Summer Tasks Redux: Suddenly Thinking a Lot About Pre-Algebra

Well that changed quickly. Just two days after posting about what I wanted to work on this summer, I found out that my teaching assignment for next year has changed. Originally I was schedule to teach one section of fifth grade and three sections of sixth grade.[7]I wrote this post on 7/10 but waited until the news was shared with my colleagues before I posted it. I have taught both of those courses in the past -- fifth grade for the last five years and sixth grade once six years ago. The plan now is to switch that fifth grade course with a seventh grade course which is brand new to me.

While the sixth grade course is not a new course for me, it certainly feels like one. I first taught grade six in my second year of teaching. Next year will be my eighth year. And, with all the changes and growth my beliefs and practices have undergone in the last five years, I am basically planning sixth grade from scratch.

Seventh grade pre-algebra is an even greater challenge. I have never taught that course before. Moreover, seventh grade is in a different division of my school.[8]Grades 3-6 are part of the Lower School and grades 7-9 are part of the Upper School. Teaching in the Upper School will mean a few significant differences from my past five years of teaching exclusively fifth grade.

  1. I will be teaching in two different divisions of my school. Teaching in the Upper School will mean balancing different schedules, norms, and practices under two different bosses. I have confidence in both divisions of the school, but I can't ignore that balancing the different cultures of the divisions will be something that will take effort and time. For example, the Lower School and Upper School write report cards at different times of the year, have a different advisory system, communicate and track student progress with different procedures, and provide academic support in different ways. None of these difference are unnavigable, but finding my way through the less-familiar Upper School routines and practices will definitely be a challenge
  2. The Upper School services a different student body than the Lower School. Between sixth and seventh grade, my school grows from about 42 students to about 80 students in each grade level. With these new students comes a wider variety of learning needs, experiences, and academic backgrounds. Most notably, my school's boarding program begins in seventh grade. Many of the boarders are students from other countries living in the United States for the first time. This is exciting! But, it also will put new demands on my practices as a teacher particularly in working with English language learners
  3. I will not be the only teacher teaching my course. This will be the first time in five years that I am teaching a course that a different teacher (two teachers actually) is also teaching. In the past, I have had free will to make changes and adjustments to my course. I will need to work with colleagues to balance those changes this year. I am comfortable socially with both of my new colleagues, but I have never worked with them directly. I am, however, looking forward to having colleagues teaching the same course
  4. My school begins tracking students in seventh grade. I will, by request, be teaching the "regular" section of the course.[9]There is also an "advanced" section of the course which is designed to cover the same content, but separate students by ability. In eight grade, students are placed into one of three courses: 1) a two-year Algebra 1 course, 2) a one-year Algebra 1 course, or 3) an "advanced" one-year Algebra 1 course. While researchers know tracking is not in most (if not all) students' best interests[10]NCTM made this point in this presentation (see page 25) on Principles to Actions. this is a circumstance of the school I teach at (and many many others). Given that, I prefer to work with the students deemed lower-achievers, so I can try to ensure they have access to the rigorous and challenging mathematics education they deserve.While no classroom is homogeneous in terms of ability, my seventh grade course will be the first "tracked" course I have taught in many years. I know I will have some work to do to promote a positive mathematical self-concept among these students as I have already seen changes in them since I last taught some in fifth grade. I am not sure how impactful it will be for these students to have been placed in the lower track, but I plan to do what I can to combat the negative connotation that comes with sectioning 12 and 13-year olds by ability
  5. Teaching in the Upper School also means using a curriculum/text that is very different from the text I use with 5th and 6th graders. In fifth and sixth grade, my school uses the Connected Mathematics Program 3 -- a problems solving and investigations based curriculum. In pre-algebra they use Larson Pre-Algebra (2012). The Houghton Mifflin Court curriculum skews towards more traditional mathematics instruction. Each unit or section introduces a single topic (ex: solving 1-step linear equations by multiplying both sides), details a new skill/algorithm, and then has students solve nearly identical problems.My personal beliefs align much more closely with the Connected Mathematics Program 3 model in which students learn best by solving problems rather than through direct instruction. Here is what the publishers of Larson Pre-Algebra says about problem solving "Holt McDougal's four-step problem-solving plan guides students through the process of problem solving. At the beginning of each book, the problem-solving process is introduced, and practice appears throughout."[11]Source

I am both excited and nervous about this change. Excited because I am eager to grow as a teacher. I am looking forward to developing the expertise that only comes from having taught a course. I am nervous because of the increased workload and demands teaching two (essentially) new courses will place on me. I always want to do the best job I can and I get really frustrated when I feel as though I am being pulled in so many directions that I can't do the sort of job I want to. I am going to have to work hard this summer and this fall to make sure that doesn't happen. Here is an updated list of what I am working on this summer.

Summer To Do List Update

  • ***Access my school's pre-algebra text - I got in touch with the other teachers who teach the pre-algebra courses and they shared a digital copy of the student edition of Larson Pre-Algebra (2012). I am waiting to get hard copies of both the student and teacher editions of the text.
  • ***Outline what is covered in pre-algebra - I used the chapter reviews in the Larson Pre-Algebra text to make an outline of the content the text covers. I need to speak with the other teachers in more detail, but my understanding is that they stick close to the content and the order in which it is presented
  • ***Make pre-algebra standards - There are 93 sections in the text each covering a separate topic (ex: 1.3 is on order of operations). I won't make each section a standard because 93 is just too many standards, so I need to go through and combine relevant content. For example, "Adding and Subtracting from Both Sides to Solve an Equation" and "Multiplying and Dividing Both Sides to Solve an Equation" are separate sections but could easily be part of the same standard on solving simple single variable equations. I am not even sure if I will need to separate 1-step and multi-step equations. While the latter is more demanding, they aren't necessarily distinct ideas
  • ***Collect tasks for pre-algebra course - Each section in the text is very traditional. It introduces an ultra-specific skill, shows how to use it, then asks students to practice those skills. It is very much a rote learning approach. I want to replace these lessons with problem-solving/investigation-based tasks. So, I have been scouring the web and identifying tasks that would work for teaching certain concepts. Geoff Krall's problem based curriculum maps have been extremely helpful with this
  • Be a Good Husband - Tyler is developing this skill. There is, however, still room for growth
  • Review and Update 5th Grade Standards - No longer relevant due to teaching assignment change
  • Develop 6th Grade Standards - Have not started
  • Add SBG Information to Email Signature for Parents - I am on the hunt for a good article I can share. I posted a question on MESE, but I may end up having to just write a summary myself because I have yet to find an article or resource that is what I am looking for
  • Read Research on Rational Numbers - In progress. I will share some reviews/summaries of what I have been reading in future posts
  • Create 6th Grade Pencasts - Have not started
  • Develop ≥9 Challenge Problems - I have a few problems picked out and am looking for more
  • Class Openers - I have started collected Always/Sometimes/Never tasks, but I have not fully developed this yet
  • Investigated CMP3 Videos - Have not started
  • Additional Parent Resources in Email Footer - Have not started
  • Plan a Math Coffee - Have not started
  • Plan "Emergency Absence" Lessons - Have not started
  • Python program for emailing SBG progress - I have figured out how to send emails using python.[12]I have definitely been misusing this newfound power. My poor buddy Doug got emailed a list of the first one million triangle number. His wife got emailed all of the lyrics to "999 Bottles of Beer on the Wall". I also know that I will not be able to access google docs with python because of my school's web settings. This can still work if I make a summary document that I download and go from there. I will work on this more once I get my standards written for 6th or 7th grade
  • Python Program for Printing Advisees' Effort Grades - I think I have this working, I am just not sure if the web address I am pulling the efforts from changes each time they are updated. And, I won't know that until the school year starts

***Newly added since my last post