think that we have to find a way to address these problems, but what do you give up?  We know, for example, that multiplication skills are sub-par, but what do you give up in the 3rd grade curriculum to put more time into multiplication.  And, if you do find a way to adjust the curriculum, what skills may become deficient (that currently aren't) due to this change?

We have been told that these vertical articulation meetings will continue throughout the next school year, but they are supposed to be held on a monthly basis.  At the end of this spring's meeting, we were tasked with coming up with a peer study topic.  Our group chose to look at examples of low-income schools that are doing great things - have turned themselves around.  It is our hope that by addressing large-scale problems (school dynamics), some of the smaller scale problems (work ethic, students struggling with topics, etc) will improve as well.

Note:  I am in no way trying to say that all of our problems lie in the elementary grades.  I am simply using multiplication skills as an example.