Patterns Make Me Feel Stupid: How I'm Turning That Into a Positive For My Students

Having just completed Jo Boaler's How to Teach Math course thought Stanford's MOOC I am left contemplating the importance of studying patterns in Algebra. I understand they are more meaningful than empty equations. But as I study them for myself while trying to develop how I will use them in the classroom I have two reactions I didn't anticipate; 1) They make me feel stupid, and 2) I don't get how they relate to the real world.

Why They Make Me Feel Stupid

I'm talking specifically about working with visual patterns like those found on Fawn Nguyen's website.  I typically have little problem wrapping my head around how the patterns grow. My difficulty comes in finding the 43rd pattern and modeling the growth with an algebraic expression to find the nth case.  As soon as I recognized my internal voice commenting, "I hate these" and "I'm not good at these" I immediately realized that is how many of my students feel. So what was making me think these things? Im a teacher for goodness sake and I should know better. The answer; because they take forever for me to figure out. Epiphany! I was falling into the same trap my students do; if I can't figure it out in a few minutes then I must not know how to do it.  As much education as I have in teaching mathematics I still fall into that crappy old trap. How easy it must be for my students to fall into the same trap!

How Do They Relate to the Real World

Now I get that there is a great deal of learning that goes on in understanding patterns and using algebraic expressions to model them but how does that really relate to the real world? As i pondered the answer I took a walk on the beach during a family vacation. I found myself looking at the footprints and, noticing that some were partially washed away by the waves, I wondered how many waves it took to wash them away? And how does that differ with the varying depths of the footprints?  And why do some footprints vary in their depth? Then I wondered what caused the shoreline to jut out in certain areas and not others? 

So then I began to question whether the study of patterns was really a study of science rather than mathematics. Wasn't it really a question of the physics behind the waves that I was really wondering about? Then it hit me. I was asking the questions because I had been studying patterns.  thats what caused me to look for the patterns in the world around me.  And it is the existence of patterns and our wonderment about their cause that is the basis of science! Epiphany number two!  Happenstance does not give birth to scientific theory. Patterns do!  When we see things that occur regularly and with form; that is when we ask why.  Why does that happen? What is the cause? Can we recreate it?  By looking at patterns and working to model them with algebra we lay the foundation for scientific discovery and wonderment. That is how it relates to the real world. 

In the Classroom

In the end I am sticking with my desire to make the study of patterns much more prevalent in my classroom. I have decided that even though I am not so great at writing algebraic models for patterns, I will learn a great deal by sharing that journey with my students. We will truly be learning together. I will share with them how studying patterns initially made me feel and how important it is to remind ourselves that time and intelligence are not linked. And I will share with them how that created a curiosity in myself to see patterns everywhere and how to use them to explain the world around me. Ultimately I have come to realize that studying patterns is the seed to cultivating curiosity.  And that is more important than than my own feelings of inadequacy. 

Flipped Mastery: My Blueprint

As the school year draws near it has come time to finalize some decisions and layout my game plan for running my Algebra 1 course as a "flipped mastery" course.  Here is that blueprint, which includes the following:

• Background
• General Policies
• Assessments
• Class Structure
• Student Work Flow
• Students Who Do Not Finish Curriculum
• Physical Set-Up of Classroom

Background
I will have ninth graders all year as part of a new Freshman Academy initiative in our building.  The benefit for my flipped-mastery approach is that I won't have to get new students used to the routine and new approach each trimester.  Last year I flipped the entire year of Algebra 1.  Although I have many videos and guided notes to reuse this year, the first three units will need major revamping.  I changed things quite a bit during the first trimester last year as I found what worked (and didn't) for myself and my students.  I am also changing our practice assignments quite a bit from last year.  They are now tiered with a points systems that allows students to have a choice in the problems they do and the difficulty.  It allows for greater differentiation.

I also have the following resources in my classroom:

• 1 cadet teacher (an upperclassman)
• 15 netbooks in the classroom with Wifi
• 24 mp3 players (for students who don't have internet access at home)

General Policies

• Students can move at their own pace.  A “minimum pace” will be established and documented in a class calendar available to parents and students through class website.  
• Benchmark of 70% for assessments (quizzes and unit assessments).  Students must meet this in order to move to next concept/unit.
• Assignments that are not completed on pace will be marked “missing”.  If assignments are not completed by the Unit Assessment date they will become a zero until students complete them.  Note: I have decided to do it this way because I feel that my students will need the "incentive" and parents will need the grade to reflect that a student is behind. I know there is debate about putting in zeros for work that is not complete and I am not sure I will always do it this way, but I need to make some decisions for a starting point and this is it. 
• Parent contact: Contact home will be made if students fall a few days behind pace. Note: This very well will be done by the student themselves during class.
• Students behind pace: Students will have a 1 week window to complete what is “on pace”.  If they become 1 week behind I will call home and require after school tutoring to catch up. If students do not attend after school tutoring they will be required to attend academic lunch detention.  Note: We have free after school tutoring with transportation home. The academic lunch detention will be run by our Link Crew (some of whom are also Cadet Teachers).

Assessments

• Concept quizzes and retakes will be done in class in a "testing area". There is a "Today's Quiz" folder that contains multiple class copies of a "unit" quiz; broken down into sections by concept. Students do not write on these. Each concept has 4-5 questions. I have 12 versions of "Today's Quiz" and put out a new version each day. Students use the version for that day for their initial quiz or retake, whichever they are doing that day. Students have a quiz answer tpacket (SEE EXAMPLE) that they write down their work and answers to make grading easier. Note: I got this idea from @crystalkirch. It is how she has found to be the most efficient way to run paper-pencil quizzes and keep your sanity while grading them!
• Unit assessments will be taken in class during the on pace assessment date. Students who are behind will still take the unit assessment. If they do not score 70% or better they will retake it after completing the outstanding material. Note: I have struggled with what to do with this aspect of my flipped-mastery approach. I feel without the pressing assessments students will fall desperately behind. I may be selling them short and will revisit this if it seems necessary to do so. By having students take the assessments (even if not "ready") I can at least better ascertain how they are doing on the material they have learned.
• Unit assessments retakes will be done before or after school according to a set schedule. Students will need to fill out a "Retake Request Form" (I still need to develop this). This will require students to explain what they didn't understand on the prior assessment (with corrections to their mistakes attached), what they did to prepare, what their original score was, and what they anticipate scoring on the retake.

Class Structure

• Whole-class activity (see BLOG POST of these ideas)
• Check-In during which students get into groups, testing area, netbooks, etc.
• Flex-time during which students have their individual or small group work time (see Student Work Flow)
• Check-Out during which students fill out check out slips to help them reflect on and plan their time (SEE EXAMPLE)

Student Work Flow

From the students perspective, here is the work flow:

• Watch video and complete all guided notes & summary questions (via Google Form)

When they submit answers they are given link to responses. They can check their answers against mine and see how I have coded their answers (GREEN=good, YELLOW=almost, RED=wrong). They will record the date of their submission and the color score on the front of their guided notes packet (I call them VIP Packet - SEE EXAMPLE)

• Complete practice assignment: Students grade their own at the "grading station" and record their score on the front of their VIP Packet. They may work individually or in a group.
• Teacher Conference: Students must get their VIP Packet signed off by me under the "Info & Notes" column. We have a brief discussion about their practice problems and I look over their notes.
• Take concept quiz: The student then takes that day's version of the quiz and turns it in. I will return them, graded, the next day. Students keep track of their scores on the front of their Quiz Packet
• Passed - student moves onto next concept
• Did not pass - student reviews mistakes, gets reteaching in small group or individually with me then reassesses.

Students Who Do Not Finish

Although we are on trimester I will have students all year.  At the end of the trimester any assignments/assessments that students have not completed will be given a zero and that grade (failing if they have not completed curriculum) will be "finalize".  When the next trimester starts any student behind will pick up from where they left off.  Therefore, their "failing" grade is not "final".  At the end of the year if any student is still behind they will come in for summer school and finish what they have not yet completed.   If they do not come in for summer school they will take the last trimester of Algebra 1 at the beginning of their sophomore year.  I do not anticipate anyone being more than 1 trimester behind by the end of the year.  Note: In years prior if a student failed a trimester they had to repeat that trimester until they passed.  We had some students take a trimester over and over again.  My hope is that this will prevent that from happening.

Physical Set-up of Classroom

I have my classroom organized similar to "centers" as follows:

• Groups of desks for students to work together/helping each other or by themselves

• Small table for small group work with me or the cadet teacher

• Testing area for assessments

• Digital Work Station where netbooks will be set up and students can watch videos and do online submissions

• Grading Station where students can check their practice assignments against the answer key. (This used to be my desk. I've decided to give it up!)

I would greatly appreciate your thoughts. If there is something I've forgotten, let me know and I'll do my best to address it. This is just the beginning of what I'm sure will be an interesting journey!

~Lisa

Preventing Teacher Burnout

After experiencing the awesome EdCampHome I took some time to reflect about what I learned in my session "Preventing Teacher Burnout".  It's a topic near to my heart because I struggle to balance a husband, five children, and a career that I love. Much has changed in the five short years I've been teaching.  There is so much in the way of sharing information, education reform, and technological advances its easy to be overwhelmed. How do we as educators keep the fire within us burning bright without burning out?

We had some great discussion focused around the following areas; 

1. Time management

2. Filtering and curating information

3. Maintaining a positive focus

4. Getting and staying connected

Time Management

Time is finite.  We only have so much of it so its important that we spend it carefully. Try first documenting where your time currently goes. Then prioritize it, compartmentalize it and do what you can to save it.

• Google Chrome extension "Time Tasker" helps you monitor on which websites you spend your time online.  
• The Pomodoro Technique helps you learn how to manage your time by teaching you to develop appropriate time limits for tasks and setting them.  
• Prioritize your time! I recently made a priority list for my goals that includes; this summer, this year, next year, in 3 years, in 5 years, and pipe dreams. I limited myself to five things in each category and out everything I was trying to accomplish into a category. I quickly realized that my "this summer" and "this year" categories were filled. I made some tough decisions about what to put off until next year.  Those decisions have helped to reduce my stress load.
• Compartimentalize your time using something like Priority Matrix app.  This also helps with your prioritizing and keeping track of important tasks.  
• Consider using It This Then That website or www.ifttt.com. This website allows you to create "recipies" that put the internet to work for you by letting you identify a trigger that causes an action you specify.  For example, if i favorite something on Twitter also save it to Evernote.  
• Filter through blogs by using a service like Feedly or Zite.  This helps keep you from randomly perusing the internet during your blog reading time.

Filter & Curate Information

One of the problems I struggle with is having too many ideas for the time I have. So how do I filter it and keep track of it?  We talked about needing to filter out all the "crap" by using two filters; community and experts.  It's helpful to realize that good ideas will surface again and again. For example, I realize I spend more time than I should following Twitter feeds for fear I'll miss a good idea.  Well, if its a good idea it won't be mentioned only once.  The community you surround yourself with (in this case Twitter) will make sure that good ideas catch your attention. The other filter is created by finding experts in our particular field and following them, whether it be their websites, blogs or Twitter feeds.  Those experts are usually pretty good at curating information so it comes to you already filtered. 

Maintaining a Positive Focus
It's important to focus on the positive.  Negative things tend to grab onto our attention and drag us down. This exacerbates teacher burnout.  Work toward focusing on the positive by keeping a journal or sharing your positive happenings. Use #eduwin or #edugood to share those positive experiences on Twitter. Or go to http://www.whatisyoureduwin.com/ to share.  Negative things will always happen but we have to work at acknowledging them without dwelling on them if we are to prevent teacher burnout.

Getting and Staying Connected
We agreed that finding a network of positive people to share with and support us is invaluable.  Twitter has been and continues to be a great source for connecting with colleagues.  No more do you have to be isolated in your classroom, building, or district. The people you connect with can help keep you sane when it seems like your world is falling apart.  I have personally experienced needed reminders about giving myself a break and not taking on too much from people I never would have met otherwise (thanks Jon Bergmann!) Twitter has personally been a live saver for me.  We all agreed, getting and staying connected is important!

Whole-Class Ideas for Asynchronous Flipped Mastery

When I think of moving to flipped-mastery I think of all the advantages; students moving at a pace right for them, meeting all of their individual needs, showing mastery instead of just moving on, etc. And I know that I will have students congealing into self-identified groups.  But what I don't want to lose are those whole-class group activities and conversations I've experienced from my traditionally run classroom.  And I want them to be much more in-depth and meaningful than I have done in the past.  I also want the ebb and flow of my classroom to be efficient and organic.

I think there are benefits to having whole-class discussions and activities that take the entire period, are short and sweet, and happen over the course of several days.  Therefore, I'm thinking about having a mix of all of these.  I also want to focus on perseverance with my students this year.  I believe they get stuck in a problem or don't even know how to start because they don't know what questions to ask.  I want to help them with that.  I also believe that they have difficulty finding their mistakes and seeing alternative routes to solutions.  I want to help them with that too.  

Since my students will be in different places due to being asynchronous I want to focus these discussions on the mathematical practices rather than on the content.  By that I mean these discussions don't have to be around the content in that unit or "paced out" for that day. I believe that I, as a teacher, have been stifled in trying to move to a more problem-solving  based classroom because I have always tried to find an activity/problem that correlated with a "standard" set for a particular day.  Rather than focusing on "does it fit in my curriculum" I'm giving myself permission to use anything that I think will help my students, regardless of the correlation to CCSS-M or pacing guide.

So here are some of the ideas I've been mulling around.  I'd love your thoughts and comments.

What's the Error?: Show a problem done incorrectly (from student work or our text, which surprisingly has a good number of these) and have students discuss in their groups what the error is and how to fix it.  These would correlate with the concepts being learned in the current unit. This would also give rise to discussions of alternate solutions depending upon the problem.

What's Your First Question?: Using Dan Meyer's 101 Questions show a picture or video and have students share the first question that comes to mind.  Here, there is no pressure to find the answers to the questions or do any "math" per se.  The idea I have is to build students' confidence and ability to ask questions which I think is so vitally important to perseverance.  Eventually some of these may be used to actually answer the questions posed in future class periods (via 3-Act Math - Dan Meyer style, see below) .

How Big Is It?: Using Andrew Stadel's Estimation 180 to help build students' number sense.  Show a picture and have students estimate how big something is or how much of it there is.  Let students work in groups and report out, not only their answers, but their methods as well.  Great use of constructing viable arguments and attending to precision.

Would You Rather?: Using John Steven's Would You Rather? give students a question to for which students must choose their answer and justify it. For example,  "Would you rather carry a bucket with 5.62 liters of water or carry a bucket with 1.85 gallons of water?".  These could lead to some great discussion about what information is necessary to answer the question and how do you find that information.  Which could break into some great learning opportunities regarding searching methods on the internet and unit conversions.

What's the Pattern?: Fawn Nguyen's Visual Patterns gives students the first three iterations of a pattern and asks them about the 43rd. I anticipate needing to give my students more than snippet of class time but learning to look for and make use of structure takes time.  And the opportunity for discussion of multiple solutions is rich.

Can You Create This?: Daily Desmos gives students a graph and asks them to use their online graphing calculator (or other) to create the graph.  Now some of these are rather complicated graphs and beyond what I think my students could do.  However, whose to say some student might not figure it out? And why does everything we ask students to do have to result in an "answer"? Can't the process itself be the point of it all? How much learning could take place if we give kids time to play with the graphs?  How much might they learn about domain and range even if they can't figure out the actual function that makes it? I think sometimes, play time is enough.

Over the summer I have been reading a bit about teaching with Dan Meyer's 3-Act Math  and I believe it to be a worthy thing to include in my class.   However, along with moving to flipped-mastery I am instituting 20% Time/Passion Projects with my students.  I have relegated one day a week toward this endeavor and feel that it will be difficult to take yet another class period for something like a 3-Act task. This all has me wondering if I couldn't divide the 3-Acts over several days.  Here's what I'm thinking...

Day 1: Introduce the problem (Act 1). What questions does the image/video give rise to in students? Document these.

Day 2: Focus on one question and discuss what information we need to answer it (Act 2).

Day 3-4: Work on answering the question.  

In essence this could be worked over the course of the week.  I believe there is benefit to wrestling with a problem, walking away, and coming back to it.  I can't tell you how many times I solved problems in the shower when I was in college because I took time to "walk away".

Well...those are the thoughts that have been rambling around in my brain.  I'm not sure how it will all pan out and I bet there are some future blog posts on whether or not they do.  I welcome your thoughts and ideas.  And if anyone is thinking along the same lines and wants to collaborate on developing specifics together, please let me know!

  

Concerts & Collaboration: How Your PLN is Like a Band

As I sat thoroughly engaged in a concert last night (Guster, Ben Folds Five, Bare Naked Ladies, if you must know!) I began to see correlations between concerts, teachers, and collaboration.  And how your PLN through Twitter might be better than any in your building.

How many times have you gone to a concert of one? Even if there is only one "performer" there is a multitude of supportive people around them; stage hands, song writers, etc.  As I watched the performance last night I got to see evidence of all of the collaboration that must go on.  These musicians work together, tossing around ideas of how do a montage of a wide variety of other artists' songs in a way that was not only meaningful and organic but entertaining and engaging.  Members from Guster jumped in and performed with BNL.  Musicians in Guster jumped from one instrument to another.  They made full use of their strengths and overcame their weaknesses, together.  They WERE better together.

Having a husband who has been in numerous bands over that the last twenty plus years I have also come to know the behind the scenes drama that can ruin a good band.  It's inevitable that the drama creeps in.  Some bands overcome it, others do not.  When your only collaborator(s) are within your own building it sometimes becomes difficult to push aside drama.  I'm not saying that your PLN through Twitter is without this, but I am suggesting that because you can have a working relationship with your Twitter PLN and they are not in your same physical space, you have the opportunity to physically work away from any drama that might arise.

My husband has a former boss that had a steadfast rule; don't become friends with the people you work with.  He was friendly with them, but didn't maintain a friendship outside of work.  It has worked well for him and I can see the advantages.  What I think a Twitter PLN has is the best of both worlds.  You can let friendships grow without the worry or concern for it directly affecting the physical space of your job.  And you can collaborate with others who may have different experiences than those within your building, thus building on the strengths of each member.

I'm still finding myself in my Twitter PLN.  I've made some connections but am still working toward that deep collaboration.  And that's ok.  All good things take time.  And when it happens I know that what we create together will be as amazing and engaging as a great music concert.

Self-Doubt: A Lesson in Trust

It's taken me five years to figure out who I am as a teacher.  And I came to teaching later in life, having turned 40 my first year of teaching.  My first five years were filled with self-doubt that affected me greatly.  It got me questioning my effectiveness even though those around me sung my praises.  It sucked away my self-esteem and left me empty.  It's a horrible thing we do to ourselves sometimes; let our personal criticism define us.  Until we realize that it doesn't have to be defining.  It can be empowering.

As I have struggled to turn around my self-doubt I've learned to recognize it as an opportunity to grow rather than a definition of my failures.  Let's face it, we all fail.  At something.  Sometimes.  But not everything.  And certainly not always.  If I am trying to get my students to trust me to be comfortable in making mistakes then shouldn't I be comfortable in making them myself? Just as I ask students to be able to recognize a mistake as an opportunity to grow, shouldn't I as well?  And when I celebrate my students' successes shouldn't I also be able to celebrate my own?  Even if my success wasn't a result of my first attempt?

It's not often that we have the opportunity to be in a career that gives us so many opportunities to give and receive.  There is a symbiotic relationship we have with our students and I think I have (for far too long) not recognized the beauty in that.  As much as I teach them to trust, I have learned to trust.  Not only in my ability to accomplish what I set out to do, but in my ability to learn from my failures and not let them define me.  I'm learning to become strong from my weaknesses.

I have also learned that I will never be the teacher I imagine for myself. Because with each step I take toward that ideal, I reflect, I grow, and I re-imagine my perfect self.  And I have come to realize that my failures and short-comings are not what define me but it is what I do with the recognition of them that does.  Perfection is not what you do, or don't.  It is how you trust in your imperfections to let you become the best of who you are.  Imperfections and all.

So when your next lesson flops, or that video isn't quite what you wanted it to be trust that it is what it needs to be for now.  Trust that it is the next step that you need to take.  Trust your journey.  It is the perfect journey just for you.

Struggling with Standards: My Journey to Balance

With many educators scrambling to understand and implement the Common Core State Standards (CCSS) I feel the need to comment upon them and my own journey to understand them. In my humble opinion they are not the Holy Grail for which some of us had hoped.  They are no more narrow than the Michigan High School Content Expectations (HSCE's) under which educators in my state had been operating. They are still a "mile wide and an inch deep".  I continue to find myself struggling to "meet" all of the standards much to the dismay of my administration. I continue to fight for my students with my never ending rant that there is no way (or reason for that matter) that I should try to "cover" all of the standards laid out in this national plan called CCSS.

Let's get real for a minute.  We have an educational system that continues to function on the premise that social promotion supersedes mastery.  Until I no longer have students in my high school Algebra 1 course that have potentially failed the last 2-3 years of mathematics (and I have them), I refuse to proceed through a laundry list of standards.  The CCSS are built upon the assumption that students have achieved "fluency"(see here and here) at the lower levels.  This, my friends, does not always happen.  Even if a student has passed their lower grade mathematics courses they may have barely done so.  This is because moving through our current system is based upon a passing grade and not mastery.  And I hate to call out the elephant in the room but many times that grade is based upon effort not understanding.

Now let me step off my soap box.

In the summer of 2012 my district gave us the opportunity to work with our ISD's K-12 Math Coordinator for Math Instruction at unpacking the CCSS.  Almost all of our math teachers grades 5-12 were there and we worked for three days to wrap our heads around the CCSS and the expectations for us and our students.  It was a wholly worthwhile experience.  We had an opportunity to have real vertical alignment discussions that brought to light assumptions some of us had about what was covered at the lower levels.  And those at the lower grades had a much greater understanding of where it is that our students were being asked to end up at the end of their high school careers.  It was eye-opening for all of us.

We began by taking an individual standard and deciphering what it really meant. We used a worksheet to begin to call our attention to the nouns and verbs used in individual standards. We then wrote "I can..." statements using teacher language and then "This means I can..." in student friendly language.  In essence, we took vague and hard to understand standards and broke them down into their collective pieces and wrote them in student friendly language. Now at times this was difficult because sometimes we didn't even know what the standards were really trying to get at.  We looked at examples and found the Illustrative Math website to be quit helpful. You may also want to visit this LiveBinder and go to "Content Unpacked" and then "flipbooks".  There you will see unpacked standards from many states with instructional strategies and examples.  I personally find this flipbook put out by McGraw-Hill to be something I cannot do without.  It has standards broken all the way down to "I can" statements for you.  Quite frankly they are better than the ones we came up with, in most cases.  Having said that, do not underestimate the value in unpacking standards yourself.  It is a wholly worthwhile process.  I have a better understanding of the standards because of it and our district has better vertical alignment because of the conversations we were able to have while doing it.

Now, even though it may seem that I am poo-pooing the CCSS there is something that came out of their development that I believe is a game changer; the Mathematical Practices.  I have heard it said that our state HSCE's had something similar woven throughout.  However, by specifically addressing those skills, characteristics, and practices that are indicative of good critical thinkers I believe we can bring our mathematics education in this country to the 21st century.  Those eight, simply stated practices eloquently address a focus for our math instruction that moves beyond mathematics itself to skills that will help our students be successful in an ever changing global society.  They support something I have always believed and said; mathematics is the vehicle to developing critical thinking.  That goes beyond understanding that the sum of a rational number and an irrational number is an irrational number (that is seriously a Common Core standard, see N.RN.3).

Last school year (2012-2013) after unpacking the standards and aligning our curriculum we also chose to have a focus on the Mathematical Practices.  We discussed them with students and called attention to at least one in a lesson. Although we didn't get the results we were looking for I believe we did get a better understanding of their importance.  I've come to personally realize that to focus on all eight is difficult as we transition to CCSS, both for us and our students.  I have decided to choose two to focus on in this upcoming school year; (1) making sense of problems and persevering, and (3) constructing viable arguments and critiquing the reasoning of others.  I've written a previous post. Teaching Perseverance. on my initial game plan for developing the first math practice in my students.

In the end, I've come to develop my own personal balance between CCSS and my students needs.  They do not all need to "cover" or even be exposed to every standard.  Right or wrong, I see them as a guide.  However, I see so much value in the Mathematical Practices that they have become my focus.  For me, the standards have become a vehicle to teach the Mathematical Practices.  Just like you wouldn't take an electric car on a 500 mile trip with nowhere to recharge, not every standard is necessary to develop the Mathematical Practices.  I will choose wisely which standards to use. I will consider the needs and experiences of my students and for what next math course I need to prepare them.  It is how I have personally found balance.  How will you?