Making Sense of Decimals in 5th Grade, Pt. 1

A fifth grade teacher shared with me last month her concerns about her students that were struggling with decimals. They didn’t understand place value. They had trouble identifying greater than or less than. They confused the tenths with the hundredths.

One of the ideas she was interested in pursuing was Choral Counting. We had done work in the past on various talk routines, including Number Talks and Which One Doesn’t Belong. I consulted another coach (remember how I get by with a little help from my friends?) and made sure I was clear on the strategy.

So we started simple. A choral count by 0.25. I used this planning tool my coach colleague suggested to think ahead about what I would scribe on the board.

I planned to stop and look at patterns, but I realized that my structure didn’t lend itself as well for beginning choral counters. So, I changed the number of rows.

That made more sense. A pattern of increasing by one in each column was easily distinguishable with four rows. We could look at why that happens (0.25 is equivalent to 1/4, and our numbers are grouped in 4’s.) Hmm…

They picked up on this pretty quickly. All I had to do was ask:

  • What do you notice?
  • Do you notice any patterns?
  • Can you predict what would be ____? (I put that blank space in the 3rd row of the next column).
  • How could you prove it without counting?

The teacher liked this strategy, but still felt like her students were struggling with the idea of greater than, less than, and the concept of decimals as compared to whole numbers. She wanted to explore the clothesline number line.

It was a couple of weeks later, and I wanted to see if the students remembered the choral counting. I remembered that they thought it was pretty easy, and they were engaged with it, so I thought we’d warm up with a choral count. So, we counted by 0.03. This made for some fascinating conversations that went a little longer than I planned. I wrote 0.03, 0.06, 0.09, and then asked:

  • What number comes next? How do you know? – That elicited 1.2 and 0.12. So I wrote them both up there.
  • Convince me that one of these is correct. – They practiced with their partners first.

Once the group was convinced that it was 0.12 (one of the students had said, well, there are 12 hundredths and that is the same as one tenth and 2 hundredths), then we kept going on. Eventually the count looked like this (without the fourth column):

So I asked if there were any patterns. I waited (did I wait 10 seconds? I need to work on that), then gave them partner talk time so they could orally rehearse. Sometimes I pull sticks after this but this time I preselected a volunteer. He can be a reluctant student, but he noticed a pattern of 12’s with his partner, which he explained to the class that at the bottom he sees 12 x 1, 12 x 2, 12 x 3. So I wrote that on our count, purposefully leaving the misconception on the board. I asked, if that is true, what comes next? A student volunteered 48. So I wrote that on the board, then asked the students, what do we think? Does that make sense?

Discussion ensued, and I noticed it got more lively as they started to realize what happened. I listened in to conversations, and once I was comfortable that the partnerships were prepared, I pulled a stick. The student explained that it should be 0.48. I asked, “Why?” Another student explained the pattern was counting by 12 hundredths, not twelves. So, I changed 48 to 0.48. I again asked if it made sense. They looked around at each other. This time I remembered my wait time! Eventually the partner talk picked up, I called a volunteer, and the student explained that the 12 x 1 and so on should have been 0.12 and so on. Aha! We spoke for a minute about the importance of precision in math (SMP 6), and then moved on.

How long did this routine take? About 10 minutes. Lots of partner talk and making sense of math, with a very easy to implement routine. In part 2 I’ll talk about the number line.

I Get By With a Little Help From My Friends

I cringe just a bit when I hear coaching referred to as a lonely job. The job requires nearly constant collaboration, and so I’m talking with someone most of the day. Really, teaching can be a lonely job too. You spend the day with your students, none of whom can collaborate with you on the professional level, and at the end of the day, you’re faced with all kinds of things to do.

This is where I feel like the power of the coach comes in. No one wants to be wrong or treated as though they were being fixed. But many of us want someone to talk to who will be focused on our problems. A teacher colleague next door might be helpful, but s/he has their own problems that may take over the conversation. A coach comes in and is focused on you and your needs. It’s one of my favorite parts of the job, and has helped me overcome some guilt over leaving the classroom. I spent my first six months on the job haunted by this meme as I pondered my role as a coach:

Now I know better. I spent time yesterday talking with a teacher who is investigating guided reading. Now there is an overwhelming task to take on without formal training (yet…it is coming soon…). So, we worked on breaking it down. Why do guided reading? What are you hoping your students will get out of it? What information do you really need to make that happen? How do you get started? There are so many birdwalks to take in this area that talking it out with someone who can paraphrase your thinking, and help you sort through your thoughts, can be exactly what you need. Sure enough, the five minute planned conversation about a running record procedure turned into a 45 minute coaching conversation, and at the end the teacher said, “sometimes it helps just to talk it out.” Exactly!

So who coaches the coaches? It would be unfair to turn around on those teachers we coach and expect them to reciprocate – that’s not their job and they haven’t been trained to do that. They already have more than enough on their plates. Fellow coaches and I have organized a job alike afternoon once a month, where we join together and share out celebrations, ideas, new learning, and challenges. I’ve come across several articles on the power of these coaching get togethers. I was first inspired by the idea of the Mastermind group from the Cult of Pedagogy. But, when talking to other coaches, we thought we might keep it more loose at first – no specific agenda. No one in our group had done this before, and we didn’t want to formalize too much at first. I suppose this is the “forming” part of our group, but I’m not sure that it fully fits that framework, as we don’t have a “performing” goal at this point.

We looked at some coaching models in our first meeting. Although at this point our district has focused the coaching training on Cognitive Coaching, we talked a bit about other models that are out there. Student Centered Coaching is one that we started to investigate briefly, based on an article one member of our group shared.

But the best part was how the group organically shifted into sharing challenges while staying focused on solutions. Venting is a part of any job I suppose, but it doesn’t solve problems. TeachBoost says,

Coaches must keep in mind that they need to restore themselves first before their work of restoring others can happen.

In a job alike group, we can certainly do some venting, and empathize with the challenges each other faces, but we also know we can brainstorm solutions. We didn’t formally do a Problem of Practice protocol, but we did end up investigating one of the challenges in more depth. In the process, I came up with my own new ideas for our guided reading book room while taking into account the pitfalls described by my colleague.

It was exactly what I needed, when I needed it. A reminder that we are not alone in this work. That no one has a perfect gig, nor does anyone expect perfection. No one “fixed” a coach, nor did anyone need “fixing.” Sometimes we just need to talk it out. In the process, we are validated, we are understood, and we feel like problems are not insurmountable.

How do you stay connected with colleagues and avoid the feeling of isolation?

2019 Goals: Writing

In this last of my 2019 goals series, I’m focusing on writing. Hence the blog! I figure if I’m going to help teachers and students write, then I need to be in the process myself. There is actually a record of me saying I hate teaching writing on Facebook, back in 2009 when posting answers to 25 questions about yourself was trending. Shortly thereafter, I came to discover that I actually loved teaching writing. It was through a professional development series that was actually based in technology that I grew to love the writing process. It’s funny how things can work out that way. Take something I love (technology) and then embed something I’m not interested in (writing) and a spark ignites. I’d like to think that same thing happens for our students as well.

So how did I go from hating writing to loving writing? The process was based in helping my students navigate their brand new laptops (our grade level had been given a laptop cart to share). While they were writing letters to pen pals, I started to realize that I couldn’t try to correct everything possible in their writing. It would sound unnatural – not like a 4th grader. I also learned that there would be many, many questions in this process, and I couldn’t spend 10 minutes with each child. Writing conferences became more like writing drive through’s, where I would know of one or two items in the student’s writing that s/he was working on, and I would focus my brief attention there. I never focused on spelling during these writing stages – I’d file that information away for a lesson to be done shortly thereafter. Plus, I made sure they were aware of how to use spell check! The whole world of writing opened up to me – I realized the power of a mini lesson and the power of meeting students where they were at. Now, Google docs (through the use of Google Classroom) really makes the writing process a fun one for teachers and students. Click here for a short overview of what I love about Google Docs.

I’m super excited to take a group of teachers to see Carol Jago at the end of January, as she presents on opinion writing. I love that she is not only talking about the process, but also how to provide feedback and manage the paper load that teaching writing creates.

One of my biggest interests is in the area of mathematical writing, and will likely be the focus of many future blog posts. Currently, I’m working with many teachers on a set of lessons based out of Think It, Show It Mathematics.

This was suggested to me after attending a workshop from a professor at UC Davis, where she had shared lessons they had created from this book. So, we have worked with them and tweaked them for the needs of our teachers. At this point, we’ve had rave reviews on our PD. Teachers who have really focused on mathematical writing are finding that by having a rubric by which to evaluate the work, along with language for the writing itself, has helped their students’ explanations soar. Here are a couple of examples of fourth graders’ recent math writing. Note the use of transition words and a clear statement of the answer.

Clear statement of the answer. What might be your next steps with this student?
What understandings does this student have?

I just happened to grab a couple of snapshots as I was in the room for another purpose – to observe their collaboration as partners! But, I was so struck by the fact that after collaborating with partners, there weren’t any questions of “How do I explain this?” It was fascinating to not only observe their conversations, but then see them explain their thought process so clearly on paper.

I’m looking forward to doing even more investigation into mathematical writing with my teachers, through a few different lenses. First, there’s work from UConn including the original recommendations from the Elementary Mathematical Writing Task Force. Linked there, but I think also important to link here is the article, “Why Should Students Write in Math Class?” from Educational Leadership (2017). Last, is a piece that I found on Twitter a week ago called 17 Prompts For Writing in Mathematics. See a glimpse below:

So that’s it – my three big goals this year are to investigate Intervention, Listening & Speaking, and Writing. Keep in mind though – all of these investigations will also come through the lens of coaching and support, so I certainly intend to blog about coaching as well. What are your goals this year?

2019 Goals – Speaking & Listening

Another goal for 2019 is to locate and develop resources strategies around our Speaking and Listening standards. This is urgent for three main reasons. First and foremost, we know that speaking and listening are key literacy and life pieces. To produce the citizens of tomorrow, it is imperative that we teach them to be effective speakers and active listeners. In looking at the 2020 Top 10 Job Skills prediction, it would seem that consistent instruction and application of listening and speaking would greatly benefit our students.

Second, our new report card includes a grade area for listening and speaking. So, our teachers are actively seeking support and professional development to help them assess these standards.

Last, our test scores indicate that there is a need for better understanding about the listening standards. While I feel the need to make it clear – summative test scores are a snapshot and absolutely do not solely define the child – I do think they are valuable to use in making programmatic decisions. It would be unfortunate for our students to have low scores simply because we didn’t analyze the situation and identify causal factors.

As a result, a group of coaches and I are planning an optional, introductory PD to these standards. Although the idea of listening and speaking is not new – consider our EL supports and PD over the past several years – we recognize the need give sharper focus to these standards. After a solid brainstorming session today we realize that even two hours doesn’t seem like enough. How do we include information about SBAC, ELPAC, the CCSS, prior ELD strategies that could be brought back, resources that are available, resources that we have created, our new report card, and of course the classroom management challenges that speaking and listening can bring?

We are particularly inspired by three Teaching Channel videos:

  • Listening & Speaking: Formative Assessment – in this video, the teacher uses a checklist during an academic conversation in order to record who is meeting the learning targets of the conversation. Simple, low prep activity with high engagement, that is rooted in the standards.
  • Evidence Based Academic Discussion – this is the “prequel” to the prior video, showing how the teacher set up the conversation so that students came to the circle prepared for discussion. In the “exit ticket” there is space at the bottom for students to reflect after the conversation – a great way to look for evidence of listening (since a look on the face can be deceiving!)
  • Formative Assessment: Collaborative Discussions – we were hooked in this video by the use of the poster to help students organize their thinking during their discussions.

We continue to look for formative assessment ideas around the speaking and listening standards that are easy to use and provide good feedback for next steps in instruction. Any suggestions, please leave them in the comments!

2019 Goals – Intervention


I’m not sure this blog post is appropriately titled! These may still be wishes at this point, or maybe better termed focus areas for 2019. The plan is in process.

Response to Intervention

I started to title this “Intervention” but I can’t make that a focus. Because high quality first instruction is so critical, that I can’t think about intervention without making sure that I’m supporting high quality first instruction. Any time intervention comes up, I need to remind myself and others that first we teach and teach well.

So with that said, assuming excellent high quality first instruction, we can reasonably expect RTI to look like this pyramid. I like this one because it looks at academic and behavioral instruction, even though the focus of my work is generally academic. The MTSS model as explained in PBIS.org.

We cannot throw around interventions like spaghetti, hoping they stick to the wall. So my plan for 2019 is to investigate assessments that will best target our goals. In the DuFour PLC model, this would revolve around the question, “How will we know if they’ve learned it?”

Assessments we currently have in place universally in our district for K-6 ELA include:

  • Spelling Inventory
  • Fluency
  • K1 Phonemic Awareness
  • K1 Phonics

We also have a decision making tree to help decide what other assessments might help us target need. The plan for 2019 is to continue to guide thinking around these assessments, and coach teachers in understanding the results of these assessments, as well as planning for intervention based on the results.

Assessments we have in place universally in our district for K-6 Math include:

  • <This space intentionally left blank.>

So there is clearly a need to understand math assessment and intervention. The plan for 2019 then is to understand the first two PLC questions, “What do we want them to learn?” and “How do we know if they’ve learned it?” My first step in understanding is to look at two common statements I hear from teachers – “They don’t know their math facts.” and “They can’t do our work because they are low.”

For the first question, we want them to know their facts, but we don’t know if they’ve learned them. So I’m going to investigate Math Running Records in more depth, with a couple of specific classes. We will do running records for the entire class, and look at trends as well as possible interventions.

For the second question, I’m curious about how we define “low” as well as how we can have student access grade level math despite any areas of need. One of the projects I’m looking into was something Graham Fletcher brought up last summer at the Virtual Math Institute called the Georgia Numeracy Project. I’m going to adopt a couple of classes with this as well, to see how we might use the materials to specifically identify areas of intervention and thus maximize our intervention results.

Phew…and I’m just getting started on 2019 Goals. 🙂 It’s going to be a great year! Any advice on high quality first instruction or targeted intervention is welcomed in the comments!

2018: Year in Review

This year I tried to understand the role of the instructional coach in more depth. Here are the top 10 things I’ve learned:

10. Intense PD doesn’t happen during statewide testing. Edutopia

9. PD needs to be interactive. Gone are the days of the sit and get PD! Do the fire drill, don’t just glance at the map. Robert Kaplinsky

8. The instructional coach and administrator relationship is critically important. Balanced Reading

7. You can’t easily measure your impact as a coach. Learn to live with ambiguity while we study the role in depth. Barkley

6. Teachers are partners in learning. The instructional coach is not an expert in the field – but a coach should be able to help guide thinking and keep the learning moving forward. Instructional Coaching Group

5. Twitter is an incredible source of knowledge and inspiration! Follow me on Twitter!

4. Coaches need coaching too. Start a Mastermind of coaches. Cult of Pedagogy

3. Your role as a coach requires you to be present in the moment. You are released from the classroom to release you from those every day stresses so that you can help shoulder the incredible weight of the teachers you serve. Self care is critical. EdWeek

2. You can’t be all things to all people. Offer coaching to all and feed the hungry. ASCD

1. Develop your vision and mission. ASCD

And So It Begins…

My 2019 goal was to start a blog. And I’ve started! Goal is complete already and I haven’t even left 2018! I have to admit that this blank space is somewhat intimidating. What if I have absolutely nothing to say?

Since school is out for a few more days, it’s time for some reflecting and planning. Tomorrow I’ll reflect on the successes of 2018, and then on Tuesday I’ll start planning for 2019. Today, I’ll rest after the fun of decorating the page. Let me know your thoughts on the design in the comments.