A Fraction Isn’t a Number: The Importance of Coherence

I was playing a game with my soon to be 5th grader when he asked me to pick a number between 0 and 10.  Being the math teaching mom I am, I obviously selected 1/2 much to his dismay.

Jackson: “Mom, I said to pick a number.”

Me: “I did.  I picked 1/2.”

Jackson: “Mom, that’s not a number.  1/2 is a fraction not a number.”

Me: “Jackson, fractions are numbers.”

Jackson: “I thought you taught math, fractions totally aren’t numbers.”

 

It was a super fun morning at my house!  However, it really made me reflect on exactly why I am so very passionate about the work at Open Up Resources.  Jackson is a great math student, he has had wonderful teachers, he scores well ahead of his grade level on standardized testing and yet somehow he has missed the beauty that is the cohesiveness of mathematics.

Jackson is a great math student, he has had wonderful teachers, he scores well ahead of his grade level on standardized testing and yet somehow he has missed the beauty that is the cohes

I am not going to lie, I never truly stopped and thought about the importance of coherence until my first Core Advocates Convening and from that moment on I made it my mission to start finding the connections between each and every standard I taught.  In Kentucky, when the Common Core Standards came out we, like many other states, immediately started deconstructing and removing the coherence by turning them into a check list of skills to be mastered rather than focusing on the connections as intended by the authors.  I decided after that first Convening that I was going to bring that coherence back.  There was one problem…building in coherence is HARD.  Managing 120 students a day, lesson planning, grading, communicating with parents, and then adding to that trying to make connections to previous grade levels, previous units, and upcoming units was more than this teacher could do successfully.  There were times when I really hit the mark and did some really cool lessons that were conceptual and coherent but I am going to be honest, most of the time coherence took the back burner.  I started every year with the plan that I was going to teach all of 7th grade math through the lens of proportional reasoning and then the year would start, I would get bogged down and would revert right back to my old faithful standards checklist.

Enter Open Up Resources Math 6-8 Curriculum into my life and what I thought I knew about doing coherence well was blown out of the water.  Those lessons I occasionally did well, that were coherent, and brought in major work of the grade were nothing compared to a year-long curriculum that was spiraled, coherent, and truly finally taught 7th grade math through the proportional reasoning lens that I had always dreamed of.  I began to see what a truly coherent curriculum could do for struggling learners.  It took math from a list of skills, rules, and procedures that were done to them to something they could own and make sense of.  My most struggling learners started looking for proportional relationships in all types of problems in order to make sense of them before just trying to “solve” them.  They looked at equations for a constant to see if it was  proportional, they made tables to check for a constant of proportionality, they found tax by  first finding the unit rate or k.  I know it probably sounds crazy or that I am over simplifying it but truly for the first time in 13 years when I posed kids with a difficult problem before just saying “I don’t know what to do” they would at least first try to make a table and look for a relationship.

Jackson is a great math student, he has had wonderful teachers, he scores well ahead of his grade level on standardized testing and yet somehow he has missed the beauty that is the cohesiveness of mathematics. (3).png

Then we came to the rational numbers unit and for the first time in my teaching career I discovered a way to make subtracting integers make sense for struggling learners.  I had tried every manipulative in the world; integer chips, algebra tiles, army men, thermometers and more, and when that didn’t work and the kids still struggled I cracked and taught terrible tricks that I am ashamed to even admit here (I am not proud but we’ve all done it).  Then Open Up taught the topic by simply posing the question “how far apart are the two numbers on the number line?”.  Are you kidding me?  It was that simple!  My kids were subtracting integers like pros!  I have a first grader at home that was working on subtracting in math also so I began to notice that she subtracts the same way…using a number line.  I can’t wait to see her subtract integers with Open Up in a few years.  It’ll be coherent to her.  I wish I had done that for the first 12 years of kids I taught.

So back to Jackson and his fraction his problem.  I believe whole heartedly that it all goes back to this concept of coherence. He has wonderful hardworking teachers but again coherence is hard to build in as teacher if you don’t have a curriculum that has planned for it.  They are forced to revert to the checklist just like I was.  We are done with multiplying and dividing whole numbers kids…guess what we are going to learn about next…fractions!  It seems innocent enough but without coherence fractions aren’t numbers to my 5th grader.

Jackson is a great math student, he has had wonderful teachers, he scores well ahead of his grade level on standardized testing and yet somehow he has missed the beauty that is the cohes

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When All Really Means All: My Personal Journey

I have changed a lot in thirteen years of teaching. From a wide-eyed first year agriculture teacher ready to change the world to my early days of teaching math when I assigned the ever popular 1 through 20 even, followed by 1 through 20 odd the next night for homework, I am thankful for the many ways in which my community of educators has helped me grow and change.

One of the things that has stayed consistent, however, is my belief that all has to mean all when it comes to kids and education.  Every student has the ability to learn and do math at a high level, and I have truly tried to make all means all the mission statement of my classroom.  Unfortunately the other thing that has stayed consistent is the lack of materials and resources that made all means all attainable for me as a teacher. Like all teachers, I have made it through curriculum adoptions, computer programs that promised the world, the newest research trends that promised great gains, and ever-increasing demands to move kids further and faster.  

The problem remained though that one group always seemed to be left out.  If I moved one subgroup another got left behind, if it managed to serve all GAP kids my high achievers growth was left stagnant, if it served the high achievers my most struggling learners were left feeling defeated and hating math.  Eventually, as I wrote about earlier this year, I gave up on depending on curriculums and developed my own materials that finally moved ALMOST everyone. My mission however remained all means all… not all means almost all.

It was almost four years ago now that the Kentucky Department of Education asked for volunteers to do a one unit pilot for a group trying to get funding to write a free middle school math curriculum that would better support students’ conceptual understanding.  The words free and conceptual were enough to pique my interest and I said sure. The materials were in very draft form at that point, but I knew at the end of that pilot unit, when I saw some of the highest scores I had ever seen on that particular unit test, that something special was going on with this curriculum.

Three years ago, someone suggested I apply to review a free math curriculum that a nonprofit called Open Up Resources was developing with the phenomenal team at Illustrative Mathematics – the same folks behind the unit I’d loved I  signed on for the year-long review process. I started “borrowing” some of the activities to try with my kids and they loved them. I knew after reviewing the first units that I had to do whatever I could to bring these materials to my school building – and we were able to!  I will forever be thankful to my 6th and 7th grade colleagues for taking a leap of faith and jumping into to Open Up Resources with me last year. It was a big change for all of us. We were excited and scared, but we did it.

Something amazing happened this year.  My mission was finally fulfilled. All finally meant all.  With the help of the amazing, free curriculum from Open Up Resources,  ALL 100+ students in my room grew leaps and bounds. Kids came into the year ranging from a 1st grade math level to and 8th grade math level, and left between a 3rd grade and college math level.  All students averaged almost two years of growth while my GAP students such as English Language Learners and Students with Disabilities grew well over two years, making a great start at closing the achievement gap.  Those 100 kids turned into mathematicians this year. They reasoned, they discussed, they modeled, and they grew. All meant all, and it was magical.

As a teacher, I grew so much, too.  I thought I understood conceptual teaching, but this year took it to a whole different level. I noticed this shift in my instruction almost immediately, and even found myself blogging about it in September. I would say things before I taught the unit like “why in the world would they teach it that way?” and then by the end of the unit would be saying, “why in the world hadn’t I thought to teach it that way before?”  With the support of beautifully-crafted curriculum, I learned how to be better at eliciting student thinking, how to give stronger and more meaningful feedback, and how to have an even more student centered classroom.  I will always be thankful that I got to grow right alongside my kids this year.

Justice & power must be brought together, so that whatever is just may be powerful, & whatever is powerful may be just. (2)

I had a magical year in so many ways and for so many reasons. But this spring I was faced with a difficult decision.  My district went through a districtwide textbook adoption and selected a more traditional textbook for use K-12, which meant I would no longer be able to use Open Up Resources 6–8 Math curriculum in its entirety.  I struggled a lot with what that meant for me. I am a teacher to the depth of my core, but also hold firm to my mission that all means all. And believe wholeheartedly that Open Up Resources curriculum is the way to achieve that high level of learning for all students.  So I made one of the hardest decisions of my professional career and chose to leave the classroom next year.

I am deeply excited about my next chapter: I’m joining Open Up Resources to develop an educator community around their excellent free curricula – starting with the 6–8 math curriculum authored by Illustrative Mathematics.

I am passionate about access and equity; so is Open Up Resources.  I am passionate about making sure all kids and schools have access to aligned and high quality materials; so is Open Up Resources.  I am passionate about connecting teachers and sparking them to have meaningful conversations around math education materials; so is Open Up Resources.  I am passionate about propelling kids to greater success in math; so Open Up Resources. All means all at Open Up Resources, and I am so excited that they are giving me the opportunity to join their team as Community Manager.

I also know that excellent curriculum can empower excellent teaching – but it isn’t easy teaching. The math curriculum stretched and improved my practice, and I grappled a lot with how to get that right. I found myself connecting with teachers around the country about the work – via Twitter, and when the Open Up Resources team helped us to connect in web chats – and those connections made me more confident in the shifts I was making. I believe that a national community of educators on the same journey can accelerate everyone’s success with the Open Up Resources curricula, and my own experience tells me that this will be incredible for our kids.

This wasn’t a decision I took lightly or made quickly, but for now it is the best way to continue to fulfill my All Means All mission.

I am excited about what we have the opportunity to do as teachers in the Open Up Resources Community.  We can all be a part of something so much bigger moving forward. Teachers from around the country gathered around a free curriculum that supports all learners sharing resources, ideas, struggles, and successes… I truly think it can be the largest, most engaged, fun, and meaningful community education has ever seen around a teaching & learning movement.  We have the power to really work together and do something special around this work, and I am so excited to have the opportunity get to that with you.

Justice & power must be brought together, so that whatever is just may be powerful, & whatever is powerful may be just. (3)

To The One Who Comes After Me

To The One Who Comes After Me,

Never forget the person that gave you your first chance.  For me it was Terri Miller at James Wood Middle School.  I had big hair, a bigger accent, and even bigger and loftier ideas but for some reason she saw what I could be and hired this Kentucky girl to come to her Virginia school as an agriculture teacher.  I will always be thankful she took a chance on me.

Never forget the person that pushes you to be a little bit better every day.  For me that person was hands down Kate McAnelly.  She was the person that in so many ways pushed me from good to great by insisting that all really did mean all.  She constantly asked me to look at things from other ways, to try new methods, and to read the latest research so I could help the most kids.  She also let me experiment a lot.  It didn’t always work but she always trusted me.  I will always be thankful that she believed in the work I was doing.

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Never forget the teammates that you work with each day.  They are the people that understand the children you teach better than anyone else.  They are the ones that have a relationship with the kids you can’t seem to get.  They are the people who will help you get your emergency sub plans ready, pop popcorn for 300 + kids with you, sit and cry with you when you need it, and go along with all your crazy ideas.  If you are coming after me it means you are inheriting the best team, full of people that compliment each other’s strengths and weaknesses so very well that you will become family before you know it.  I am thankful I had the honor to be a part of the Equestrian team.

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Never forget the coworkers that you spend more time with than your own family many days.  These are the people that will laugh with you, cry with you, comfort you, and support you.  Enjoy them…(and never miss the Algebra Meetings…they are priceless).  I am thankful for the second family I created at work.

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Never forget that kids you teach need to be seen as individuals and not as statistics, data, or test scores.  They want you to know their dog’s name, that they scored a soccer goal, and that they can’t get their homework done because they have to babysit their siblings while their mom or dad works.  They want to love you and want you to love them.  Never forget to take the time each day to laugh with them and show them a piece of who you are as a person.  Be honest with them, love them, and nurture them.  Oh and always keep blue jolly ranchers in your desk, those are always their favorite.  I am thankful that I had the privilege to teach some amazing kids.

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Never forget that the best math classes come from kids experiencing math and owning their learning and not from you doing the teaching.  Remember that you only get 65 minutes a day for 177 days to turn them into mathematicians that see the logic and beauty in math rather than seeing it as a punishment or a set of rules and procedures. Make most of your time.  I am thankful that I got the chance to change the way some kids looked at school and at mathematics.

Never forget to stay humble.  No matter how long you teach, how high your test scores, how great your student survey results there is always something to learn.  The best teachers never stop pushing themselves to get better and are continuously learning.  I can’t think of one day in 13 years that I couldn’t have improved upon and I think most excellent teachers feel exactly the same way.  Never stop seeking feedback, new ideas, and current research to continue to refine your craft.  I am thankful that I don’t think I ever got good enough to not be humble.  I could name 100 things today that I wish I had been better at or done differently.

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Room 406 was a special place for me for the last 7 years and I have no doubt that it will be for you too.  As for me, as my Uncle Bill Keightley would say, that’s still “To be continued”.

When I leave this Earth, I think I'll have it inscirbed on the monument _To Be Continued..._

 

Blink

I have been re-reading Malcolm Gladwell’s “Blink” this week and have found myself looking at it through a much different lens than I did the first time.  Perhaps it is because I have spent so much time during the last three years immersed in the curriculum review and adoption world but numerous points Gladwell makes throughout the book stood out to me in regard to education.

up to 70% off

The quote above really hit me head on.  Lots of people after observation in my classroom comment on the “looseness” and flexibility of the lessons we do each day.  They aren’t wrong necessarily, I do pride myself on letting the kids take the math and the topic of the day where they need it to go but that is far from random.  It takes a tremendous amount of planning, anticipation, and extra prep to prepare for this degree of spontaneity so that I can ensure I am ready for wherever the kids may take the math that day…it isn’t just me standing up saying “alright y’all what should we do today” or hopping on a website 5 minutes before class starts to find something that looks fun.

The best curriculums allow for this spontaneity for teachers.  I think that is one of the reasons that I have liked the Open Up Resources authored by Illustrative Math curriculum because they created much of the structure needed to make sure the content was covered but left room for me as a teacher to allow for spontaneity in the classroom. When the kids needed more time on one activity or if I wanted to change something they planned as a partner activity to a gallery walk fast when I knew my kids had to get out of their seats before they lost their mind.  They did the work to ensure my spontaneity wasn’t random so I could focus on what makes teaching great.

We have virtually unlimited amounts of data at our fingertips ...but what I have sensed is an enormous amount of frustration with the unexpected costs of knowing too much.

Perhaps my biggest takeaway from reading Blink again is something I have had a gut feeling about for a long time…teachers have too much data.  Hear me out on this, I agree data is important but Gladwell’s thoughts on data slicing being just as accurate as vast quantities of data really resonated with me.  Teachers are asked to keep enormous amounts of data on every kid that steps in their doorway and then make informed decisions based on that data for each and every child; but what if all that data is, as Gladwell argues, less accurate than a quick slice from teachers as trained professionals.  I frequently learn more from a 5 second conversation with a child than looking at pages and pages of information containing state testing, district testing, norm referenced testing, and a variety of other numerical data pieces.

My daughter is a prime example.  She is a struggling reader.  Data will tell you that she can only read level E books and that is what the data will decide she needs to read.  A quick conversation with her will let you know that those books don’t interest her and take her confidence away by making her feel dumb.  Instead, we talked to her and decided to let her read more advanced books with some help on the hard words with the expectation that she would read all the words on her level and attempt the words that are not.  She has grown more in the two weeks since we started that than she had a month prior reading level E books.  Knowing her was much more valuable than the data.

There are a ton of companies right now selling their products as the end all be all in education because of how they can differentiate practice for kids, provide live data, and differentiated instruction all without needing teacher input.  That’s crazy to me in many ways but reading Blink further reminding me just how far fetched this idea is.  A teacher’s blink decisions based on slices of their interactions with  students are more valuable and accurate than any online text book company can ever promise to be.  Good teaching, curriculums that help teachers be spontaneous not random, and teacher driven data… those things will always matter.

Holding Back

The world we could have is so much richer than the world we have settled for.

As teachers we are told frequently to make sure we don’t “teach to the middle”, meaning we have to make sure we help catch up our struggling learners while still pushing our gifted learners to continue to move beyond what they already know.  This balancing act in the classroom isn’t easily achieved but yet is the expectation for all teachers.  I personally have spent hours figuring out how to differentiate activities and structure my lessons so that every student can learn and improve each day…it’s what good teachers do.  My questions today is this, how do we professionally differentiate for teachers?

This question has stayed on my mind a lot lately.  I wonder how districts are supporting their struggling teachers while still elevating their master teachers to higher levels.  How are districts differentiating professional development, evaluations, and professional duties in order to recognize their most successful teachers and improve the teachers that need them most help?  So far, the answer I have some up with is that most aren’t doing this at all.  I fear that in many districts we are actually doing to teachers exactly what we are told not to do students…teach to the middle.  I believe strongly that we hold our best teachers back while providing ineffective supports for struggling teachers in hopes that in the end things will all even out.  No one, not teachers or students, benefits from this model.

I have heard of many districts in the past year adopting curriculums due to ease of use for their struggling teachers.  Comments like, “_________ just won’t be able to use that curriculum” or “it’s what’s best for our teachers who need help” seem to be the norm in many districts and I can’t help but think that isn’t acceptable.  A curriculum whether good or bad won’t fix a struggling teacher and while a good curriculum can make a strong teacher even better a bad one severely limits their effectiveness.

A bad teacher with a bad curriculum is still a bad teacher but a good teacher with a bad curriclum has their effectiveness and impact severley limited.

I believe we are at a time in our profession that we must realize that simply ignoring this problem will not make it go away.  Teacher effectiveness is a key factor to student achievement and the issue of helping struggling teachers must be addressed with the same focus and resources that we give to other important educational issues (some of which would no longer be issues if teacher effectiveness were improved!).  At the same time as a profession we must find ways to make career paths for master teachers who want to stay in the classroom but broaden their impact beyond just their four walls.  We need to create more mentorship, co-teaching, coaching, and leadership opportunities for the teachers who have proven through data to have effective instructional strategies and methods.  We can do better than teaching to the middle.

Closing the Gap

I am excited for my kids to take our yearly state assessment this year.  Don’t get me wrong, I am still stressed.  I could use two more weeks before testing to fully give the Open Up Resources IM Curriculum Units 7 and 8 a bit more time to develop conceptually with my students but I also know that my kids know what we have gotten to very well.  From proportional reasoning to solving equations they truly own the math they’ve learned this year.  Unfortunately, it takes quite a while into next school year before we get that state assessment data back so for now I get to be really excited about how my kids performed on NWEA’s MAP test this year.

If you aren’t familiar with MAP,  it is norm-referenced by grade level and my district gives it 3 times per year to monitor growth.  Typically in 7th grade a year’s growth is considered 6 points.  I started the year with kids in my collaborative class that ranged in score from a 1st grade level to an 8th grade level…no easy task to differentiate for.  Even still, I couldn’t hide my excitement as my kids begin to report their scores to me and see their excited faces when they realized they reach their goal.  I give each of my students a note on the day of MAP testing.  One side features a motivational quote and the other side has a had written note from me along with their goal for the test.  I like for them to have a frame of reference so that as they finish they don’t have to ask me if “they did good”.  Instead, they can evaluate their performance against their goal themselves.

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To summarize how they did…they killed it.  Our principal challenged us to have each child grow one and half years this year and on average my class more than did that with 1.7 years of growth.  While it did make me happy that all kids grew, it made me more excited that the Open Up Resources IM curriculum helped close the achievement gap with my English Language Learners showing 2.3 years of growth while my Students with Disabilities grew an average of 2.5 years.

Average MAP GrowthYears Growth

The same kids that came into the class ranging from 1st grade level to 8th grade level ended the year with on levels that ranged from 3rd grade to high school, proving that the curriculum can both challenge advanced learners and foster their growth while still helping to catch up our most struggling students.  I knew before the MAP test that my GAP students had grown considerably just by observing their confidence level and reasoning ability but seeing the quantitative date prove the qualitative data I had observed further deepened my belief that this curriculum truly does work for all learners.  With three weeks to go before our state assessment I am more confident than ever in the work we have done in my classroom this year.  We did more than “prep” for a test.  Instead my students turned into real mathematicians that reason, struggle, and think to make sense of difficult problems rather than just rushing to “do math”.

Rising Up

Disclaimer – This post is cathartic writing for me.  Hopefully I will be back to lesson blogging this week!

And we'll rise upi, like the waveswe'll rise up in spite of the ache

The last few weeks have taken their toll on me.  The people closest to me notice the difference.  I am much less talkative, seem far away a good part of the time, and my mind is always somewhere else.  I have tried to snap myself out of it but it has been difficult to overcome.  Plain and simple this legislative session has taken its toll on me.

My fellow teachers and I have been called unimaginable things by our Governor.  We have been accused of being the reason that children get abused and try drugs.  We have seen the people that we elected to serve our communities turn their back on us and try and cut public education to its core in closed door meetings and back room deals.

I have lost friendships because people couldn’t separate their political beliefs from the need to just to do what is best for children.  I have lost respect for people who perhaps unintentionally hurt me to my core with their lack of support for public education, making arguments that much like our Governor’s made no sense.

Here is the thing you may not know about teacher’s though…we get knocked down 100 times a day and get back up.  We can be cursed by a child in one minute and the very next minute consoling that same child because of something that is going on at home.   We can walk into a school upset about what is happening to our profession and then as soon as the bell rings be “on” for another academy award deserving performance in front of our class to get them excited about learning.  We can survive 8 hours without having 30 seconds to run to the restroom and can eat our lunch in 21 minutes standing in the cafeteria while tutoring some kids, discipling others, and adjusting our lesson for the second half of the day.

Teachers have been more than knocked down over the last few weeks but now is the time they rise up yet again.  They rise up for the children who will be so very excited to see them Monday morning.  They rise up for the student teachers who haven’t given up on being a teacher and are learning so much from them about how to teach content while loving kids.  They rise up for the children at home who look up to them as role models and have learned from them how to handle adversity with grace and class.

I am not fully sure what I will do with myself now that I am not constantly monitoring legislation and watching hours of live coverage from our house and senate.   I do know that I will continue to give the 120 kids I teach as much love as I can while finishing up teaching them the content they need before 8th grade.  I know I will continue to be a voice at the state level for kids who don’t have one.  I know I will keep being vocal about my support of public education and it’s importance in our society.  I know I won’t quit rising up for kids because they deserve it.