Mathematical Practices

So I'm now officially more than half-way through getting my second master's degree.  My first degree is from the University of Oklahoma, officially titled "Master of Education in Educational Instructional Psychology and Technology" - a long title for teaching with technology with some extra thought about the human mind and how we think.  Although I was glad to get the degree at the time, I've found that much of the technology is now outdated.  Since I took 12 years off from teaching to have my kiddos, I thought that it was time to learn about current educational theory.

Shameless plug…
I researched for quite a long time because I wasn't interested in going back to school for a master's of pure math.  Basically (being totally honest here) because I've been teaching just algebra for so long, I was afraid I wouldn't remember anything at a higher level.  On a complete fluke, I came across mention (In a discussion thread, buried way down somewhere) about a program at Montana State University.  I did some research and calling around and found that this program offers a Master's of Science in Mathematics for Math Educators!  I've been in now for a year and a half and I think it is fantastic.  It is mostly online with a small requirement for three weeks during one or two summers at the campus (which is in a beautiful location in Bozeman, MT, not too far from Yellowstone NP).  If you're looking to further your education, this is a GREAT program!

Ok… back to Mathematcial Practices.  This class I took this summer was all about teaching around the new Common Core standards and the Mathematical Practices.  I'll tell you what, I understand them so much more and will definitely have to look at my units and see if I'm covering everything.  I was back in my classroom a little this week and was thinking that I wanted to post something about the practices so my students are familiar with them.  As I was browsing online I came across these:

Oh my…. they are AWESOME!  The practices are listed and broken down easily for the students to understand.  Now I take absolutely no credit for these, but they were easily available by just doing a search for "math practices" and then clicking on images.  Search around and you'll be able to find several PDFs already created for you.  I can't wait to post them on my bulletin board!

Minds-On Mathematics - Book Study

Today I'm linking up with Sherrie at Middle School Math Rules! for a book study on "Minds-On Mathematics" by Wendy Ward Hoffer.

 

This week we're in chapter 1, which is an overview of the "math workshop", which, as the title states, is used "to develop deep understanding in grades 4 - 8".

Questions for this chapter:
1.  What were your biggest ah-ha moments from this chapter?
2.  What components of math workshop are already present in your classroom?
3.  What are your next steps for planning for math workshop in the coming year?

What were your biggest ah-ha moments from this chapter?
Since I already use a version of this (learner-centered classroom), I don't think I had a huge ah-ha moment.  I liked learning about the history and purpose of math workshop, especially the thoughts of Vygotsky and his theory of proximal development, which really states that working in groups is great for kids (p.2).  I also liked that Hoffer linked the need for math workshop to the Common Core Standards.  As stated, math workshop allows students to "experience focus... congruence... and rigor" (p.2).  I loved the belief that students are capable of brilliance!

What components of math workshop are already present in your classroom?
The format of my classroom is very similar - warm-up; mini-lesson; reflection; and a huge chunk of work time.  I usually do my mini-lesson during the middle of our 111-minute block as a way to break up some of the time.  I thought it was interesting in the sample lesson in the book how the teacher modeled by using "think-aloud" and then had the students pair up and discuss what they saw.  There was a lot of think-pair-share going on and that type of discourse is something I'd like to work on. 
The biggest difference in the book model and what I do is the type of problems given during the work time.  I completely understand the ideas in the book, but I wonder if there is a balance between working multiple problems and working the challenging tasks.  I hope that is addressed in a later chapter.

What are your next steps for planning for math workshop in the coming year?
My next steps are to continue planning for a math workshop type classroom (I only field-tested this type of model for one unit in one class last year).  There is a lot of front loading and I think that assessments need to be completed first.  You cannot be a fly-by-the-seat-of-your-pants type of planner.  I believe this takes much forethought and planning to implement it properly.  I'm up for the challenge... are you?

Setting up Interactive Math Notebooks (INB, MSG)

At the Annual NCTM conference in Denver I was inspired by a booth and presentation on foldables. I am in love with them!!!  I'm not such the creative type myself, so I purchased two books full of templates ready to go.  Then, I found myself overwhelmingly inspired by all of the photos and information on Pinterest as well!  I've even gotten to the point that I had to get out of my "School" album and create and album for foldables and INBs all on its own!

So, now that I have all these resources, I decided that I actually needed to sit down and do something with them.  I've been toying with the idea of interactive notebooks for the last semester or so.  Our science team uses them and I think they have the potential to be totally cool and useful.  There are so many fantastic ideas and as much as I'd love to fit every single one of them into the notebook, I don't think that's possible!  So, here are the things I decided I wanted to do: (oh, and I'm going to call them Math Survival Guides, or MSGs)

Inside Cover & First Page:
I have two web sites the kiddos need to keep track of and I cannot tell you how many times someone would come up to me and tell me they forgot their logon information.  I decided they could glue a little strip to write that information on to the inside cover so that it is always available to them.  I'm sure I'll still get asked… but maybe a little less.  I also took one of the manilla pockets that divided the notebook into 3 sections and cut it up and glued it to the inside cover as a pocket.  I felt like this will give them a sturdy place to put items that need to be glued or flash cards.  The right side is the cover page, and I'm hoping the students will be a little more creative than I have been :).

Inside Cover w/ pocket and Cover Page

Table of Contents:

I'm still working on this page.  I am going to have them color code each unit, so you can see that Unit 1 (Geometry) is going to be green.  I'll give all the students one paperclip to hold the five pages they'll need for the TOC together so they don't have to flip through them every time they open the MSG.  I'm also going to have them include the date for each page, but I don't want to do that here since I'm hoping to use this for multiple years.  On the left I'm still thinking about what to put… rubric, standards (this is what I'm leaning towards), rules, etc.

TOC - still working on left side

The next four pages are for "reminders" of geometry formulas.  By 8th grade (according to Common Core) they should have already learned everything except for the Volume formulas, so these are basically a place for them to refer to as needed.  Notice that under each flap I've used pencil. I think color is great, and for their titles, drawings, etc I'd like them to be as creative as possible.  However, when they are doing actual math manipulation, I think it is important that they use pencil even in their notebooks.

Reminder formulas

More reminder formulas

The next four pages are the start of the real "meat" of the first unit.  We are going to start with transformations.  After looking at many, many examples, I decided that foldables and drawings will be on the left side and and response items will be on the right.  This is basically because I really dislike writing on the left side of a notebook because the spiral gets in my way the closer I get to the end of the page!  Just personal preference.  My first foldable I appropriated from tothesquareinch and I think it's fantastic!  I don't have a school budget for colored paper (*sigh*), so I added color to the actual figures instead.

Transformations #1

You'll notice my right side.  I've decided to complete one page a day on the right (remember, we have 111-minute blocks, so plenty of time).  The top (Write) part is where I may have the students put vocabulary for the day, work out a problem, jot down an important note, etc…  The middle part (Reflect) I will have them do during the middle of our class during "mini-lesson" time.  The bottom part will be completed at the end of class (sort of like an exit slip), but I won't always collect them (ohhhh, I have so much more to write about this - but another day).

Transformations graphic organizer

I'm still working on this page (transformations day #2), but I liked this graphic organizer from the Alden Schools.  I've written "What are the properties of transformations?" on the outside flap.  

I'm hoping that now that I've started this that things will move a little faster.  This is probably close to about 3 hours worth of work, but I had to make a lot of decisions about placement and other things (this is my type-A coming out here).  Let me know your thoughts and what some of your ideas for interactive notebooks are!

Creating Effective Warm-Ups

I'll confess… I love warm-ups.  They are my sanity keeper.  They give me just a moment of peace at the beginning of class to get my head back into place after the chaos (organized chaos, of course) of the last period.  They allow me just a minute or two of silence where, in my mind, I can just sit back and close my eyes and relax.  In reality, peaceful though it may be, this is my time to take attendance, address small issues, and make sure I'm ready to begin another 111-minute class period.

I like the structure that having a warm-up allows as well.  My students know that when they come into the room, that they go straight to the shelf near the door and the warm-up will be sitting there.  I just love if there is a day that I've forgotten to put the warm-up out changed routine and a student comes up to me and says, "Where's our warm-up?".  It just makes me smile…

In the past we've used Math Minutes or MathMate's as part of our warm-ups.  Since I'm in the process of integrating both 8th grade Common Core standards as well as Algebra 1 or Geometry into the same year (see my previous post about this craziness), I'm worried that the pace we'll have to work at will not allow for as much processing time as I'd like for each topic.  Depth of knowledge is also a concern, but that's for another post.  This summer I'm working with the other two 8th grade math teachers and we are going to come up with our own warm-ups that will both review previous topics as well as look at what was learned in the last class session.  I'm in charge of the first 10 and have gotten a jump on them. I think I'm going to call them "Recap & Reviews" since the first 5 questions will be related to things that they students learned in the past and the second 5 questions will be related to the homework topic.  (With 111-minute class periods a 10-question warm-up is quite doable.)

Here's a sample of my RR for the second day of learning.  The first 5 questions come from 7th grade standards since we won't have been in 8th grade for more than a week yet, and the second 5 questions are covering translations and reflections from the prior class.

I'm hoping, that by including the Review section, we will be able to continually remind students of things they learned during the year instead of trying to have them remember just before state testing time.  I'll keep you posted on my thoughts...

Implementing Common Core

Colorado is a Common Core state and this year we are officially past the transition period.  I like the idea of Common Core and think there is a lot of value in it.  Here's my dilemma: our school district has an initiative that all 8th graders will finish middle school having completed Algebra 1.  So, instead of teaching 8th grade math, I teach both Algebra 1 and Geometry.  However, since we have not yet transitioned to the PARCC assessments (correct me here, but I think with PARCC the students can test on the actual class they are taking??), I have to pack in both 8th grade Common Core standards as well as either Algebra 1 or Geometry standards into one year.

This isn't so difficult with Geometry since these kids are advanced and I can cover most of the 8th grade standards within warm-ups.  It's a lot tougher with those kids in Algebra 1 since, for many of them, this is their primary introduction into algebra.  Although I've been able to create a scope and sequence for the year, I'm worried about depth of knowledge.  I guess I'll be doing a lot of progress monitoring this year and have to reevaluate at the end of the year once more.

Here's what I've come up with:
Unit 1 - Transformations, Triangle Properties, Parallel Line Properties
Unit 2 - Number System (focusing on irrational numbers), Radicals, Pythagorean Theorem, Distance Formula, and Exponents
Unit 3 - Solving Equations
Unit 4 - Functions
Unit 5 - Graphing Linear Functions
Unit 6 - Systems of Equations
Unit 7 - Polynomials
Unit 8 - Quadratics (the algebra part - we moved the graphing part to the beginning of Geometry for time)

Units 1 - 4 are first semester and Units 5 - 8 are second semester.  I have about 35 blocks each semester per class to work with.  My goal is to continually use the items in Unit 1 within the other units if possible (for example, bring back transformations with graphing to work on slopes and equations of the line).  I don't want to teach something in August and not have them see it again until state testing in March!

What types of issues are you encountering with the implementation of Common Core?  What has been successful?