Friday, July 22, 2016

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?

Monday, July 18, 2016

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.

Thursday, May 26, 2016

Summer has arrived!

Summer break has arrived!  Technically, it arrive about 2 days ago.

This summer's to-do list is quite lengthy.
  • I want to completely rework at least the first semester's worth of geometry materials.  I've managed to make it through 2 units (out of 6) already.  The unit on transformations is my next to tackle and I foresee that taking a bit.  (Add to this we have a new teacher in our department next year that will also be teaching geometry.  I am super happy to have him join us, but I feel like there is that much more pressure on me to be as good as I can be.)
  • I get statistics back next year after a 3 year hiatus.  (We haven't had enough students sign up for the class for it to meet the last 3 years.)  My binder of materials is lacking in the fun-and-engaging category.  
  • PreCalc felt like it flowed well this year, but I would like to be able to cover more material in a year's time.  As it stands right now, we make it through functions first semester and trig second semester.  This year we had about 5 weeks left and began doing some work with derivatives as several of the students in class were registered for a calculus 1 course this coming fall.  I am hoping that #precalchat will help with that a bit.  
  • I start a new Master of Science in Education in Mathematics Teaching program in about 3 weeks.  I am SUPER nervous about this.  I know it is a small class, but I can't help but be curious about the ages of the other students.  Gotta be done, though.  
  • My son joined the Marine Corps and has successfully completed boot camp and his infantry training.  His next level of training will be somewhat lengthy so seeing him some this summer would be lovely but may be a stretch.  
  • The youngest child (to be eighth grader) has recently been asked to join the high school marching band as a mallet player.  This means two weeks of percussion/band camp for this summer have recently been added to her schedule that already included a week at church camp.  
Somewhere in the mix of all this stuff, I want a VACATION!  I'm thinking a beach or Disney World sounds great, but it will (at least partially) be up to the hubs where we end up.  Whatever it is, it needs to be in the next 3 weeks.  Nothing like waiting until the last minute.  

Here's to a great summer!  Enjoy a cold glass of lemonade, take a dip in the pool, read a good book, do whatever relaxes you and makes you happy.  

Monday, August 17, 2015

2015-2016 Day 3

Geometry started today by going over the worksheets from last week (Tower Task and Patchwork).  This went swimmingly.  The kids were able to set up the equations much more easily after seeing the blocks rearranged into rectangles rather than in the stacked form.  We followed a similar process with the squares in the Patchwork problem.  The whole point of these worksheets was to get the students used to thinking outside of their traditional methods.  We then took our first set of notes for the year - basically review of things the kids already knew.  Points, lines, segments, rays, etc were the topics of the day.

Pre-Calculus finished up their summer packet review.  I love this set of worksheets and the insight they have given me into what the kids already know.  I am a little concerned about the lack of comfort they have with graphs of parent functions.  At this point, they are only comfortable with graphing a line, a quadratic, and a cubic function.  They are far less comfortable with square and cubic root functions, absolute value functions, exponential and logarithmic functions, sine and cosine...  These are the parent functions of my course.  I fear what will not be covered in class due to the time we'll spend on these topics.  Later this week, the students are completing a placemat activity on solving various types of equations, including two-step equations, quadratics requiring factoring or the quadratic formula, cubic and quartic equations, absolute value equations, square roots equations, etc.  I expect the kids will do well with these.  The first few days of school have already taught me SO much about what skills these kids are lacking and the areas in which they have a firm foundation.  My next step is to create some lessons and activities focused on domain, range, increasing/decreasing/constant intervals, etc.  Not quite sure what I'm dong there yet.  (Suggestions gladly accepted.)

On a more productive note, the other geometry teacher and myself completed our list of chapter projects and their corresponding rubrics.  Geometry students are required to complete one project per unit.  We basically went with what I had mentioned in this post, but eliminated option 6.  We decided the openness of that option would be too difficult to grade/create a rubric.  

Saturday, August 15, 2015

2015-2016 Day 2

Day 2 was a productive one. The geometry students took a pretest for the semester and, while the results were less than great, it just means that we can't go anywhere but up.  It's nice in December to see what they've learned and retained over the course of the semester.  This is the same test I gave last year, so I will be anxious to see the results of this year compared to last year.  My #1 goal this year is to work on comprehension and retention.  

In PreCalc we continued working through the problems on the summer packet.  We determined yesterday that domain and range, increasing/decreasing/constant intervals, as well as piece-wise defined functions need some more detailed study when they come up in our lessons.  This isn't shocking to me as it is a common issue each year.  The kids do have a firm grasp on finding zeros via factoring or graphing, end behaviors, maxima and minima as they apply to linear, quadratic, and polynomial functions.  Our summer packet concludes with rational, radical, exponential, and logarithmic functions.  There is also a little bit of right triangle trig thrown in.  I expect most things in these areas will be things that they students aren't as comfortable with as they were taught late in the Algebra 2 class.  We were also fortunate to have a foreign exchange student join our class yesterday.  I can't wait to see what that adds to our class.  


Thursday, August 13, 2015

Day 1 - Tower Task

Every year about this time I come home and crash.  I generally forget how exhausting the first day of school really is. It's amazing to me how tiring reading and discussing the syllabus can be.

Since the routine of checking out books and reading through the syllabus doesn't take long, we spent the rest of each geometry period working through what I call the Tower Task.  The task is based off of one available through MAP called "Skeleton Tower."  We broke down the task into simple substeps that lead the student through the process of finding a equation relating the total number of cubes to the number of cubes in the center stack.  This is the second year that I've given this task and I really enjoy watching the kids work on it.

In PreCalculus, we spent the last half of the hour going over problems on the summer packet.  I like that I have this time to learn what they do and don't know.  It also gives the students time to talk to me and start to feel comfortable feeling vulnerable.  I think vulnerability plays a large role in why students typically don't ask for help. My goal is to break that feeling and to replace it with a feeling of mutual trust.

I can't wait to see what this school year holds!

Wednesday, August 12, 2015

2015-2016 Ready for day 1

Ready for day 1:
     While yesterday was the first day that teachers and staff were required to report for this school year, I stared revisiting my mess of a room nearly two weeks ago.  Files are now organized,  shelves are stocked, and (most of) my first day copies are ready.  I'm all ready for students to come in tomorrow!

Here's my setup this year:
     My little corner of organization.  This is just all the things I like to have close at hand.  My wonderful husband came from his room (down the hall) to hang a small magnetic dry erase board I bought from Target.  I intend to use this to keep track of my to do lists and all of those little papers we need to keep at hand.  The yellow folders hanging on the whiteboard is where I keep papers that are graded and ready to be returned to the students.
     These are my bulletin boards.  The one at the back of the room displays the mathematical practices.   The border on both the front and back boards is just gathered pieces of burlap..

     The front bulletin board is just inside the door.  It shows the emergency posters that must be posted and a place for me to write the daily assignments.  I may remove those, though, as I post the assignments multiple places on line already.

     The trays on top of the bookshelf are where students pick up the worksheets or notes that are necessary each day.  The shelves underneath hold the dry erase boards, markers, and erasers, as well as the Chromebooks that I have accessible for my freshmen students to use.  (The sophomores-seniors all have them assigned to them.)  The file boxes on the bottom shelf are a new addition.  I am always looking for ways to organize the worksheets/notes left over each day so that absent students can get ahold of them easily.  I have hanging folders in each day of these week and each day of the previous week.  There is also a folder to hold extra papers for those that are from weeks that have passed.  
     The bookshelf below houses graph paper, scissors, tape, rulers, etc.  
The pictures below show various views of the room. 


I am READY for tomorrow.  Cheers to another great year!