Brave, Safe Spaces

Teachers are the guardians of spaces that allow students to breathe and be curious and explore the world and be who they are without suffocation. Students deserve one place where they can rumble with vulnerability and their hearts can exhale.

– Brene Brown

Yesterday, I watched one of my amazing coach colleagues deliver a demo lesson in a 6th grade classroom that I did a demo in earlier this year. I promised her: you will love teaching in this classroom. In watching the demo of this ELA strategy (more on that on a different day), I once again noticed everything I loved about this group.

  • Everyone participates.
  • They cheer each other on.
  • They laugh with and enjoy each other.

So, how do you get to this place? Where 6th grade is not a chaotic madhouse at the end of the school year, but a calm, safe spot where students know exactly what is expected of them as a member of the community?

Of course I asked the teacher! She told me she did her entire Master’s thesis on building classroom community. In her student teaching experience, she was surprised in a second grade classroom where blending started immediately day 1. Shouldn’t a community be built first? So that’s what she does.

She explicitly tells them, “I won’t let you fail.”

During the demo, the coach communicated the same safe space to the students. She built rapport with the students through a calm, casual voice. She appreciated them out loud, telling them “I am so impressed by how you walked into the room.” She connected with them where they were at, introducing the lesson (about analyzing text evidence for meaning – no easy feat) with Tupac, Taylor Swift, and Kevin Hart. She taught by walking around the room, getting close to each of the groups and making eye contact. In group discussions, she circled around the room, listening in to the students, asking questions, pushing on thinking.

Two students yesterday especially caught my eye. I know they’ve struggled in the past. They were especially vulnerable, both standing up to analyze a quote on the board. One started to sit back down, but with the class cheering him on, he pulled out an answer that was a diamond in the rough. Where it could have slid into a shaming event – the teacher might have corrected the grammar, the stuttering, the “close but no cigar” – instead the teacher praised the diamond inside, which was the insight into the quote that was personal and insightful. The class “clam clapped” (tapping fingers together like a clam but without the crazy noise to annoy the class next door). The second student started to share his response and then said, “No, I just can’t say it right.” The coach said, “I totally get it. Tell me some of the words in your head right now.” The student started and stopped. The coach smiled and waited as he regathered his thoughts. Soon, he brought out another wonderful insight into the quote they were studying. Clam clapping ensued.

There is a common thread among all the teachers I work with who have classrooms similar to these. It is an empathetic, relaxed demeanor that communicates, “I’ve got you. I’ve got this.” These teachers know what they want the students to accomplish, and are convinced every student can accomplish it. They are well aware that their students are bringing in lots of baggage in many different forms. They know this because they have taken the time to get to know every student in their classroom. They are also well aware that not every student will perform in the same way. When they talk about their students, they don’t focus on the baggage. They focus on the growth. They don’t categorize the students as “low” or “high”, they categorize them all as learners. These teachers talk about successes on the part of the students, and when their students fall short of success, these teachers look for ways to grow their own practice instead of blaming the student. Their quest for knowledge is ongoing – students are always bringing to us new challenges to overcome and the world of education is ever evolving.

Teaching is a difficult job, and none of what I’ve described above is easy. It is tempting to slip into the blame and shame routine as the pressures of administration, testing, and parents mount. In this week of Teacher Appreciation, I am grateful to all who work tirelessly to prioritize and create these brave, safe spaces for our students to grow not only as learners, but as courageous and vulnerable human beings.

Why a Math Writing Rubric?

I Googled “rubric” just to see what kind of images came up, and up popped Rubik’s Cube. This is actually a perfect symbol of the way I feel about any rubric placed in front of me. It’s almost there, but not quite right. No amount of tweaking ever gets it to where I want it to be. And if I somehow get to that sweet rubric spot, someone else will look at it, and see the cube above. The tweaking begins again.

So what is the point of a rubric, and in our case, a math writing rubric? As we debated and wordsmithed and debated some more, we knew that we wanted it to be :

  • a tool for feedback to students AND
  • a tool to inform instruction

If we reduce a piece of writing down to just a grade, then only the grade is recorded in the student brain, not the corresponding learning. We considered a single point rubric, but also thought about whether teachers wanted to write more feedback or highlight feedback on the rubric itself. To save teacher time, the single point rubric has been tabled, but may be revisited at a later time. We considered the feedback from teachers in our last cohort and used their thinking to improve the rubric.

We borrowed language from the SBAC. When stuck on a rubric for a piece of work, I like to use the score description words. Does this feel like a Full & Complete answer, or at least a Reasonable one? Maybe it’s Partial, and not quite Reasonable. Now that I have a feeling on where it falls, I can look at that column to find bullet points or adjust up and down accordingly. We purposely left score “points” off. While we might have labeled this 4, 3, 2, or 1, we chose instead to avoid the idea of giving it a “score”. I know this is a tough one for teachers, who have requirements at varying levels to have documented grades in the gradebook.

Coherence between the lessons and the evaluation were important to us. We used language from the writing lessons we have been developing for our own use as the criteria for evaluation. What we saw from scoring tons of papers using our old rubric is that we would have decent explanations from some students – who had serious math misconceptions. It is lovely to read their writing to understand better their thinking process and misconceptions, so in terms of explanation and justification, they would have scored much higher. But in a holistic rubric, where one of the requirements was correctness, we ended up with a whole slew of the same low score. In using criteria, we hoped to discriminate between correctness and justification in order to better target the needs of the student or group.

We also wanted to link the criteria to the Standards for Mathematical Practice (SMPs) so that we could build awareness and understanding of them. Writing is not the only way to evaluate the SMP’s, but it certainly lends itself to being one way to see how a student is using the practices.

The Rubric (version 2.0)

Curious about version 1.0? Click here.

I have to admit, to put so much work into something that looks so simple is really quite humbling. Not to mention, even though this is not my work alone, I’m definitely feeling vulnerable sharing it out. With that said, I’m also constantly inspired by Graham Fletcher’s quote, “All of us are smarter than one of us.” So, I put it out here for feedback and sharing.

How Would I Use It?

First, our lesson series basically has students come up with these on their own. In introducing this rubric, I’d show how it connects to what they have identified as valuable in mathematical argumentation. Once students have had that grand conversation, then we’d go over the wording in this rubric, and trace how it changes from stage to stage. Academic language such as “accurate”, “element”, and “logic” would need to be addressed, along with any others that may be confusing to students.

We’d evaluate preselected anchor papers together, which is part of our lesson series. Discussion among partners, groups, and whole class would help calibrate our understanding of each level and criteria.

After some lessons on how to write mathematical argument (a topic for another day), we’d use one row for partners to give feedback to each other. As teachers, I’d use a preselected row to give feedback on. As proficiency grows, I might use the rubric to score a class and look at where the scores fall. Do I have a lot of Full & Complete for direct response, but only partial for justification? Might be a need for a whole class reteach. Do I have a small group that have Partial for direct response? Might pull a small group and work on identifying the question or statement to defend, and how to make sure I’ve directly responded to it.

I always put myself back in my classroom shoes, where I know my next question is “How do I grade it?” Now that I know more, I’d tell myself, “Don’t. Give feedback instead.” Eventually though, I want to report progress. So, once they’ve had plenty of feedback, I might assign a task as an assessment – when I know they understand the expectations. In my grade level PLC I’d want to determine what constitutes an “A” across the classrooms. I might collect tasks along the way as a portfolio, and look for growth. I also might play around with the concept of A/B/C/D and decide which descriptor warrants the A. Quite honestly I’d err on the positive side as long as I saw a progression in their learning. It’s not the grade that matters. It’s the learning.

Our Next Steps

For us, our next steps are to test this out with some class sets that we’ve saved from our writing series. We want to calibrate and see if there is anything we are missing or inconsistencies that make the rubric confusing. We will update our series of lessons to include this version 2.0 of our rubric. And this summer, we present again. We’ll offer extended coaching in the fall, learn more with some new teachers and share out with our prior early adopters. During that time, we’ll measure again for growth with this new tool. We predict we will see more targeted data to help us better identify needs for our lessons and/or task selection.

Leave thoughts in the comments! I’d love to hear your tweaks to our rubric, or ideas for using in the classroom.

On My Soapbox About Elementary Math

I’m still digesting and processing all the great learning I had at NCTM San Diego 2019! It is truly awesome to think of all the knowledge and brainpower I was surrounded by in San Diego.

With that said, there is still something that doesn’t sit well with me, from a few years ago, that was reiterated at this conference. Steve Leinwand told a large group of coaches in a workshop I attended a couple of years ago that a mediocre K-5 education can be overcome, but 6th grade is where math really takes off. Linda Gojak echoed that in her presentation, but added that she thinks 5th grade is really that important turning point. In talking with coaches at different elementary school districts, I’m learning that various school districts de-emphasize the importance of math at K-5.

It just doesn’t sit well with me.

At the same time you’ll hear that algebra is the “gateway to college access” (WestEd, 2015), and that students who fail Algebra 1 the first time are unlikely to pass it the second time. Performing just slightly above the proficient line on the CST’s in 6th grade offered only a 50/50 chance of passing Algebra. I’m looking for similar data from SBAC assessments but haven’t seen an updated version yet. WestEd details a summer intervention between 6th and 7th grade as a support, acknowledging the limitations of such a short time frame.

But I still don’t understand! If a proficient (albeit barely) performance on our state standardized assessments only gives you a 50/50 chance at success in algebra, then why aren’t we concerned about the mathematics education of K-6? Isn’t this a huge equity issue? Who gets access to algebra, and thus college?

They don’t start learning mathematics in 6th grade. It starts in kindergarten. We can’t *assume* it started before that. Of course, in the ideal world the babies were counting everything in sight with their parents, comparing more and less, starting to subitize small quantities, etc. Their early numeracy trajectories could have started well before kindergarten. But for others, it didn’t. The opportunity gap has begun before they even stepped into their brightly colored kinder room.

I can’t accept that the choice of college is already limited upon walking through the kinder door. We have to do better than that. However, our elementary teachers are charged with the critical goal of teaching children how to read – no easy task by any stretch of the imagination. It’s hard work, stressful, and compounded by a society that doesn’t value elementary education – as demonstrated by the “teacher pay penalty” (EPI, 2018).

Is this why we give K-5 the “pass” on mediocrity in math? We just can’t burden elementary anymore?

I can’t accept that either. In the meantime, our students suffer and the opportunity gap widens. We know what is working from other countries – here is a very partial list (NCEE, n.d.):

  • Longer school days
  • Preschool
  • Early childhood focus on literacy AND numeracy
  • Ongoing teacher development and collaboration

It’s not a secret. In order to compete globally, we have to provide a stellar education from Pre-K through 12th grade. Even with the limited amount of time in American school days (this really has to be changed but it is a subject for a different day), we can’t expect even a preschool teacher to spend the entirety of every day on literacy. Early numeracy, conceptual understanding, basic fluency, and positive math interactions are critical to their secondary education. We cannot wait to focus on 6th grade – at that time they have had 6 prior years of math “mediocrity” that has potentially established math anxiety, math hatred, or math avoidance. Undoing 6 years of learning is too tall a task for a summer intervention.

Instead of accepting mediocrity, let’s invite success. The opportunity gap has already started before they walked through that kinder door. We must change that math narrative into one where the algebra gate is readily open to all, due to their stellar K-5 preparation.

They Just Don’t Know Their Facts

They Just Don’t Know Their Facts…

I’m pretty sure I’d be rich if I had a dollar for every time a teacher has said that to me. To be fair, I’m pretty sure I’d be rich if I had a dollar every time I said it in my career. But, when you know better, you do better, so here is what I now know.

My career started as a student teacher in 1998. That was the first time I heard the complaint about not knowing facts. The answer was always – they need to practice their flash cards at home. If only they practiced. If only their parents made them practice. If only they weren’t lazy. If only they cared about school. If only they paid attention.

“If only” and “just” may be the enemy words of progress and innovation. It takes complete responsibility off of the person saying them. I started to realize this later on in my career, and began listening carefully to those words. These are the words of oversimplification, of self justification, and of saving face in front of a situation that seems out of hand.

“Yet” is the new buzzword. So, “They just don’t know their facts” turns into “They just don’t know their facts yet.” It’s an improvement for sure – a growth mindset that might lead to some new learning around how students “know facts.” It still boils math down to “just” – a word that continues to scare me. Are these students really just one flashcard away from knowing their facts? Or is there something else that we haven’t considered?

My new recent learning is sadly not “new” at all. I hope that the more people that share learning, the more rapidly it spreads, so that we can stop blaming the students and start finding the solutions.

Fact Fluency Through Games, Not Timed Tests

First, if you haven’t read Jo Boaler’s Fluency Without Fear, then stop right here and go read it. If she doesn’t convince you to stop giving timed tests, then I’m not sure what will. However, for those beginning the journey away from timed tests, the easiest entry point is to practice with games. Her “How Close to 100?” game is actually a lot of fun, even as an adult playing with students. Plus, when you get kids playing games, they now have an independent activity that frees you as a teacher to confer with students, hear their math explanations, and probe thinking.

Games engage students to build fluency while simultaneously building number sense.

In my career, games became my initial step away from timed tests. If they weren’t going to memorize them from timed tests (anxiety, lack of feedback, practicing wrong answers…) then wouldn’t they memorize them from play?

Sure. For many students, the games did the job of practice and developing fluency. For others, they needed a different kind of help. I relied on multiplication charts to help them out when we were learning a different concept that needed the fact fluency to be there so that their cognitive energy was freed up for the other thinking. Why teach what a computer can do inevitably faster than a human can?

Yeah, but…

“Not everyone has a grid in front of them to draw a picture, and they need to be able to do problems like 342 x 74 with relative speed.”

“They are still failing their math tests.”

“They won’t have a multiplication chart on the SBAC.”

“I don’t have time for these games when I need to get through the textbook.”

Hmm. 🤔

So these are questions I had asked myself at one point, and then asked others, and now have others ask me.

The Math Wars in the 1980’s and 1990’s created some serious debate over the role of technology in math. I think the Common Core does a good job bridging this debate – students must be able to understand number relationships. If we focus on that development of number sense, then we truly can rely on technology for the speed piece. If we neglect the sense making, then no technology is going to support our work.

So let’s focus on the statement, “They are still failing their math tests.” I have been spending time giving the IKAN and GLOSS assessments from the Georgia Numeracy Project, which has based their work on NZMaths from New Zealand. For background info and directions for assessment, check out Graham Fletcher’s page here. The IKAN written assessment gives numeracy stage scores in 4 domains – Number Sequence & Ordering, Fractions, Place Value, and Basic Facts. Which one do you think was the lowest? Which was the highest?

Out of every class I’ve scored (at this point I’ve scored 12 classes of about 28 kids each), every single class had the highest score in Basic Facts, and the lowest score in Place Value. Now I realize that this is in no way scientific research, but the trend is fascinating. Maybe we are missing the point when it comes to “they don’t know their facts”?


What is going on behind these facts and this place value idea? Here is the document I’m currently digesting:

Now I’m putting my fourth grade teacher hat on, and I’m thinking, but this seems so basic? The thing is, do we really know that our students have had enough experiences with number to move them through this trajectory? If my students don’t know “know their facts”, then can they visually recognize something like this:

Can they tell me what one more is (without recounting)? One less? Yes? What about this? How far away is it from 10? From 0? Can they tell me two numbers that make up this number? Do they see the 3 and 2 or the 4 and 1? Yes? Then what about this?

And why do things like this need to be searched for and even bought from TPT, when they should be free to all? Under my fourth grade teacher hat, which up until a few years ago didn’t have this knowledge, all of this seems like too much. Just have a go with the flashcards and don’t be lazy. But I know better, and now I do better. The thing is, in the classroom, I affect 28 students for one year. How do we spread this knowledge, so that all teachers are armed with the understanding, as well as armed with the materials and skill to dig deep into children’s mathematical understanding?

The Basics of Fact Fluency

Procedural fluency is skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.

Common Core State Standards Initiative, 2010

Flexibility • Efficiency • Appropriate strategy use • Accuracy

There’s the definition . Does a timed test measure any of these? How do you know? Before you can say, “They just don’t know their facts,” we have to carefully reflect on this definition. How did we prepare them for flexibility in choosing strategies? How did we prepare them for accurate calculation? What did we do to help them understand efficiency? And how have we spent our time to help them see appropriate strategy use vs. ineffective strategy use?

In conclusion, dig deeper.

We have decided upon some screeners (including the GLOSS along with the IKAN, as well as some ideas from Build Math Minds) to get at some answers to these questions. Yes, many of these are one on one, but when in doubt, ask the students! The interview process can take some time, but it is enlightening to find out how students are thinking – not to mention on the job professional development for the teacher. If we can understand where a breakdown in understanding has happened, we can intervene more precisely. I’m also interested in doing more work with math Running Records, which involves more interviewing to understand what strategies students are using to add, subtract, multiply, or divide. If our end goal is for them to be fluent but flexible with numbers, then it would help us to know where their current level of understanding is.

In the meantime, my fervent hope is that teachers take the time to do Number Talks (or Fraction Talks) every day. I’m not sure there is a more powerful way to help students explore number relationships. For our teachers, we are working on a repository of resources so that Number Talks are not something they have to spend lots of time searching for – the resources will be at their fingertips. Games will also be provided so that teachers can easily pick from games that will not only engage but help students build number sense.

For me, I’m working on coming up with a more straightforward answer to “They just don’t know their facts.” This post is a start, but nowhere near a final version! I’ll be seeking out more understanding with my colleagues, with Twitter, with the research, and most important with the students we serve. Would appreciate your comments below!

Math Writing at Empower 19

ASCD Empower 19
Chicago, CA
March 16-18, 2019

Just got back from Chicago, and have so many thoughts rolling around in my head!! Blog ideas about navigating the conference, Ron Clark, Doris Kearns Goodwin (this is my new role model – her storytelling, her presence, her speaking ability and intelligence are all qualities I aspire to), presenting do’s and don’ts, and writing ideas are all swirling around in my head. So, in trying to stay focused, I’m starting with my big passion – communicating mathematically.

There were few workshop options in the math writing/communicating world, and the first one I went to was titled Elevating ELL Discourse in the Mathematics Classroom, presented by Sherry Ayala and Sylvia Olmos. Although the title didn’t reference writing, the summary did. Much of this workshop turned out to be similar to work we have done in our district around the 5 Practices. Lately as I’ve attended workshops, I’ve noticed quite a bit of similar learning, which leads me to look for the “nuggets”, or the new piece of learning that I can attach to prior knowledge. In this case, my nugget was how we teach and practice math vocabulary.

Students partner up, and explain their thinking around a problem, such as 324 – 165. As a teacher, you’ve considered what vocabulary they may use around this problem, such as subtract, add, ones, tens, hundreds, regroup. You provide the students with a small table, so that the listening partner can tally the number of times the partner used the vocabulary words.


From there, the listening partner can paraphrase back to the speaker what s/he said, and the speaker can self assess. Why didn’t I use regroup (or ones/tens/hundreds/etc). Did I need to? How could I explain differently so that I could use a different vocabulary word? I’m super curious to try this out in a classroom to see how students respond. The vocab words chosen are all based on what you have taught and what you expect them to use – being aware that the flexible thinkers you have molded will likely be able to find ways to explain that would change the vocab you are looking for.

The other workshop I went to was titled Strategies for Teaching Effective Mathematical Communication, from the book by the same name, presented by Laney Sammons and Donna Boucher. This one intrigued me because it was directly on mathematical writing, and I’m searching for different research based opinions and ideas to round out the work we have been doing so far. Again I saw many similar ideas to what we have already been doing with discourse (oral communication ideas, using CRA in math progressions). I noticed that this workshop also brought up the idea of developing math vocabulary, including the use of the Frayer model (along with a foldable that I’ve referenced in many of my own trainings).

Another nugget from this workshop was the inspiration to redo our criteria on our rubric. Their suggestion, based on work from the Ontario Ministry of Education, was to examine:

  • Precision regarding details, strategies, observations, and calculations
  • Explanations of assumptions and generalizations made
  • Clarity in logical organization
  • Cohesive arguments presented
  • Elaborations that explain and justify mathematical ideas and strategies
  • Appropriate use of mathematical terminology

I think that this list makes for a nice set of criteria beyond what we have used up to this point, and the work now will be to blend it with our current rubric:

So what is next for my math writing partner in crime and myself? We are looking at streamlining our presentation so that the focus is not the lessons that are prepared for classes, but instead an approach more linked to disciplinary literacy. An approach in which the vocabulary is introduced, clearly understood and practiced. One where there are multiple criteria for success and we can narrow lessons down to one or two of those criteria each time to develop, strengthen, and support their communication in writing. Plus, we need to go over the book, Strategies for Teaching Effective Mathematical Communication, to look for more ways to refine our thoughts and our rubrics.

The last nugget, that I should probably save for my navigating the conference post, is: Just because you didn’t attend the session doesn’t mean you can’t spy on the notes! So the Connecting Math and Literacy session by Alex Kajitani was at the same time as another session. In his presentation, he had this wonderful quote from Marilyn Burns. Besides wondering why I hadn’t seen it before, I was struck by the clarity it brought me.

Writing in math class isn’t meant to produce a product suitable for publication, but rather to provide a way for students to reflect on their own learning and to explore, extend, and cement their ideas about the mathematics they study.

Marilyn Burns
Educational Leadership, 2004

Spoiler alert – that one will be in our next presentation. Thanks to all who developed and presented at the conference! You challenged us to develop and refine our own thinking, and I am grateful for it.

Coaching and Not Having My Own Class as a Laboratory

“Today we are trying something new out, and I need you to let me know what you think when we are done.”

My students were entertained when I told them that because it meant we were doing something outside the ordinary. They also liked being my “expert opinion.” One thing about coaching – I miss that relationship with students where they would give me an honest answer. Sometimes this was a great trick to engage them when I knew it would be a tough lesson. But typically, they were my guinea pigs after receiving some new professional development.

So I was working with a 6th grade teacher recently, who is new to the grade level and fairly new to the classroom. How do I plan for everything? Can you boil this down for me? There’s just so much! These are hard questions for all teachers, so as a new teacher, they can be overwhelming. One teacher colleague had quite bluntly suggested that coaches and administrators don’t understand because they aren’t in the classroom. While my many feelings about that statement are best left for another post, I do agree that it is important to consider the point of view of those I support (teachers, administrators, paraeducators, among others). Since it was a 6th grade teacher, who is relatively new to our school, I thought about what my lesson plan would look like if I were her.

As a coach we receive lots of learning – typically from that 30,000 foot point of view where it sounds good in theory but putting it into practice is a different story. I informed my ELA planning from a recent Tim Shanahan post, Why Aren’t American Reading Scores Higher? In it, he suggests that there should be 120-180 minutes of reading and writing instruction per day. Shanahan writes:

This instructional time should be devoted to explicit teaching and guided practice aimed at developing knowledge of words (including phonemic awareness, phonics, letter names, spelling, morphology, vocabulary); oral reading fluency; reading comprehension; and writing. And, for English learners (and perhaps poverty kids too)—explicit oral language teaching.

I used this teacher’s basic schedule (I guessed at PE, library, and computer times to make it more complicated) to see if I could make it happen. Then I layered on current thinking in math. I wanted to make sure tasks happened, and I thought about the NCTM Thinking Through a Lesson protocol. And I know the value of Number Talks, so I considered what kinds of number talks might support the current math chapter (to be honest, I also guessed at that based on recent conversations – the teacher and I hadn’t talked specifically about math.)

Then I thought about the learning objective/intention/target. The words get used interchangeably in our district, and some schools in our district have studied these more extensively than others. Since the work we’ve done as coaches has highly valued these learning targets, I wanted to make sure I put those in where possible. I thought about putting success criteria in too, but time was getting away from me at this point. I realized that I’m still working on my own clarity with these ideas!

Our school has focused on the use of social emotional learning curriculums such as Second Step, Morning Meetings, Responsive Classroom, so I made sure I fit in some time for that. We also have required ELD (English Language Development) time for our EL students, during which time small group instruction would be happening for other students. I didn’t plan that out, because I’d be making up a lot of information for students. So I generalized it to ELD, intensive comprehension work, learning center pullout (for those on IEP’s), and enrichment.

Shanahan (and many others) also point to background knowledge as a critical piece to comprehension, so I wanted to make sure there was time for science and social studies. Our reading curriculum of course has science and social studies readings, but we need to dive deeper into the content. Since I don’t have online access to those curriculums, they are blank for now, but my thought was that this is a time to build content knowledge through key readings (especially primary sources), academic discussions, and hands on science.

So here was my stab at making sense of the current teacher’s dilemma. (Side note – as a coach I have no intention of just giving the work away and telling the teacher to do it my way. It wouldn’t build capacity and would likely have the opposite effect of creating dependency. Not to mention..this isn’t even done completely…)

This thought process for a week took me two hours. And I’m tired! Not to mention, I still have a whole slew of other things to do (as a teacher that might include grading papers and planning copies…as a coach that currently includes planning PD for our Monday staff meeting and prepping for two presentations this week). But, as I worked through this plan (which still needs work), I was able to metacognitively view the process. Some takeaways:

  • Redoing the ELA block into the key elements of reading and writing was really helpful. Our curriculum can be difficult to navigate, so as I viewed it through a lens of Word Study/Phonics, Vocabulary, Comprehension, Fluency, and Writing, I felt more confident in meeting the skills in all areas. Instead of tying it directly to standards, it was tied to the science of teaching students to read. I relied on the curriculum to be standards based.
  • Redoing the math block into Number Talk and Lesson forced me to consider what number talk I’d be doing each day. I also thought it might be helpful to call the block the Mathematical Goal, and then add another row to include Tasks.
  • There really isn’t enough time during the day. I was able to schedule it all in (note that Wednesday afternoon is actually gone because of the early out schedule that gives teachers PLC meeting time.) At some point 20 more minutes of PE is necessary due to the 200 minute PE biweekly requirement, and VAPA is basically a Friday afterthought. Things will have to overlap – an art lesson that is embedded in reading, or PE movement activities scheduled as brain breaks during the day.
  • This still assumes a near perfect classroom environment. Classroom management must be intact: tight transitions, clear expectations, a plan for student behavior (those that need to take a break, be offered choices, sent to a buddy room or calming room…). Lessons must be tight, focused, and engaging to keep students on task.
  • This also assumes zero interruptions. We know that isn’t always the case – the office calls, or another teacher calls, or a student is leaving early, or there is an assembly, or a field trip, or, or, or…… Need I say more?
  • Proper planning prevents poor performance. My master teacher 20 years ago taught me that, and yet proper planning takes time. My teachers have 45 minutes each day in their contract for planning, parent contact, grading, collaborating with peers, and any other paperwork as needed. As professionals, if we want to keep to that contract time, we have to protect that 45 minutes.
  • This schedule also assumes that you have plenty of tricks in your toolkit for lesson design. I based it all off of information found in the curriculum itself – but the curriculum doesn’t know you or your students. Continuing education in best practices is needed.
  • There is still a shorthand in lesson planning. Which parts must be written down, and which must you rely on the curriculum to have at your disposal? How many sticky notes died as I made notations in my manual of questions to ask or things to notice?

I remember in the classroom, feeling confident and relaxed that I could get all of these things done. Experience in many ways is the best teacher, so lesson planning became second nature as I knew the pitfalls to avoid and the long term outcomes I was working toward. Even now, out of the weekly practice, the rustiness slows me down. I wished our school day was longer, so we could really do some great things with art, music, and PE. I still do wish that were the case, but that isn’t in my realm of immediate control. So to inform my coaching, here are some possible questions I’d expect to ask a teacher who is struggling with planning.

  • How might you arrange your schedule to ensure the five elements of literacy (phonemic awareness, phonics, vocabulary, fluency, comprehension) are all given time?
  • In what ways does your curriculum address those five elements?
  • What professional learning do you need to feel confident with those elements?
  • How do you know your students proficiency levels with those five elements?
  • How does your classroom environment support or prevent instruction with those elements?
  • In what ways do your curriculums overlap? How might your writing time be linked to science or social studies?
  • What are your learning targets? Is the target achievable within the time frame you’ve allotted?
  • Are your students reading plenty of complex text each day, and increasing in stamina? How might you scaffold the reading for struggling readers? How might you increase their stamina for silent reading as the year progresses while holding them accountable for the reading (i.e. not just sit and stare)?
  • What problems are you encountering in your current lesson plan? What have you tried so far to address them? What strategies have worked?
  • How will you know the students have met the learning target(s)? How might you keep that checking for understanding to a minimum of time for maximum information?

Walking through planning a week again was a really grounding experience. I love applying theory to practice and feeling the stress, excitement, and frustration as the ideal world meets the real world. I appreciate the empathy it allows me to have as I help my teachers negotiate the challenge of planning.

How do you help teachers plan for the week? The day? The lesson?

Making Sense of Decimals in 5th Grade, Pt.2

So about that number line I mentioned in part 1. I love clothesline math! I loved it before I knew there was a blog about it. I loved it when a colleague said, “Hey, did you see this?” There are so many possibilities with putting numbers on a number line, and discussing things like:

  • Convince me 7/4 is in the correct spot.
  • Why did Johnny put 1.2 on top of 12/10?
  • Do you agree that 1.25 belongs between 1.3 and 1.4? Why or why not?

The discussion with the partners is so interesting. And then putting numbers on your own white board. And the formative assessment that comes with that! And then magically having numbers in the correct order without having to stack them on top of each other with place values lined up.

Quite honestly, I’m not sure how you teach math without a number line at this point. I’ve had so much fun with it that it makes me want to be back in the classroom exploring it. But, I’m enjoying exploring it with my teachers as well.

So, my 5th grade teacher who was looking for strategies probably felt my excitement about doing the number line, so she agreed to try it. After warming up with some choral counting, we jumped right in. I had consulted Kristin Gray’s blog, KG Math Minds, and got some great ideas there. Check the post out here to get far better description of how I planned using many of her ideas. A couple of the ideas she reflected on were where to place the 0 and how many cards to give partners. I decided I’d start the conversation by putting the 0 in the middle of the number line. I asked the students if that was OK, and why. They agreed that the left was negative and the right was positive. Since that seemed clear, I moved the 0 to the left and told them we’d only be focusing on positive numbers today. Then I held up 1/2. Where should this go, I asked. The students were hesitant. Rightfully so, as there was no benchmark for the whole. A brave soul came up and placed it. We had a brief conversation about the choice, and the realization dawned that it didn’t really matter till we placed the 1. So, I tested the theory. Instead of a 1, I held up a 2. A brave volunteer came to place it. She placed it so that it the 1/2 was equidistant from the 0 and the 2.

Aha! Misconception. Keeping my poker face (isn’t that hard when you want to raise an eyebrow and say nope, try again?), I applauded her bravery and asked the class, how do we feel about the placement? Talk to your partner about why you agree or disagree. The students worked to find the words to say that 1/2 should be closer to 0 than 2. They eventually got there.

Now the cards were spread out, and we added in the 1 to help settle some disagreements. So, I handed out the decimal cards to pairs of students. Here is the end result:

First, don’t make fun. I know the cards are too small. I was anticipating bringing them to the carpet for a closer experience, and I thought my number line would be much smaller. I hated the overlap when I used full sized index cards in the past and was trying to avoid that. Plus, proper planning prevents poor performance – I should have planned this part out with the teacher but the time crunch got to me. So, I overthought this a bit and ended up with a problem. But, the kids assured me they could see it, and that my phone did not take an accurate picture (side note…why do iPhone pics look so much further away than the reality?)

Second, I took the picture at the very end when I realized I had no visuals to share with others about the clothesline. It didn’t start as well spaced out. Plus, there were some answers that needed more immediate revision, and we had to discuss those. Coaching note…take more pictures during lessons. Visualization is important!

One of my favorite events of the lesson was the partnership that had 7/4. During the questioning in choral counting and the beginning of the number line, I had noticed a couple partnerships talking at a pretty high level. So as I passed out the decimal cards, I handed out a couple of fractions that I figured would be a little more challenging at this stage in their learning. This partnership put 7/4 to the right of 2…suggesting it was more than 2. I let that go for a bit, as we debated a few of the other decimals (mainly spacing them accurately between 1 and 2.) Suddenly one of the partner’s hand went up. When I called on him, he asked if he could move the fraction. I agreed and he moved it to the left of 2. Why did he move it? Ensuing partner talk.

During the partner talk I chatted for a bit with the teacher. She was surprised at some of the discussions her kids were having, but also at some of the misconceptions that surfaced in the placement of the numbers. She realized that they needed to do some more work with placing numbers accurately on the number line.

In the debrief later on, the teacher shared with me that she had continued the number line work, and was using it as they considered comparison of decimals. She was interested in using it as they moved into fractions. I’m excited for her as she journeys on with the number line, and I’m excited for her students who begged me to stay and keep working with the number line. I’m excited for the student who discovered his own error and was willing to revise his work in front of the group.

In my own reflection, my math goal was really to seek information about their understanding of numbers on a number line. The difficult part about demos is that even though a teacher shares knowledge and data on where the children are at, there is still the reality of being in the room with students day in and day out, and the deep understanding that comes with knowing what you’ve taught, where they’ve struggled, and where that zone of achievable challenge is. The teacher and I both saw that moving forward they needed to work on the distance between numbers, justifying that distance, and understanding the link between fractions and decimals. Too often we rely on kids “understanding” as demonstrated by a conversion worksheet, but we discover in the number line that their “understanding” is limited to a procedure. I do wonder how much of this affects 5th grade SBAC scores. I look forward to seeing what they do with the number line over the next few weeks!

Any best practice ideas for implementing the clothesline in the classroom? Comment below!